Sequential g-computation and IPW#

This study validates SequentialGComputation (ICE) and SequentialIPW (Hajek and Horvitz-Thompson) with GLM nuisances. The estimators fit a parametric regression or mechanism at each node and report an influence-curve interval from the stacked estimating equations. The section sequential g-computation and IPW states the estimators, their refusals and their exact-law witnesses. The study reads each estimate as an estimate of a known population value, and it reads each reported standard error against the sampling spread.

This page is Python property evidence. No canonical implementation is compared in this study. The R comparator parity is fixture-level. The test tests/unit/test_sequential_baselines_ltmle_r.py compares the estimate with R ltmle 1.3-0 on one panel (witness W9). The test tests/unit/test_sequential_baselines_stremr.py compares it with R stremr. Neither test reports a coverage, a bias or a standard-error ratio, and neither belongs to this study.

What was tested#

setting	declaration
estimators	`SequentialGComputation`, and `SequentialIPW` with `normalization="hajek"` and with `"horvitz_thompson"`. Every nuisance is a `GLM`
primary laws	`D2` and `G`. `D2` has two nodes, binary covariates and censoring, and a three-arm treatment at node 2. `G` has three nodes, continuous covariates, binary treatment and censoring, and a continuous outcome
other laws	`D2B` (binary node 2), `D2S` (absorbing event), `D2C` (two competing causes), `GM` (continuous doses and a modified policy), and `X` (`G` with squared terms that make every main-terms `GLM` wrong)
primary estimands	on `D2`, the means of `static_12`, `static_00`, `rule` and `policy`, and the contrast of `static_12` against `static_00`. On `G`, the means of `treat_all`, `treat_none` and `rule`, and their contrast
primary size	1,000 replications of 8,000 rows. The three estimators of one law read the same draw
truth	a finite sum over the support for the `D2` family, and a closed form for `G`, `X` and `GM`
intervals	pointwise 95% Wald intervals from the influence curve, with `g_bounds = (0.01, 1)` and `q_bounds` at the support of the outcome
Monte Carlo inference	99% intervals around every declared endpoint

The module tests/studies/sequential_baselines_laws.py imports nothing from cleverly. Its truths are an independent statement of the g-formula.

Accuracy against known truth#

law	estimand	what was tested	implementation	bias (99% interval)	coverage	SE ratio	result
law D2: two nodes, a three-arm second node, censoring; sequential IPW, Hajek	`ate_regimen[static_12 vs static_00]`	difference in mean outcome between the plans “assign arm 1 first, then arm 2” against “assign arm 0 at both times”	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0014 to 0.0021	0.9590	1.0054	pass
law D2: two nodes, a three-arm second node, censoring; sequential IPW, Hajek	`ey_regimen[policy]`	mean outcome under the plan assign arm 1 first, then draw the arm from the known policy (0.2, 0.3, 0.5)	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.000766 to 0.000721	0.9500	1.0180	pass
law D2: two nodes, a three-arm second node, censoring; sequential IPW, Hajek	`ey_regimen[rule]`	mean outcome under the plan follow the covariate-dependent rule	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0014 to 0.0012	0.9510	0.9766	pass
law D2: two nodes, a three-arm second node, censoring; sequential IPW, Hajek	`ey_regimen[static_00]`	mean outcome under the plan assign arm 0 at both times	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0018 to 0.000831	0.9550	0.9983	pass
law D2: two nodes, a three-arm second node, censoring; sequential IPW, Hajek	`ey_regimen[static_12]`	mean outcome under the plan assign arm 1 first, then arm 2	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0014 to 0.0010	0.9490	0.9937	pass
law D2: two nodes, a three-arm second node, censoring; sequential IPW, Horvitz-Thompson	`ate_regimen[static_12 vs static_00]`	difference in mean outcome between the plans “assign arm 1 first, then arm 2” against “assign arm 0 at both times”	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0017 to 0.0019	0.9490	1.0093	pass
law D2: two nodes, a three-arm second node, censoring; sequential IPW, Horvitz-Thompson	`ey_regimen[policy]`	mean outcome under the plan assign arm 1 first, then draw the arm from the known policy (0.2, 0.3, 0.5)	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.000788 to 0.000705	0.9530	1.0170	pass
law D2: two nodes, a three-arm second node, censoring; sequential IPW, Horvitz-Thompson	`ey_regimen[rule]`	mean outcome under the plan follow the covariate-dependent rule	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0012 to 0.0018	0.9530	1.0002	pass
law D2: two nodes, a three-arm second node, censoring; sequential IPW, Horvitz-Thompson	`ey_regimen[static_00]`	mean outcome under the plan assign arm 0 at both times	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0019 to 0.000876	0.9490	1.0045	pass
law D2: two nodes, a three-arm second node, censoring; sequential IPW, Horvitz-Thompson	`ey_regimen[static_12]`	mean outcome under the plan assign arm 1 first, then arm 2	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0016 to 0.000875	0.9510	0.9958	pass
law D2: two nodes, a three-arm second node, censoring; sequential g-computation (ICE)	`ate_regimen[static_12 vs static_00]`	difference in mean outcome between the plans “assign arm 1 first, then arm 2” against “assign arm 0 at both times”	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0015 to 0.0021	0.9500	0.9957	pass
law D2: two nodes, a three-arm second node, censoring; sequential g-computation (ICE)	`ey_regimen[policy]`	mean outcome under the plan assign arm 1 first, then draw the arm from the known policy (0.2, 0.3, 0.5)	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.000778 to 0.000703	0.9510	1.0163	pass
law D2: two nodes, a three-arm second node, censoring; sequential g-computation (ICE)	`ey_regimen[rule]`	mean outcome under the plan follow the covariate-dependent rule	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0014 to 0.0012	0.9480	0.9732	pass
law D2: two nodes, a three-arm second node, censoring; sequential g-computation (ICE)	`ey_regimen[static_00]`	mean outcome under the plan assign arm 0 at both times	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0018 to 0.000834	0.9450	0.9905	pass
law D2: two nodes, a three-arm second node, censoring; sequential g-computation (ICE)	`ey_regimen[static_12]`	mean outcome under the plan assign arm 1 first, then arm 2	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0014 to 0.000988	0.9520	0.9913	pass
law G: three nodes, a continuous outcome, censoring; sequential IPW, Hajek	`ate_regimen[treat_all vs treat_none]`	difference in mean outcome between the plans “treat at each of the three times” against “treat at none of the three times”	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0023 to 0.0040	0.9470	1.0070	pass
law G: three nodes, a continuous outcome, censoring; sequential IPW, Hajek	`ey_regimen[rule]`	mean outcome under the plan follow the covariate-dependent rule	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0045 to 0.0022	0.9530	0.9876	pass
law G: three nodes, a continuous outcome, censoring; sequential IPW, Hajek	`ey_regimen[treat_all]`	mean outcome under the plan treat at each of the three times	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0023 to 0.0026	0.9410	0.9801	pass
law G: three nodes, a continuous outcome, censoring; sequential IPW, Hajek	`ey_regimen[treat_none]`	mean outcome under the plan treat at none of the three times	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0031 to 0.0017	0.9460	0.9964	pass
law G: three nodes, a continuous outcome, censoring; sequential IPW, Horvitz-Thompson	`ate_regimen[treat_all vs treat_none]`	difference in mean outcome between the plans “treat at each of the three times” against “treat at none of the three times”	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0027 to 0.0047	0.9470	0.9968	pass
law G: three nodes, a continuous outcome, censoring; sequential IPW, Horvitz-Thompson	`ey_regimen[rule]`	mean outcome under the plan follow the covariate-dependent rule	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0050 to 0.0021	0.9520	0.9930	pass
law G: three nodes, a continuous outcome, censoring; sequential IPW, Horvitz-Thompson	`ey_regimen[treat_all]`	mean outcome under the plan treat at each of the three times	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0025 to 0.0024	0.9430	0.9791	pass
law G: three nodes, a continuous outcome, censoring; sequential IPW, Horvitz-Thompson	`ey_regimen[treat_none]`	mean outcome under the plan treat at none of the three times	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0043 to 0.0022	0.9450	0.9806	pass
law G: three nodes, a continuous outcome, censoring; sequential g-computation (ICE)	`ate_regimen[treat_all vs treat_none]`	difference in mean outcome between the plans “treat at each of the three times” against “treat at none of the three times”	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0019 to 0.0033	0.9610	1.0126	pass
law G: three nodes, a continuous outcome, censoring; sequential g-computation (ICE)	`ey_regimen[rule]`	mean outcome under the plan follow the covariate-dependent rule	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0014 to 0.0026	0.9520	1.0022	pass
law G: three nodes, a continuous outcome, censoring; sequential g-computation (ICE)	`ey_regimen[treat_all]`	mean outcome under the plan treat at each of the three times	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0012 to 0.0026	0.9500	1.0021	pass
law G: three nodes, a continuous outcome, censoring; sequential g-computation (ICE)	`ey_regimen[treat_none]`	mean outcome under the plan treat at none of the three times	`cleverly` sequential g-computation (ICE) and sequential IPW, Hajek and Horvitz-Thompson, with GLM nuisances	-0.0019 to 0.0019	0.9500	1.0119	pass

Theory properties#

The property families use the draws named in the table. Each positive cell must put the standardized bias inside the margin, the SE-ratio interval inside the calibration band and the coverage interval inside the coverage band. A control must leave the band on the predicted side.

family	cells	role	what it shows
`interval_calibration`	43 labels at n = 2,000, and `D2C` at n = 8,000, with 8,800 replications each	positive, plus two controls per label: a standard error shrunk by 0.70, and noise added to the estimate	the interval is calibrated when every nuisance is correct. The controls show that the band detects a short standard error and a noisy estimate
`root_n_and_efficiency` and `root_n_rate`	the six contrasts at n = 2,000, 4,000 and 8,000	positive	the empirical spread falls at the root-n rate, and the reported standard error follows it
`misspecification_control`	the contrast of `treat_all` against `treat_none` on law `X`, for each estimator	control	with every main-terms `GLM` wrong, the estimate is biased and the interval does not cover. The control must fail. See the declared negative control
`fixed_mechanism_se`	`G` and `D2` draws, IPW estimators	diagnostic	the standard error without the mechanism term lies above the calibration band
`first_node_se`	`G` draws, ICE	diagnostic	the first-node term alone lies below the calibration band
`adaptive_learners`	the contrast on `X` with the default learner library, ICE and Hajek, n = 1,000, 100 replications	diagnostic	point estimates only. The package reports no interval for a data-adaptive nuisance

property	cell	role	what was tested	what must hold	measured	result
`adaptive_learners`	`hajek_x_contrast__n_1000`	diagnostic	sequential IPW, Hajek: law X, treatment at all three times against none: the default learner library on law X, at n = 1,000	reported only	bias 0.0958 to 0.1483, coverage 0.7249 to 0.9213, SE ratio 1.1064	reported
`adaptive_learners`	`ice_x_contrast__n_1000`	diagnostic	sequential g-computation (ICE): law X, treatment at all three times against none: the default learner library on law X, at n = 1,000	reported only	bias 0.0433 to 0.0966, coverage 0.6788 to 0.8916, SE ratio 0.8133	reported
`first_node_se`	`ice_g_contrast__first_node`	diagnostic	sequential g-computation (ICE): law G, treatment at all three times against none: the spread of the first-node term alone, without the later chain terms	the SE-ratio interval must fall below the calibration band	SE ratio 0.0331 to 0.0347	reported
`first_node_se`	`ice_g_treat_all__first_node`	diagnostic	sequential g-computation (ICE): law G, mean under treatment at all three times: the spread of the first-node term alone, without the later chain terms	the SE-ratio interval must fall below the calibration band	SE ratio 0.2350 to 0.2445	reported
`first_node_se`	`ice_g_treat_none__first_node`	diagnostic	sequential g-computation (ICE): law G, mean under no treatment: the spread of the first-node term alone, without the later chain terms	the SE-ratio interval must fall below the calibration band	SE ratio 0.2302 to 0.2396	reported
`fixed_mechanism_se`	`hajek_d2_policy__fixed_mechanism`	diagnostic	sequential IPW, Hajek: law D2, mean under arm 1 then the known three-arm policy: the mechanism is fitted, and the standard error omits its estimation term	where gated, the SE-ratio interval must rise above the calibration band; otherwise reported	SE ratio 0.9922 to 1.0309	reported
`fixed_mechanism_se`	`hajek_d2_rule__fixed_mechanism`	diagnostic	sequential IPW, Hajek: law D2, mean under the rule A1 = L1, A2 = 2 L2: the mechanism is fitted, and the standard error omits its estimation term	where gated, the SE-ratio interval must rise above the calibration band; otherwise reported	SE ratio 0.9782 to 1.0178	reported
`fixed_mechanism_se`	`hajek_d2_static_12__fixed_mechanism`	diagnostic	sequential IPW, Hajek: law D2, mean under arm 1 then arm 2: the mechanism is fitted, and the standard error omits its estimation term	where gated, the SE-ratio interval must rise above the calibration band; otherwise reported	SE ratio 0.9855 to 1.0245	reported
`fixed_mechanism_se`	`hajek_g_contrast__fixed_mechanism`	diagnostic	sequential IPW, Hajek: law G, treatment at all three times against none: the mechanism is fitted, and the standard error omits its estimation term	where gated, the SE-ratio interval must rise above the calibration band; otherwise reported	SE ratio 1.1397 to 1.1850	reported
`fixed_mechanism_se`	`hajek_g_treat_all__fixed_mechanism`	diagnostic	sequential IPW, Hajek: law G, mean under treatment at all three times: the mechanism is fitted, and the standard error omits its estimation term	where gated, the SE-ratio interval must rise above the calibration band; otherwise reported	SE ratio 1.0469 to 1.0877	reported
`fixed_mechanism_se`	`hajek_g_treat_none__fixed_mechanism`	diagnostic	sequential IPW, Hajek: law G, mean under no treatment: the mechanism is fitted, and the standard error omits its estimation term	where gated, the SE-ratio interval must rise above the calibration band; otherwise reported	SE ratio 1.0586 to 1.1004	reported
`fixed_mechanism_se`	`ht_d2_policy__fixed_mechanism`	diagnostic	sequential IPW, Horvitz-Thompson: law D2, mean under arm 1 then the known three-arm policy: the mechanism is fitted, and the standard error omits its estimation term	where gated, the SE-ratio interval must rise above the calibration band; otherwise reported	SE ratio 1.2525 to 1.3015	reported
`fixed_mechanism_se`	`ht_d2_rule__fixed_mechanism`	diagnostic	sequential IPW, Horvitz-Thompson: law D2, mean under the rule A1 = L1, A2 = 2 L2: the mechanism is fitted, and the standard error omits its estimation term	where gated, the SE-ratio interval must rise above the calibration band; otherwise reported	SE ratio 1.1376 to 1.1831	reported
`fixed_mechanism_se`	`ht_d2_static_12__fixed_mechanism`	diagnostic	sequential IPW, Horvitz-Thompson: law D2, mean under arm 1 then arm 2: the mechanism is fitted, and the standard error omits its estimation term	where gated, the SE-ratio interval must rise above the calibration band; otherwise reported	SE ratio 1.3321 to 1.3860	reported
`fixed_mechanism_se`	`ht_g_contrast__fixed_mechanism`	diagnostic	sequential IPW, Horvitz-Thompson: law G, treatment at all three times against none: the mechanism is fitted, and the standard error omits its estimation term	where gated, the SE-ratio interval must rise above the calibration band; otherwise reported	SE ratio 1.3816 to 1.4375	reported
`fixed_mechanism_se`	`ht_g_treat_all__fixed_mechanism`	diagnostic	sequential IPW, Horvitz-Thompson: law G, mean under treatment at all three times: the mechanism is fitted, and the standard error omits its estimation term	where gated, the SE-ratio interval must rise above the calibration band; otherwise reported	SE ratio 1.0541 to 1.0937	reported
`fixed_mechanism_se`	`ht_g_treat_none__fixed_mechanism`	diagnostic	sequential IPW, Horvitz-Thompson: law G, mean under no treatment: the mechanism is fitted, and the standard error omits its estimation term	where gated, the SE-ratio interval must rise above the calibration band; otherwise reported	SE ratio 1.3908 to 1.4461	reported
`interval_calibration`	`hajek_d2_contrast__correctly_specified`	positive	sequential IPW, Hajek: law D2, arm 1 then arm 2 against arm 0 at both times: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9440 to 0.9560, SE ratio 0.9788 to 1.0192	pass
`interval_calibration`	`hajek_d2_contrast__noise_control`	control	sequential IPW, Hajek: law D2, arm 1 then arm 2 against arm 0 at both times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8193 to 0.8401, SE ratio 0.6892 to 0.7169	pass
`interval_calibration`	`hajek_d2_contrast__shrunken_se_control`	control	sequential IPW, Hajek: law D2, arm 1 then arm 2 against arm 0 at both times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8200 to 0.8407, SE ratio 0.6853 to 0.7118	pass
`interval_calibration`	`hajek_d2_policy__correctly_specified`	positive	sequential IPW, Hajek: law D2, mean under arm 1 then the known three-arm policy: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9412 to 0.9535, SE ratio 0.9765 to 1.0160	pass
`interval_calibration`	`hajek_d2_policy__noise_control`	control	sequential IPW, Hajek: law D2, mean under arm 1 then the known three-arm policy: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8225 to 0.8431, SE ratio 0.6864 to 0.7142	pass
`interval_calibration`	`hajek_d2_policy__shrunken_se_control`	control	sequential IPW, Hajek: law D2, mean under arm 1 then the known three-arm policy: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8171 to 0.8380, SE ratio 0.6840 to 0.7109	pass
`interval_calibration`	`hajek_d2_rule__correctly_specified`	positive	sequential IPW, Hajek: law D2, mean under the rule A1 = L1, A2 = 2 L2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9386 to 0.9512, SE ratio 0.9729 to 1.0117	pass
`interval_calibration`	`hajek_d2_rule__noise_control`	control	sequential IPW, Hajek: law D2, mean under the rule A1 = L1, A2 = 2 L2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8302 to 0.8504, SE ratio 0.6996 to 0.7270	pass
`interval_calibration`	`hajek_d2_rule__shrunken_se_control`	control	sequential IPW, Hajek: law D2, mean under the rule A1 = L1, A2 = 2 L2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8153 to 0.8362, SE ratio 0.6812 to 0.7082	pass
`interval_calibration`	`hajek_d2_static_00__correctly_specified`	positive	sequential IPW, Hajek: law D2, mean under arm 0 at both times: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9407 to 0.9531, SE ratio 0.9709 to 1.0107	pass
`interval_calibration`	`hajek_d2_static_00__noise_control`	control	sequential IPW, Hajek: law D2, mean under arm 0 at both times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8176 to 0.8384, SE ratio 0.6839 to 0.7103	pass
`interval_calibration`	`hajek_d2_static_00__shrunken_se_control`	control	sequential IPW, Hajek: law D2, mean under arm 0 at both times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8171 to 0.8380, SE ratio 0.6800 to 0.7069	pass
`interval_calibration`	`hajek_d2_static_12__correctly_specified`	positive	sequential IPW, Hajek: law D2, mean under arm 1 then arm 2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9398 to 0.9523, SE ratio 0.9790 to 1.0185	pass
`interval_calibration`	`hajek_d2_static_12__noise_control`	control	sequential IPW, Hajek: law D2, mean under arm 1 then arm 2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8290 to 0.8493, SE ratio 0.6986 to 0.7270	pass
`interval_calibration`	`hajek_d2_static_12__shrunken_se_control`	control	sequential IPW, Hajek: law D2, mean under arm 1 then arm 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8177 to 0.8385, SE ratio 0.6853 to 0.7126	pass
`interval_calibration`	`hajek_d2c_relapse_h2__correctly_specified`	positive	sequential IPW, Hajek: law D2C, relapse incidence by t = 2 under arm 1 then arm 2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9428 to 0.9549, SE ratio 0.9768 to 1.0168	pass
`interval_calibration`	`hajek_d2c_relapse_h2__noise_control`	control	sequential IPW, Hajek: law D2C, relapse incidence by t = 2 under arm 1 then arm 2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8222 to 0.8428, SE ratio 0.6885 to 0.7159	pass
`interval_calibration`	`hajek_d2c_relapse_h2__shrunken_se_control`	control	sequential IPW, Hajek: law D2C, relapse incidence by t = 2 under arm 1 then arm 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8181 to 0.8389, SE ratio 0.6842 to 0.7118	pass
`interval_calibration`	`hajek_d2s_contrast_h2__correctly_specified`	positive	sequential IPW, Hajek: law D2S, risk difference by t = 2 against arm 0 at both times: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9410 to 0.9533, SE ratio 0.9854 to 1.0232	pass
`interval_calibration`	`hajek_d2s_contrast_h2__noise_control`	control	sequential IPW, Hajek: law D2S, risk difference by t = 2 against arm 0 at both times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8333 to 0.8534, SE ratio 0.7027 to 0.7309	pass
`interval_calibration`	`hajek_d2s_contrast_h2__shrunken_se_control`	control	sequential IPW, Hajek: law D2S, risk difference by t = 2 against arm 0 at both times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8141 to 0.8351, SE ratio 0.6896 to 0.7166	pass
`interval_calibration`	`hajek_d2s_risk_h1__correctly_specified`	positive	sequential IPW, Hajek: law D2S, risk by t = 1 under arm 1: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9410 to 0.9533, SE ratio 0.9778 to 1.0169	pass
`interval_calibration`	`hajek_d2s_risk_h1__noise_control`	control	sequential IPW, Hajek: law D2S, risk by t = 1 under arm 1: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8048 to 0.8262, SE ratio 0.6682 to 0.6941	pass
`interval_calibration`	`hajek_d2s_risk_h1__shrunken_se_control`	control	sequential IPW, Hajek: law D2S, risk by t = 1 under arm 1: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8188 to 0.8395, SE ratio 0.6848 to 0.7116	pass
`interval_calibration`	`hajek_d2s_risk_h2__correctly_specified`	positive	sequential IPW, Hajek: law D2S, risk by t = 2 under arm 1 then arm 2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9386 to 0.9512, SE ratio 0.9724 to 1.0113	pass
`interval_calibration`	`hajek_d2s_risk_h2__noise_control`	control	sequential IPW, Hajek: law D2S, risk by t = 2 under arm 1 then arm 2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8250 to 0.8455, SE ratio 0.7019 to 0.7292	pass
`interval_calibration`	`hajek_d2s_risk_h2__shrunken_se_control`	control	sequential IPW, Hajek: law D2S, risk by t = 2 under arm 1 then arm 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8165 to 0.8374, SE ratio 0.6812 to 0.7080	pass
`interval_calibration`	`hajek_d2w_static_12__correctly_specified`	positive	sequential IPW, Hajek: law D2 weighted by 1 + 0.5 W, mean under arm 1 then arm 2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9424 to 0.9546, SE ratio 0.9794 to 1.0189	pass
`interval_calibration`	`hajek_d2w_static_12__noise_control`	control	sequential IPW, Hajek: law D2 weighted by 1 + 0.5 W, mean under arm 1 then arm 2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8298 to 0.8500, SE ratio 0.7072 to 0.7345	pass
`interval_calibration`	`hajek_d2w_static_12__shrunken_se_control`	control	sequential IPW, Hajek: law D2 weighted by 1 + 0.5 W, mean under arm 1 then arm 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8162 to 0.8371, SE ratio 0.6858 to 0.7130	pass
`interval_calibration`	`hajek_g_contrast__correctly_specified`	positive	sequential IPW, Hajek: law G, treatment at all three times against none: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9452 to 0.9571, SE ratio 0.9800 to 1.0196	pass
`interval_calibration`	`hajek_g_contrast__noise_control`	control	sequential IPW, Hajek: law G, treatment at all three times against none: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8188 to 0.8395, SE ratio 0.6876 to 0.7151	pass
`interval_calibration`	`hajek_g_contrast__shrunken_se_control`	control	sequential IPW, Hajek: law G, treatment at all three times against none: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8200 to 0.8407, SE ratio 0.6856 to 0.7140	pass
`interval_calibration`	`hajek_g_rule__correctly_specified`	positive	sequential IPW, Hajek: law G, mean under the rule A_t = V: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9376 to 0.9503, SE ratio 0.9643 to 1.0028	pass
`interval_calibration`	`hajek_g_rule__noise_control`	control	sequential IPW, Hajek: law G, mean under the rule A_t = V: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8038 to 0.8252, SE ratio 0.6729 to 0.6988	pass
`interval_calibration`	`hajek_g_rule__shrunken_se_control`	control	sequential IPW, Hajek: law G, mean under the rule A_t = V: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8100 to 0.8312, SE ratio 0.6754 to 0.7017	pass
`interval_calibration`	`hajek_g_treat_all__correctly_specified`	positive	sequential IPW, Hajek: law G, mean under treatment at all three times: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9368 to 0.9496, SE ratio 0.9654 to 1.0034	pass
`interval_calibration`	`hajek_g_treat_all__noise_control`	control	sequential IPW, Hajek: law G, mean under treatment at all three times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8179 to 0.8387, SE ratio 0.6849 to 0.7129	pass
`interval_calibration`	`hajek_g_treat_all__shrunken_se_control`	control	sequential IPW, Hajek: law G, mean under treatment at all three times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8117 to 0.8328, SE ratio 0.6757 to 0.7027	pass
`interval_calibration`	`hajek_g_treat_none__correctly_specified`	positive	sequential IPW, Hajek: law G, mean under no treatment: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9416 to 0.9539, SE ratio 0.9769 to 1.0152	pass
`interval_calibration`	`hajek_g_treat_none__noise_control`	control	sequential IPW, Hajek: law G, mean under no treatment: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8150 to 0.8360, SE ratio 0.6872 to 0.7138	pass
`interval_calibration`	`hajek_g_treat_none__shrunken_se_control`	control	sequential IPW, Hajek: law G, mean under no treatment: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8147 to 0.8356, SE ratio 0.6831 to 0.7114	pass
`interval_calibration`	`ht_d2_contrast__correctly_specified`	positive	sequential IPW, Horvitz-Thompson: law D2, arm 1 then arm 2 against arm 0 at both times: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9411 to 0.9534, SE ratio 0.9779 to 1.0156	pass
`interval_calibration`	`ht_d2_contrast__noise_control`	control	sequential IPW, Horvitz-Thompson: law D2, arm 1 then arm 2 against arm 0 at both times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8239 to 0.8444, SE ratio 0.6962 to 0.7232	pass
`interval_calibration`	`ht_d2_contrast__shrunken_se_control`	control	sequential IPW, Horvitz-Thompson: law D2, arm 1 then arm 2 against arm 0 at both times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8165 to 0.8374, SE ratio 0.6835 to 0.7109	pass
`interval_calibration`	`ht_d2_policy__correctly_specified`	positive	sequential IPW, Horvitz-Thompson: law D2, mean under arm 1 then the known three-arm policy: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9420 to 0.9543, SE ratio 0.9731 to 1.0120	pass
`interval_calibration`	`ht_d2_policy__noise_control`	control	sequential IPW, Horvitz-Thompson: law D2, mean under arm 1 then the known three-arm policy: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8196 to 0.8403, SE ratio 0.6858 to 0.7131	pass
`interval_calibration`	`ht_d2_policy__shrunken_se_control`	control	sequential IPW, Horvitz-Thompson: law D2, mean under arm 1 then the known three-arm policy: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8163 to 0.8372, SE ratio 0.6810 to 0.7083	pass
`interval_calibration`	`ht_d2_rule__correctly_specified`	positive	sequential IPW, Horvitz-Thompson: law D2, mean under the rule A1 = L1, A2 = 2 L2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9389 to 0.9515, SE ratio 0.9734 to 1.0123	pass
`interval_calibration`	`ht_d2_rule__noise_control`	control	sequential IPW, Horvitz-Thompson: law D2, mean under the rule A1 = L1, A2 = 2 L2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8277 to 0.8481, SE ratio 0.6974 to 0.7258	pass
`interval_calibration`	`ht_d2_rule__shrunken_se_control`	control	sequential IPW, Horvitz-Thompson: law D2, mean under the rule A1 = L1, A2 = 2 L2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8154 to 0.8363, SE ratio 0.6802 to 0.7083	pass
`interval_calibration`	`ht_d2_static_00__correctly_specified`	positive	sequential IPW, Horvitz-Thompson: law D2, mean under arm 0 at both times: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9405 to 0.9529, SE ratio 0.9732 to 1.0128	pass
`interval_calibration`	`ht_d2_static_00__noise_control`	control	sequential IPW, Horvitz-Thompson: law D2, mean under arm 0 at both times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8177 to 0.8385, SE ratio 0.6826 to 0.7095	pass
`interval_calibration`	`ht_d2_static_00__shrunken_se_control`	control	sequential IPW, Horvitz-Thompson: law D2, mean under arm 0 at both times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8197 to 0.8404, SE ratio 0.6816 to 0.7083	pass
`interval_calibration`	`ht_d2_static_12__correctly_specified`	positive	sequential IPW, Horvitz-Thompson: law D2, mean under arm 1 then arm 2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9395 to 0.9520, SE ratio 0.9767 to 1.0157	pass
`interval_calibration`	`ht_d2_static_12__noise_control`	control	sequential IPW, Horvitz-Thompson: law D2, mean under arm 1 then arm 2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8275 to 0.8478, SE ratio 0.7009 to 0.7304	pass
`interval_calibration`	`ht_d2_static_12__shrunken_se_control`	control	sequential IPW, Horvitz-Thompson: law D2, mean under arm 1 then arm 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8174 to 0.8382, SE ratio 0.6833 to 0.7112	pass
`interval_calibration`	`ht_d2c_relapse_h2__correctly_specified`	positive	sequential IPW, Horvitz-Thompson: law D2C, relapse incidence by t = 2 under arm 1 then arm 2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9410 to 0.9533, SE ratio 0.9771 to 1.0161	pass
`interval_calibration`	`ht_d2c_relapse_h2__noise_control`	control	sequential IPW, Horvitz-Thompson: law D2C, relapse incidence by t = 2 under arm 1 then arm 2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8176 to 0.8384, SE ratio 0.6840 to 0.7112	pass
`interval_calibration`	`ht_d2c_relapse_h2__shrunken_se_control`	control	sequential IPW, Horvitz-Thompson: law D2C, relapse incidence by t = 2 under arm 1 then arm 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8179 to 0.8387, SE ratio 0.6838 to 0.7114	pass
`interval_calibration`	`ht_d2s_contrast_h2__correctly_specified`	positive	sequential IPW, Horvitz-Thompson: law D2S, risk difference by t = 2 against arm 0 at both times: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9426 to 0.9548, SE ratio 0.9879 to 1.0264	pass
`interval_calibration`	`ht_d2s_contrast_h2__noise_control`	control	sequential IPW, Horvitz-Thompson: law D2S, risk difference by t = 2 against arm 0 at both times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8243 to 0.8448, SE ratio 0.6952 to 0.7220	pass
`interval_calibration`	`ht_d2s_contrast_h2__shrunken_se_control`	control	sequential IPW, Horvitz-Thompson: law D2S, risk difference by t = 2 against arm 0 at both times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8162 to 0.8371, SE ratio 0.6911 to 0.7185	pass
`interval_calibration`	`ht_d2s_risk_h1__correctly_specified`	positive	sequential IPW, Horvitz-Thompson: law D2S, risk by t = 1 under arm 1: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9411 to 0.9534, SE ratio 0.9783 to 1.0163	pass
`interval_calibration`	`ht_d2s_risk_h1__noise_control`	control	sequential IPW, Horvitz-Thompson: law D2S, risk by t = 1 under arm 1: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8030 to 0.8244, SE ratio 0.6638 to 0.6900	pass
`interval_calibration`	`ht_d2s_risk_h1__shrunken_se_control`	control	sequential IPW, Horvitz-Thompson: law D2S, risk by t = 1 under arm 1: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8196 to 0.8403, SE ratio 0.6848 to 0.7116	pass
`interval_calibration`	`ht_d2s_risk_h2__correctly_specified`	positive	sequential IPW, Horvitz-Thompson: law D2S, risk by t = 2 under arm 1 then arm 2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9396 to 0.9521, SE ratio 0.9742 to 1.0128	pass
`interval_calibration`	`ht_d2s_risk_h2__noise_control`	control	sequential IPW, Horvitz-Thompson: law D2S, risk by t = 2 under arm 1 then arm 2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8277 to 0.8481, SE ratio 0.6961 to 0.7236	pass
`interval_calibration`	`ht_d2s_risk_h2__shrunken_se_control`	control	sequential IPW, Horvitz-Thompson: law D2S, risk by t = 2 under arm 1 then arm 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8148 to 0.8358, SE ratio 0.6816 to 0.7088	pass
`interval_calibration`	`ht_g_contrast__correctly_specified`	positive	sequential IPW, Horvitz-Thompson: law G, treatment at all three times against none: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9432 to 0.9554, SE ratio 0.9803 to 1.0210	pass
`interval_calibration`	`ht_g_contrast__noise_control`	control	sequential IPW, Horvitz-Thompson: law G, treatment at all three times against none: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8184 to 0.8392, SE ratio 0.6871 to 0.7143	pass
`interval_calibration`	`ht_g_contrast__shrunken_se_control`	control	sequential IPW, Horvitz-Thompson: law G, treatment at all three times against none: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8231 to 0.8436, SE ratio 0.6867 to 0.7143	pass
`interval_calibration`	`ht_g_rule__correctly_specified`	positive	sequential IPW, Horvitz-Thompson: law G, mean under the rule A_t = V: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9400 to 0.9525, SE ratio 0.9650 to 1.0029	pass
`interval_calibration`	`ht_g_rule__noise_control`	control	sequential IPW, Horvitz-Thompson: law G, mean under the rule A_t = V: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8064 to 0.8278, SE ratio 0.6811 to 0.7076	pass
`interval_calibration`	`ht_g_rule__shrunken_se_control`	control	sequential IPW, Horvitz-Thompson: law G, mean under the rule A_t = V: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8093 to 0.8305, SE ratio 0.6759 to 0.7024	pass
`interval_calibration`	`ht_g_treat_all__correctly_specified`	positive	sequential IPW, Horvitz-Thompson: law G, mean under treatment at all three times: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9380 to 0.9506, SE ratio 0.9655 to 1.0037	pass
`interval_calibration`	`ht_g_treat_all__noise_control`	control	sequential IPW, Horvitz-Thompson: law G, mean under treatment at all three times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8191 to 0.8399, SE ratio 0.6890 to 0.7158	pass
`interval_calibration`	`ht_g_treat_all__shrunken_se_control`	control	sequential IPW, Horvitz-Thompson: law G, mean under treatment at all three times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8108 to 0.8320, SE ratio 0.6763 to 0.7028	pass
`interval_calibration`	`ht_g_treat_none__correctly_specified`	positive	sequential IPW, Horvitz-Thompson: law G, mean under no treatment: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9387 to 0.9513, SE ratio 0.9753 to 1.0147	pass
`interval_calibration`	`ht_g_treat_none__noise_control`	control	sequential IPW, Horvitz-Thompson: law G, mean under no treatment: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8174 to 0.8382, SE ratio 0.6862 to 0.7138	pass
`interval_calibration`	`ht_g_treat_none__shrunken_se_control`	control	sequential IPW, Horvitz-Thompson: law G, mean under no treatment: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8188 to 0.8395, SE ratio 0.6829 to 0.7102	pass
`interval_calibration`	`ice_d2_contrast__correctly_specified`	positive	sequential g-computation (ICE): law D2, arm 1 then arm 2 against arm 0 at both times: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9430 to 0.9552, SE ratio 0.9702 to 1.0095	pass
`interval_calibration`	`ice_d2_contrast__noise_control`	control	sequential g-computation (ICE): law D2, arm 1 then arm 2 against arm 0 at both times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8167 to 0.8375, SE ratio 0.6859 to 0.7130	pass
`interval_calibration`	`ice_d2_contrast__shrunken_se_control`	control	sequential g-computation (ICE): law D2, arm 1 then arm 2 against arm 0 at both times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8156 to 0.8365, SE ratio 0.6791 to 0.7053	pass
`interval_calibration`	`ice_d2_policy__correctly_specified`	positive	sequential g-computation (ICE): law D2, mean under arm 1 then the known three-arm policy: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9399 to 0.9524, SE ratio 0.9709 to 1.0084	pass
`interval_calibration`	`ice_d2_policy__noise_control`	control	sequential g-computation (ICE): law D2, mean under arm 1 then the known three-arm policy: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8128 to 0.8339, SE ratio 0.6805 to 0.7066	pass
`interval_calibration`	`ice_d2_policy__shrunken_se_control`	control	sequential g-computation (ICE): law D2, mean under arm 1 then the known three-arm policy: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8161 to 0.8370, SE ratio 0.6796 to 0.7058	pass
`interval_calibration`	`ice_d2_rule__correctly_specified`	positive	sequential g-computation (ICE): law D2, mean under the rule A1 = L1, A2 = 2 L2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9353 to 0.9483, SE ratio 0.9615 to 1.0001	pass
`interval_calibration`	`ice_d2_rule__noise_control`	control	sequential g-computation (ICE): law D2, mean under the rule A1 = L1, A2 = 2 L2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8317 to 0.8518, SE ratio 0.7022 to 0.7298	pass
`interval_calibration`	`ice_d2_rule__shrunken_se_control`	control	sequential g-computation (ICE): law D2, mean under the rule A1 = L1, A2 = 2 L2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8081 to 0.8293, SE ratio 0.6730 to 0.6999	pass
`interval_calibration`	`ice_d2_static_00__correctly_specified`	positive	sequential g-computation (ICE): law D2, mean under arm 0 at both times: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9352 to 0.9482, SE ratio 0.9623 to 1.0013	pass
`interval_calibration`	`ice_d2_static_00__noise_control`	control	sequential g-computation (ICE): law D2, mean under arm 0 at both times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8133 to 0.8343, SE ratio 0.6813 to 0.7084	pass
`interval_calibration`	`ice_d2_static_00__shrunken_se_control`	control	sequential g-computation (ICE): law D2, mean under arm 0 at both times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8127 to 0.8338, SE ratio 0.6729 to 0.7010	pass
`interval_calibration`	`ice_d2_static_12__correctly_specified`	positive	sequential g-computation (ICE): law D2, mean under arm 1 then arm 2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9392 to 0.9517, SE ratio 0.9722 to 1.0119	pass
`interval_calibration`	`ice_d2_static_12__noise_control`	control	sequential g-computation (ICE): law D2, mean under arm 1 then arm 2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8245 to 0.8450, SE ratio 0.7013 to 0.7283	pass
`interval_calibration`	`ice_d2_static_12__shrunken_se_control`	control	sequential g-computation (ICE): law D2, mean under arm 1 then arm 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8151 to 0.8361, SE ratio 0.6807 to 0.7083	pass
`interval_calibration`	`ice_d2c_relapse_h2__correctly_specified`	positive	sequential g-computation (ICE): law D2C, relapse incidence by t = 2 under arm 1 then arm 2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9416 to 0.9539, SE ratio 0.9754 to 1.0153	pass
`interval_calibration`	`ice_d2c_relapse_h2__noise_control`	control	sequential g-computation (ICE): law D2C, relapse incidence by t = 2 under arm 1 then arm 2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8201 to 0.8409, SE ratio 0.6857 to 0.7136	pass
`interval_calibration`	`ice_d2c_relapse_h2__shrunken_se_control`	control	sequential g-computation (ICE): law D2C, relapse incidence by t = 2 under arm 1 then arm 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8176 to 0.8384, SE ratio 0.6830 to 0.7107	pass
`interval_calibration`	`ice_d2s_contrast_h2__correctly_specified`	positive	sequential g-computation (ICE): law D2S, risk difference by t = 2 against arm 0 at both times: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9383 to 0.9510, SE ratio 0.9774 to 1.0158	pass
`interval_calibration`	`ice_d2s_contrast_h2__noise_control`	control	sequential g-computation (ICE): law D2S, risk difference by t = 2 against arm 0 at both times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8201 to 0.8409, SE ratio 0.6871 to 0.7143	pass
`interval_calibration`	`ice_d2s_contrast_h2__shrunken_se_control`	control	sequential g-computation (ICE): law D2S, risk difference by t = 2 against arm 0 at both times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8136 to 0.8346, SE ratio 0.6842 to 0.7108	pass
`interval_calibration`	`ice_d2s_risk_h1__correctly_specified`	positive	sequential g-computation (ICE): law D2S, risk by t = 1 under arm 1: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9405 to 0.9529, SE ratio 0.9775 to 1.0157	pass
`interval_calibration`	`ice_d2s_risk_h1__noise_control`	control	sequential g-computation (ICE): law D2S, risk by t = 1 under arm 1: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8067 to 0.8280, SE ratio 0.6720 to 0.6981	pass
`interval_calibration`	`ice_d2s_risk_h1__shrunken_se_control`	control	sequential g-computation (ICE): law D2S, risk by t = 1 under arm 1: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8168 to 0.8376, SE ratio 0.6846 to 0.7114	pass
`interval_calibration`	`ice_d2s_risk_h2__correctly_specified`	positive	sequential g-computation (ICE): law D2S, risk by t = 2 under arm 1 then arm 2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9383 to 0.9510, SE ratio 0.9680 to 1.0071	pass
`interval_calibration`	`ice_d2s_risk_h2__noise_control`	control	sequential g-computation (ICE): law D2S, risk by t = 2 under arm 1 then arm 2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8268 to 0.8472, SE ratio 0.6988 to 0.7265	pass
`interval_calibration`	`ice_d2s_risk_h2__shrunken_se_control`	control	sequential g-computation (ICE): law D2S, risk by t = 2 under arm 1 then arm 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8133 to 0.8343, SE ratio 0.6778 to 0.7049	pass
`interval_calibration`	`ice_d2w_static_12__correctly_specified`	positive	sequential g-computation (ICE): law D2 weighted by 1 + 0.5 W, mean under arm 1 then arm 2: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9399 to 0.9524, SE ratio 0.9733 to 1.0118	pass
`interval_calibration`	`ice_d2w_static_12__noise_control`	control	sequential g-computation (ICE): law D2 weighted by 1 + 0.5 W, mean under arm 1 then arm 2: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8247 to 0.8452, SE ratio 0.6942 to 0.7221	pass
`interval_calibration`	`ice_d2w_static_12__shrunken_se_control`	control	sequential g-computation (ICE): law D2 weighted by 1 + 0.5 W, mean under arm 1 then arm 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8131 to 0.8341, SE ratio 0.6812 to 0.7077	pass
`interval_calibration`	`ice_g_contrast__correctly_specified`	positive	sequential g-computation (ICE): law G, treatment at all three times against none: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9381 to 0.9508, SE ratio 0.9668 to 1.0069	pass
`interval_calibration`	`ice_g_contrast__noise_control`	control	sequential g-computation (ICE): law G, treatment at all three times against none: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8275 to 0.8478, SE ratio 0.6995 to 0.7275	pass
`interval_calibration`	`ice_g_contrast__shrunken_se_control`	control	sequential g-computation (ICE): law G, treatment at all three times against none: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8132 to 0.8342, SE ratio 0.6779 to 0.7047	pass
`interval_calibration`	`ice_g_rule__correctly_specified`	positive	sequential g-computation (ICE): law G, mean under the rule A_t = V: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9401 to 0.9526, SE ratio 0.9749 to 1.0130	pass
`interval_calibration`	`ice_g_rule__noise_control`	control	sequential g-computation (ICE): law G, mean under the rule A_t = V: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8362 to 0.8561, SE ratio 0.7094 to 0.7376	pass
`interval_calibration`	`ice_g_rule__shrunken_se_control`	control	sequential g-computation (ICE): law G, mean under the rule A_t = V: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8175 to 0.8383, SE ratio 0.6823 to 0.7094	pass
`interval_calibration`	`ice_g_treat_all__correctly_specified`	positive	sequential g-computation (ICE): law G, mean under treatment at all three times: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9370 to 0.9498, SE ratio 0.9694 to 1.0078	pass
`interval_calibration`	`ice_g_treat_all__noise_control`	control	sequential g-computation (ICE): law G, mean under treatment at all three times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8214 to 0.8421, SE ratio 0.6881 to 0.7162	pass
`interval_calibration`	`ice_g_treat_all__shrunken_se_control`	control	sequential g-computation (ICE): law G, mean under treatment at all three times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8112 to 0.8323, SE ratio 0.6778 to 0.7048	pass
`interval_calibration`	`ice_g_treat_none__correctly_specified`	positive	sequential g-computation (ICE): law G, mean under no treatment: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9404 to 0.9528, SE ratio 0.9698 to 1.0096	pass
`interval_calibration`	`ice_g_treat_none__noise_control`	control	sequential g-computation (ICE): law G, mean under no treatment: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8291 to 0.8494, SE ratio 0.7038 to 0.7322	pass
`interval_calibration`	`ice_g_treat_none__shrunken_se_control`	control	sequential g-computation (ICE): law G, mean under no treatment: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8127 to 0.8338, SE ratio 0.6790 to 0.7068	pass
`interval_calibration`	`ice_gm_contrast__correctly_specified`	positive	sequential g-computation (ICE): law GM, the lowered dose against the natural course: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9441 to 0.9561, SE ratio 0.9822 to 1.0208	pass
`interval_calibration`	`ice_gm_contrast__noise_control`	control	sequential g-computation (ICE): law GM, the lowered dose against the natural course: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8162 to 0.8371, SE ratio 0.6811 to 0.7080	pass
`interval_calibration`	`ice_gm_contrast__shrunken_se_control`	control	sequential g-computation (ICE): law GM, the lowered dose against the natural course: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8191 to 0.8399, SE ratio 0.6879 to 0.7146	pass
`interval_calibration`	`ice_gm_down__correctly_specified`	positive	sequential g-computation (ICE): law GM, mean under the dose lowered by 0.5 where it stays in support: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9394 to 0.9519, SE ratio 0.9728 to 1.0103	pass
`interval_calibration`	`ice_gm_down__noise_control`	control	sequential g-computation (ICE): law GM, mean under the dose lowered by 0.5 where it stays in support: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8354 to 0.8554, SE ratio 0.7099 to 0.7380	pass
`interval_calibration`	`ice_gm_down__shrunken_se_control`	control	sequential g-computation (ICE): law GM, mean under the dose lowered by 0.5 where it stays in support: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8131 to 0.8341, SE ratio 0.6807 to 0.7074	pass
`misspecification_control`	`hajek_x_contrast__main_terms`	control	sequential IPW, Hajek: law X, treatment at all three times against none: main-terms GLM outcome regressions and mechanisms on law X, where both are wrong	declared red: the calibration rule must fail	bias 0.1306 to 0.1344, margin 0.0175, coverage 0.5072 to 0.5348, SE ratio 0.9970	fail
`misspecification_control`	`ht_x_contrast__main_terms`	control	sequential IPW, Horvitz-Thompson: law X, treatment at all three times against none: main-terms GLM outcome regressions and mechanisms on law X, where both are wrong	declared red: the calibration rule must fail	bias 0.1637 to 0.1682, margin 0.0208, coverage 0.4709 to 0.4984, SE ratio 0.9988	fail
`misspecification_control`	`ice_x_contrast__main_terms`	control	sequential g-computation (ICE): law X, treatment at all three times against none: main-terms GLM outcome regressions and mechanisms on law X, where both are wrong	declared red: the calibration rule must fail	bias 0.1075 to 0.1111, margin 0.0162, coverage 0.5952 to 0.6221, SE ratio 1.0002	fail
`root_n_and_efficiency`	`hajek_d2_contrast__n_2000`	positive	sequential IPW, Hajek: law D2, arm 1 then arm 2 against arm 0 at both times: bias, coverage and SE calibration at n = 2,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.0021, coverage 0.9272 to 0.9644, SE ratio 0.9769	pass
`root_n_and_efficiency`	`hajek_d2_contrast__n_4000`	positive	sequential IPW, Hajek: law D2, arm 1 then arm 2 against arm 0 at both times: bias, coverage and SE calibration at n = 4,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000726, coverage 0.9249 to 0.9627, SE ratio 0.9934	pass
`root_n_and_efficiency`	`hajek_d2_contrast__n_8000`	positive	sequential IPW, Hajek: law D2, arm 1 then arm 2 against arm 0 at both times: bias, coverage and SE calibration at n = 8,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000771, coverage 0.9318 to 0.9677, SE ratio 1.0021	pass
`root_n_and_efficiency`	`hajek_g_contrast__n_2000`	positive	sequential IPW, Hajek: law G, treatment at all three times against none: bias, coverage and SE calibration at n = 2,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000262, coverage 0.9260 to 0.9636, SE ratio 1.0002	pass
`root_n_and_efficiency`	`hajek_g_contrast__n_4000`	positive	sequential IPW, Hajek: law G, treatment at all three times against none: bias, coverage and SE calibration at n = 4,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.0014, coverage 0.9191 to 0.9586, SE ratio 0.9725	pass
`root_n_and_efficiency`	`hajek_g_contrast__n_8000`	positive	sequential IPW, Hajek: law G, treatment at all three times against none: bias, coverage and SE calibration at n = 8,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000214, coverage 0.9318 to 0.9677, SE ratio 1.0209	pass
`root_n_and_efficiency`	`ht_d2_contrast__n_2000`	positive	sequential IPW, Horvitz-Thompson: law D2, arm 1 then arm 2 against arm 0 at both times: bias, coverage and SE calibration at n = 2,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.0019, coverage 0.9272 to 0.9644, SE ratio 0.9823	pass
`root_n_and_efficiency`	`ht_d2_contrast__n_4000`	positive	sequential IPW, Horvitz-Thompson: law D2, arm 1 then arm 2 against arm 0 at both times: bias, coverage and SE calibration at n = 4,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000785, coverage 0.9226 to 0.9611, SE ratio 1.0018	pass
`root_n_and_efficiency`	`ht_d2_contrast__n_8000`	positive	sequential IPW, Horvitz-Thompson: law D2, arm 1 then arm 2 against arm 0 at both times: bias, coverage and SE calibration at n = 8,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000743, coverage 0.9330 to 0.9685, SE ratio 0.9966	pass
`root_n_and_efficiency`	`ht_g_contrast__n_2000`	positive	sequential IPW, Horvitz-Thompson: law G, treatment at all three times against none: bias, coverage and SE calibration at n = 2,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000020, coverage 0.9214 to 0.9602, SE ratio 0.9794	pass
`root_n_and_efficiency`	`ht_g_contrast__n_4000`	positive	sequential IPW, Horvitz-Thompson: law G, treatment at all three times against none: bias, coverage and SE calibration at n = 4,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.0012, coverage 0.9318 to 0.9677, SE ratio 1.0024	pass
`root_n_and_efficiency`	`ht_g_contrast__n_8000`	positive	sequential IPW, Horvitz-Thompson: law G, treatment at all three times against none: bias, coverage and SE calibration at n = 8,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000078, coverage 0.9295 to 0.9661, SE ratio 1.0097	pass
`root_n_and_efficiency`	`ice_d2_contrast__n_2000`	positive	sequential g-computation (ICE): law D2, arm 1 then arm 2 against arm 0 at both times: bias, coverage and SE calibration at n = 2,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.0022, coverage 0.9214 to 0.9602, SE ratio 0.9742	pass
`root_n_and_efficiency`	`ice_d2_contrast__n_4000`	positive	sequential g-computation (ICE): law D2, arm 1 then arm 2 against arm 0 at both times: bias, coverage and SE calibration at n = 4,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000727, coverage 0.9260 to 0.9636, SE ratio 0.9869	pass
`root_n_and_efficiency`	`ice_d2_contrast__n_8000`	positive	sequential g-computation (ICE): law D2, arm 1 then arm 2 against arm 0 at both times: bias, coverage and SE calibration at n = 8,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000794, coverage 0.9295 to 0.9661, SE ratio 1.0027	pass
`root_n_and_efficiency`	`ice_g_contrast__n_2000`	positive	sequential g-computation (ICE): law G, treatment at all three times against none: bias, coverage and SE calibration at n = 2,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000206, coverage 0.9260 to 0.9636, SE ratio 1.0074	pass
`root_n_and_efficiency`	`ice_g_contrast__n_4000`	positive	sequential g-computation (ICE): law G, treatment at all three times against none: bias, coverage and SE calibration at n = 4,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias -0.000243, coverage 0.9400 to 0.9734, SE ratio 1.0218	pass
`root_n_and_efficiency`	`ice_g_contrast__n_8000`	positive	sequential g-computation (ICE): law G, treatment at all three times against none: bias, coverage and SE calibration at n = 8,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000175, coverage 0.9353 to 0.9702, SE ratio 1.0061	pass
`root_n_rate`	`hajek_d2_contrast__empirical_sd`	positive	sequential IPW, Hajek: law D2, arm 1 then arm 2 against arm 0 at both times: log empirical spread of the estimates regressed on log n across three sizes	slope interval inside the root-n band and excluding -1/4	slope -0.5784 to -0.4571	pass
`root_n_rate`	`hajek_d2_contrast__reported_se`	positive	sequential IPW, Hajek: law D2, arm 1 then arm 2 against arm 0 at both times: the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5017 to -0.4988	pass
`root_n_rate`	`hajek_g_contrast__empirical_sd`	positive	sequential IPW, Hajek: law G, treatment at all three times against none: log empirical spread of the estimates regressed on log n across three sizes	slope interval inside the root-n band and excluding -1/4	slope -0.5788 to -0.4561	pass
`root_n_rate`	`hajek_g_contrast__reported_se`	positive	sequential IPW, Hajek: law G, treatment at all three times against none: the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5053 to -0.4974	pass
`root_n_rate`	`ht_d2_contrast__empirical_sd`	positive	sequential IPW, Horvitz-Thompson: law D2, arm 1 then arm 2 against arm 0 at both times: log empirical spread of the estimates regressed on log n across three sizes	slope interval inside the root-n band and excluding -1/4	slope -0.5733 to -0.4521	pass
`root_n_rate`	`ht_d2_contrast__reported_se`	positive	sequential IPW, Horvitz-Thompson: law D2, arm 1 then arm 2 against arm 0 at both times: the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5031 to -0.4999	pass
`root_n_rate`	`ht_g_contrast__empirical_sd`	positive	sequential IPW, Horvitz-Thompson: law G, treatment at all three times against none: log empirical spread of the estimates regressed on log n across three sizes	slope interval inside the root-n band and excluding -1/4	slope -0.5849 to -0.4664	pass
`root_n_rate`	`ht_g_contrast__reported_se`	positive	sequential IPW, Horvitz-Thompson: law G, treatment at all three times against none: the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5076 to -0.4983	pass
`root_n_rate`	`ice_d2_contrast__empirical_sd`	positive	sequential g-computation (ICE): law D2, arm 1 then arm 2 against arm 0 at both times: log empirical spread of the estimates regressed on log n across three sizes	slope interval inside the root-n band and excluding -1/4	slope -0.5831 to -0.4602	pass
`root_n_rate`	`ice_d2_contrast__reported_se`	positive	sequential g-computation (ICE): law D2, arm 1 then arm 2 against arm 0 at both times: the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5016 to -0.4985	pass
`root_n_rate`	`ice_g_contrast__empirical_sd`	positive	sequential g-computation (ICE): law G, treatment at all three times against none: log empirical spread of the estimates regressed on log n across three sizes	slope interval inside the root-n band and excluding -1/4	slope -0.5593 to -0.4411	pass
`root_n_rate`	`ice_g_contrast__reported_se`	positive	sequential g-computation (ICE): law G, treatment at all three times against none: the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5025 to -0.4977	pass

The declared negative control#

The three misspecification_control cells are red as declared. The record EXPECTED_RED in tests/studies/canonical_sequential_baselines.py lists them before any run. On law X every main-terms GLM is wrong, so each estimator converges to a misspecified limit. The influence curve then covers that limit and not the truth.

The ledger rows read a bias of 1.7 to 2.0 empirical standard deviations and a coverage of 0.48 to 0.61. The standard-error ratio is near 1.00 in each cell. The reported standard error is right, and the estimate is wrong.

A calibration rule that did not fail here could not detect a misspecified fit. The design test tests/unit/test_sequential_baselines_design.py computes the power of the rule against this law. The red cells confirm that the instrument works. They do not report a defect.

Result#

Every primary test and every positive cell passed. Every control other than the declared negative control passed. The three red cells are the declared negative control. The 17 diagnostic cells state no verdict.

Measured values#

Names beginning margin: are thresholds declared before the run. Everything else is measured from the committed results and checked at the precision printed.

quantity	value	source
`replicates`	1000	primary replications per scenario
`n`	8000	observations per primary replication
`independent_tests_total`	27	implementation-estimand tests against the truth
`independent_tests_passed`	27	of those, passing
`paired_tests_total`	0	external comparisons declared
`paired_tests_passed`	0	external comparisons passing
`property_cells_total`	162	repeated-sampling property cells
`property_cells_passed`	159	cells whose own and family verdicts pass. The three red cells are the declared negative control
`property_cells_reported`	17	diagnostic cells that state no verdict
`max_standardized_bias`	0.0331	largest absolute primary bias in empirical standard deviations
`min_coverage`	0.9410	lowest measured primary-study coverage
`min_coverage_ci_lower`	0.9191	lowest exact 99% primary coverage endpoint
`min_se_ratio_ci_lower`	0.9230	lowest bootstrap primary SE-ratio endpoint
`max_se_ratio_ci_upper`	1.0774	highest bootstrap primary SE-ratio endpoint
`margin:confidence_level`	0.9900	confidence level of every Monte Carlo interval
`margin:alpha`	0.0500	nominal size of the reported intervals
`margin:nominal_coverage`	0.9500	nominal coverage those intervals claim
`margin:bootstrap_replicates`	10000	resamples behind every bootstrap interval
`margin:standardized_bias`	0.2500	bias equivalence margin, in empirical standard deviations
`margin:coverage_floor`	0.9000	validity floor the coverage lower endpoint must clear
`margin:over_coverage_ceiling`	0.9900	above this, coverage is conservative rather than invalid
`margin:se_ratio_sanity_lower`	0.8000	SE-ratio screen, lower limit
`margin:se_ratio_sanity_upper`	1.2000	SE-ratio screen, upper limit
`margin:calibration_se_ratio_lower`	0.9300	calibration-cell SE-ratio band, lower limit
`margin:calibration_se_ratio_upper`	1.0700	calibration-cell SE-ratio band, upper limit
`margin:calibration_coverage_lower`	0.9200	calibration-cell coverage band, lower limit
`margin:calibration_coverage_upper`	0.9800	calibration-cell coverage band, upper limit
`margin:type_i_ceiling`	0.1000	the rate a positive cell must bound and a control must exceed. No cell of this study reads it
`margin:paired_difference`	0.1500	paired similarity margin, in pooled empirical standard deviations. No cell of this study reads it
`margin:rmse_noninferiority`	1.1000	largest external-comparison RMSE ratio bound. No cell of this study reads it
`margin:coverage_noninferiority`	-0.0250	smallest external-comparison coverage difference bound. No cell of this study reads it
`margin:calibration_noninferiority`	0.0500	largest external-comparison calibration excess bound. No cell of this study reads it
`margin:minimum_power`	0.8000	rejection lower bound a power cell must clear. No cell of this study reads it
`margin:root_n_slope`	-0.5000	contraction rate root-n asymptotics predict
`margin:root_n_slope_lower`	-0.6250	accepted root-n slope band, lower limit
`margin:root_n_slope_upper`	-0.3750	accepted root-n slope band, upper limit
`margin:excluded_slope`	-0.2500	slower rate a root-n interval must exclude. No cell of this study reads it
`margin:shrunken_se_factor`	0.7000	factor that scales the standard error of a shrunken-SE control
`margin:subject_failure_bound`	0.0100	declared share of replications a cell may lose to a recordable fitting failure
`margin:subject_failures_allowed`	10	the same bound, in primary replications

Limitations#

limit	what it means for use
no comparator study	R `ltmle` and R `stremr` agree with the estimates on fixtures only. The study reports no coverage, bias or standard-error ratio for either package
parametric nuisances only	the study fits `GLM` nuisances. A data-adaptive learner reports the point estimate only, and the `adaptive_learners` cells report that estimate without a verdict
in sample, without weights or clusters	the study does not cross-fit. The weighted cells `d2w_static_12` cover one weight law. Clusters have fast-tier evidence only
one law family per structure	the laws cover binary, survival, competing-risk, three-arm, continuous and policy structures with fixed coefficients. A law with other coefficients is not tested
a non-saturated binomial first node	the `D2` first-node regression is saturated by the design, so a binomial first node without that saturation has no coverage evidence. The fast-tier witnesses W6 and W10 cover it
the fixed-mechanism and first-node cells report	those cells state a predicted direction. They show that the calibration instrument sees a dropped term. The cell `first_node_se` is a property of the law, so it cannot fail for a broken estimator
the adaptive cell has one size	the `adaptive_learners` cells fit ICE and Hajek at n = 1,000 with 100 replications, without LTMLE. They report bias in standard deviations to about 0.1
the negative control is the only red set	the three red cells hold the declared misspecification. A misspecification of another kind has no control
positivity at small n	`D2C` needs n = 8,000. At n = 2,000 the ICE fit was singular on 227 of 2,000 pilot draws

Reproduction#

The manifest records the seeds, the margins, the estimator configuration, the source hashes and the result hashes. The fixture README gives the regeneration command. The replications and the property results carry every published row.