Stratified point-treatment TMLE

This study validates ordinary point-treatment TMLE with baseline strata, strata=["V"]. A stratum parameter is the marginal point-treatment parameter of the law inside one of a fixed number of baseline strata. The construction is the marginal result applied inside each cell of a finite partition, which is a standard step under the roadmap’s Eligibility conditions.

The fit fluctuates once. Its submodel carries one disjoint score block \(I(V=s) H_s / P_n(V=s)\) for each stratum \(s\). \(H_s\) is the marginal clever covariate built with the within-stratum arm shares. Each stratum curve is \(I(V=s) D_s / P_n(V=s)\), where \(D_s\) is the marginal influence curve computed inside the stratum. The fit also reports the marginal parameters, and the marginal estimate is the empirical mixture of the stratum estimates.

What was tested

setting	declaration
stratum	\(V \in \{0, 1, 2\}\) with probabilities 0.5, 0.3 and 0.2. The strata are unequal, so the \(n / n_s\) weight of a stratum curve matters
covariate	\(W \in \{0, 1, 2\}\) given \(V\), with rows \((0.5, 0.3, 0.2)\), \((0.3, 0.4, 0.3)\) and \((0.2, 0.3, 0.5)\)
treatment	\(g(w, v) = \operatorname{expit}(-0.3 + 0.5 w - 0.4 v)\), between 0.25 and 0.67
outcome	binary, \(Q(a, w, v) = \operatorname{expit}(-0.8 + a + 0.6 w + 0.9 v)\)
truth	exact. Every variable takes finitely many values, so tests/studies/stratified_law.py sums each truth and each efficient influence function over the 36 support points
fit	TMLE(cross_fit=False, estimands=("ey", "ate")) with main-terms logistic regressions on \((A, W, V)\) and \((W, V)\), which are correct for this law, and g_bounds=(0.01, 0.99)
primary scenario	stratified_binary, the two arm means and the ATE in each stratum, \(n = 2000\), 1,000 replications
Monte Carlo inference	exact 99% intervals around every rate, and 99% intervals around every primary endpoint

The law module records why two coefficients of \(Q\) moved before the declaration commit. At the first declared values the stratum ATEs were too close together, and the marginal-fluctuation control could not move 1 SD in stratum 0. The change also raised the treated mean of stratum 2 from 0.858 to 0.936.

The comparator is R tmle3 at commit ed72f8a, through tmle_stratified(..., base_estimate = FALSE) in two stages. The first stage is tmle_TSM_all() and gives the six stratum arm means. The second stage is tmle_ATE(1, 0) and gives the three stratum ATEs. base_estimate = FALSE drops the marginal parameter, because the marginal clever covariate is the sum of the stratum columns and would make the update collinear. References gives the source locators.

The two implementations differ in one declared way. The tmle3 ATE stage fluctuates one clever-covariate column per stratum. The cleverly fit with estimands=("ey", "ate") fluctuates the two arm columns of each stratum, as the ordinary point-treatment study pairs it.

Two facts about the comparator shape the runner, tests/canonical/tmle3_stratified/run_tmle3_stratified.R.

fact	what the runner does
fit$summary fails on a stratified spec with two base parameters. The fit stores the parameter names and initial estimates as matrices, and the summary builds 12 columns and names them with 10 names	it computes the same summary from fit$estimates: the covariance of the stacked curves with an \(n - 1\) denominator, \(\sqrt{\operatorname{diag} / n}\), and the Wald interval at 1.959964
get_strata_weights merges the stratum column with the strata table under sort = FALSE	it checks on every replication that each row’s one nonzero weight column is its own stratum, and that the weight is \(n / n_s\)

The table gives the estimands that are measured against the exact truth and not paired.

estimand	why it is not paired
ATT and ATC	Param_ATT$estimates and Param_ATC$estimates read the counterfactual tasks of the training task, not of the task they receive. On a stratum subset the arm means and the treated share are then full-length vectors beside a subset-length outcome, and the estimate is the marginal one. The two parameters also update the treatment node, and cleverly does not fluctuate it
PAR	Param_PAR is not verified as safe on a subset at ed72f8a

Accuracy against known truth

law	estimand	what was tested	implementation	bias (99% interval)	coverage	SE ratio	result
binary-outcome law with three unequal baseline strata	ate[V=0]	average treatment effect, in stratum V=0	cleverly ordinary TMLE with baseline strata	-0.0026 to 0.0024	0.9500	1.0083	pass
binary-outcome law with three unequal baseline strata	ate[V=0]	average treatment effect, in stratum V=0	R tmle3 stratified TMLE, tmle_stratified	-0.0026 to 0.0024	0.9500	1.0085	pass
binary-outcome law with three unequal baseline strata	ate[V=1]	average treatment effect, in stratum V=1	cleverly ordinary TMLE with baseline strata	-0.0014 to 0.0043	0.9430	0.9957	pass
binary-outcome law with three unequal baseline strata	ate[V=1]	average treatment effect, in stratum V=1	R tmle3 stratified TMLE, tmle_stratified	-0.0014 to 0.0043	0.9440	0.9977	pass
binary-outcome law with three unequal baseline strata	ate[V=2]	average treatment effect, in stratum V=2	cleverly ordinary TMLE with baseline strata	-0.0044 to 0.000590	0.9510	1.0001	pass
binary-outcome law with three unequal baseline strata	ate[V=2]	average treatment effect, in stratum V=2	R tmle3 stratified TMLE, tmle_stratified	-0.0044 to 0.000587	0.9500	1.0018	pass
binary-outcome law with three unequal baseline strata	ey[0][V=0]	counterfactual mean under treatment arm ‘0’, in stratum V=0	cleverly ordinary TMLE with baseline strata	-0.0030 to 0.000807	0.9420	0.9674	pass
binary-outcome law with three unequal baseline strata	ey[0][V=0]	counterfactual mean under treatment arm ‘0’, in stratum V=0	R tmle3 stratified TMLE, tmle_stratified	-0.0030 to 0.000807	0.9420	0.9674	pass
binary-outcome law with three unequal baseline strata	ey[0][V=1]	counterfactual mean under treatment arm ‘0’, in stratum V=1	cleverly ordinary TMLE with baseline strata	-0.0027 to 0.0017	0.9480	0.9747	pass
binary-outcome law with three unequal baseline strata	ey[0][V=1]	counterfactual mean under treatment arm ‘0’, in stratum V=1	R tmle3 stratified TMLE, tmle_stratified	-0.0027 to 0.0017	0.9480	0.9747	pass
binary-outcome law with three unequal baseline strata	ey[0][V=2]	counterfactual mean under treatment arm ‘0’, in stratum V=2	cleverly ordinary TMLE with baseline strata	-0.000833 to 0.0028	0.9430	1.0058	pass
binary-outcome law with three unequal baseline strata	ey[0][V=2]	counterfactual mean under treatment arm ‘0’, in stratum V=2	R tmle3 stratified TMLE, tmle_stratified	-0.000833 to 0.0028	0.9430	1.0058	pass
binary-outcome law with three unequal baseline strata	ey[1][V=0]	counterfactual mean under treatment arm ‘1’, in stratum V=0	cleverly ordinary TMLE with baseline strata	-0.0030 to 0.000506	0.9570	1.0167	pass
binary-outcome law with three unequal baseline strata	ey[1][V=0]	counterfactual mean under treatment arm ‘1’, in stratum V=0	R tmle3 stratified TMLE, tmle_stratified	-0.0030 to 0.000506	0.9570	1.0167	pass
binary-outcome law with three unequal baseline strata	ey[1][V=1]	counterfactual mean under treatment arm ‘1’, in stratum V=1	cleverly ordinary TMLE with baseline strata	-0.000962 to 0.0028	0.9470	1.0195	pass
binary-outcome law with three unequal baseline strata	ey[1][V=1]	counterfactual mean under treatment arm ‘1’, in stratum V=1	R tmle3 stratified TMLE, tmle_stratified	-0.000962 to 0.0028	0.9470	1.0194	pass
binary-outcome law with three unequal baseline strata	ey[1][V=2]	counterfactual mean under treatment arm ‘1’, in stratum V=2	cleverly ordinary TMLE with baseline strata	-0.0027 to 0.000813	0.9170	0.9850	fail
binary-outcome law with three unequal baseline strata	ey[1][V=2]	counterfactual mean under treatment arm ‘1’, in stratum V=2	R tmle3 stratified TMLE, tmle_stratified	-0.0027 to 0.000813	0.9170	0.9849	fail

Agreement with the canonical implementation

Comparator-backed: a paired comparison with tmle3-stratified on the same samples. Each row reports estimate equivalence within the declared margin, the RMSE ratio and the coverage difference, and names its comparison kind.

law	estimand	what was compared	paired difference	share of margin used	RMSE ratio bound	coverage difference	comparison kind	calibration resolution	result
binary-outcome law with three unequal baseline strata	ate[V=0]	average treatment effect, in stratum V=0	0.000001	0.000282	1.0004	0	matching implementation	0.000713 vs 0.0500	equivalent
binary-outcome law with three unequal baseline strata	ate[V=1]	average treatment effect, in stratum V=1	0.000007	0.0014	1.0037	-0.0010	matching implementation	0.0021 vs 0.0500	equivalent
binary-outcome law with three unequal baseline strata	ate[V=2]	average treatment effect, in stratum V=2	0.000001	0.000256	1.0031	0.0010	matching implementation	0.0055 vs 0.0500	equivalent
binary-outcome law with three unequal baseline strata	ey[0][V=0]	counterfactual mean under treatment arm ‘0’, in stratum V=0	4.362e-08	0.000012	1.0000	0	matching implementation	0.000017 vs 0.0500	equivalent
binary-outcome law with three unequal baseline strata	ey[0][V=1]	counterfactual mean under treatment arm ‘0’, in stratum V=1	4.438e-08	0.000011	1.0000	0	matching implementation	0.000008 vs 0.0500	equivalent
binary-outcome law with three unequal baseline strata	ey[0][V=2]	counterfactual mean under treatment arm ‘0’, in stratum V=2	-1.943e-08	0.000006	1.0000	0	matching implementation	0.000076 vs 0.0500	equivalent
binary-outcome law with three unequal baseline strata	ey[1][V=0]	counterfactual mean under treatment arm ‘1’, in stratum V=0	3.601e-09	0.000001	1.0000	0	matching implementation	0.000018 vs 0.0500	equivalent
binary-outcome law with three unequal baseline strata	ey[1][V=1]	counterfactual mean under treatment arm ‘1’, in stratum V=1	4.951e-08	0.000014	1.0000	0	matching implementation	0.000010 vs 0.0500	equivalent
binary-outcome law with three unequal baseline strata	ey[1][V=2]	counterfactual mean under treatment arm ‘1’, in stratum V=2	1.511e-07	0.000047	1.0000	0	matching implementation	0.000140 vs 0.0500	equivalent

Theory properties

The property cells fit only cleverly, against the exact truth. A label v<s>_<parameter> names one stratum parameter.

family	cells	n	replications
interval_calibration	each of the 18 stratum parameters of in-sample fits with ("ey", "ate", "att", "atc", "par"), with a shrunken-SE and a noise control each	2,000	2,400
interval_calibration	the three stratum ATEs of the default cross-fitted fit, cross_fit=True with ten folds, with the same controls	2,000	2,400
simultaneous_coverage	strata, the default band over the 24 parameters of the in-sample fits, and crossfit_strata, the band over the 12 parameters of the cross-fitted fits	2,000	2,400
double_robustness	each stratum ATE with both nuisances correct, one correct, or neither. A wrong model is intercept-only	2,000	1,200
stratum_targeting_necessity	the outer stratum ATEs of a fit whose outcome regression omits \(V\), against a longhand marginal fluctuation of the same regression on the same draws	2,000	1,200

The marginal fluctuation solves the marginal score only. A regression that omits \(V\) therefore stays biased inside a stratum. The stratified fit solves each stratum’s score, and it is consistent there because \(g\) is correct. The bias of the control is close to linear in \(V\) and its average is zero, so it nearly vanishes in the middle stratum. The family reads the two outer strata, where tests/unit/test_simultaneous_cell_design.py puts the control at least 1 SD from the truth. tests/unit/test_stratified_influence_exact.py checks the score block of every stratum.

property	cell	role	what was tested	what must hold	measured	result
double_robustness	v0_ate__both_correct	positive	average treatment effect in stratum V = 0: both the outcome regression and the treatment mechanism are correctly specified	bias interval inside the equivalence margin, with the reported standard error on the scale of the empirical spread	bias -0.0015 to 0.0031, margin 0.0077, SE ratio 1.0051	pass
double_robustness	v0_ate__both_wrong	control	average treatment effect in stratum V = 0: both nuisances are misspecified	bias interval must fall entirely outside the margin, with the reported standard error still on the scale of the empirical spread	bias 0.0383 to 0.0430, margin 0.0078, SE ratio 0.9769	pass
double_robustness	v0_ate__outcome_correct	positive	average treatment effect in stratum V = 0: only the outcome regression is correctly specified	bias interval inside the equivalence margin, with the reported standard error on the scale of the empirical spread	bias -0.0030 to 0.0014, margin 0.0074, SE ratio 1.0047	pass
double_robustness	v0_ate__treatment_correct	positive	average treatment effect in stratum V = 0: only the treatment mechanism is correctly specified	bias interval inside the equivalence margin, with the reported standard error on the scale of the empirical spread	bias -0.0023 to 0.0024, margin 0.0079, SE ratio 1.0156	pass
double_robustness	v1_ate__both_correct	positive	average treatment effect in stratum V = 1: both the outcome regression and the treatment mechanism are correctly specified	bias interval inside the equivalence margin, with the reported standard error on the scale of the empirical spread	bias -0.0024 to 0.0028, margin 0.0087, SE ratio 0.9927	pass
double_robustness	v1_ate__both_wrong	control	average treatment effect in stratum V = 1: both nuisances are misspecified	bias interval must fall entirely outside the margin, with the reported standard error still on the scale of the empirical spread	bias 0.0272 to 0.0322, margin 0.0083, SE ratio 1.0316	pass
double_robustness	v1_ate__outcome_correct	positive	average treatment effect in stratum V = 1: only the outcome regression is correctly specified	bias interval inside the equivalence margin, with the reported standard error on the scale of the empirical spread	bias -0.0034 to 0.0018, margin 0.0086, SE ratio 0.9770	pass
double_robustness	v1_ate__treatment_correct	positive	average treatment effect in stratum V = 1: only the treatment mechanism is correctly specified	bias interval inside the equivalence margin, with the reported standard error on the scale of the empirical spread	bias -0.0031 to 0.0020, margin 0.0085, SE ratio 1.0482	pass
double_robustness	v2_ate__both_correct	positive	average treatment effect in stratum V = 2: both the outcome regression and the treatment mechanism are correctly specified	bias interval inside the equivalence margin, with the reported standard error on the scale of the empirical spread	bias -0.0037 to 0.000930, margin 0.0078, SE ratio 0.9859	pass
double_robustness	v2_ate__both_wrong	control	average treatment effect in stratum V = 2: both nuisances are misspecified	bias interval must fall entirely outside the margin, with the reported standard error still on the scale of the empirical spread	bias 0.0141 to 0.0186, margin 0.0075, SE ratio 1.0358	pass
double_robustness	v2_ate__outcome_correct	positive	average treatment effect in stratum V = 2: only the outcome regression is correctly specified	bias interval inside the equivalence margin, with the reported standard error on the scale of the empirical spread	bias -0.0029 to 0.0016, margin 0.0076, SE ratio 1.0211	pass
double_robustness	v2_ate__treatment_correct	positive	average treatment effect in stratum V = 2: only the treatment mechanism is correctly specified	bias interval inside the equivalence margin, with the reported standard error on the scale of the empirical spread	bias -0.0021 to 0.0027, margin 0.0080, SE ratio 0.9806	pass
interval_calibration	v0_atc__correctly_specified	positive	average effect on the untreated in stratum V = 0: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9388 to 0.9619, SE ratio 0.9537 to 1.0259, empirical efficiency ratio 0.9752 to 1.0490, reported efficiency ratio 0.9994 to 1.0015	pass
interval_calibration	v0_atc__noise_control	control	average effect on the untreated in stratum V = 0: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8155 to 0.8548, SE ratio 0.6833 to 0.7384, empirical efficiency ratio 1.3549 to 1.4640, reported efficiency ratio 0.9995 to 1.0015	pass
interval_calibration	v0_atc__shrunken_se_control	control	average effect on the untreated in stratum V = 0: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7994 to 0.8402, SE ratio 0.6678 to 0.7193, empirical efficiency ratio 0.9737 to 1.0485, reported efficiency ratio 0.6996 to 0.7011	pass
interval_calibration	v0_ate__correctly_specified	positive	average treatment effect in stratum V = 0: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9388 to 0.9619, SE ratio 0.9492 to 1.0210, empirical efficiency ratio 0.9790 to 1.0534, reported efficiency ratio 0.9989 to 1.0006	pass
interval_calibration	v0_ate__noise_control	control	average treatment effect in stratum V = 0: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8094 to 0.8493, SE ratio 0.6862 to 0.7385, empirical efficiency ratio 1.3539 to 1.4572, reported efficiency ratio 0.9989 to 1.0006	pass
interval_calibration	v0_ate__shrunken_se_control	control	average treatment effect in stratum V = 0: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7951 to 0.8362, SE ratio 0.6639 to 0.7152, empirical efficiency ratio 0.9783 to 1.0540, reported efficiency ratio 0.6992 to 0.7004	pass
interval_calibration	v0_ate_crossfit__correctly_specified	positive	average treatment effect in stratum V = 0, from the cross-fitted fit: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9397 to 0.9626, SE ratio 0.9567 to 1.0288, empirical efficiency ratio 0.9757 to 1.0490, reported efficiency ratio 1.0029 to 1.0046	pass
interval_calibration	v0_ate_crossfit__noise_control	control	average treatment effect in stratum V = 0, from the cross-fitted fit: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8033 to 0.8437, SE ratio 0.6602 to 0.7125, empirical efficiency ratio 1.4089 to 1.5203, reported efficiency ratio 1.0029 to 1.0046	pass
interval_calibration	v0_ate_crossfit__shrunken_se_control	control	average treatment effect in stratum V = 0, from the cross-fitted fit: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8003 to 0.8409, SE ratio 0.6692 to 0.7202, empirical efficiency ratio 0.9757 to 1.0499, reported efficiency ratio 0.7021 to 0.7032	pass
interval_calibration	v0_att__correctly_specified	positive	average effect on the treated in stratum V = 0: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9369 to 0.9604, SE ratio 0.9452 to 1.0172, empirical efficiency ratio 0.9828 to 1.0582, reported efficiency ratio 0.9986 to 1.0011	pass
interval_calibration	v0_att__noise_control	control	average effect on the treated in stratum V = 0: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8050 to 0.8453, SE ratio 0.6708 to 0.7213, empirical efficiency ratio 1.3863 to 1.4902, reported efficiency ratio 0.9986 to 1.0012	pass
interval_calibration	v0_att__shrunken_se_control	control	average effect on the treated in stratum V = 0: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7933 to 0.8346, SE ratio 0.6615 to 0.7119, empirical efficiency ratio 0.9831 to 1.0576, reported efficiency ratio 0.6991 to 0.7008	pass
interval_calibration	v0_ey0__correctly_specified	positive	mean under no treatment in stratum V = 0: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9439 to 0.9659, SE ratio 0.9603 to 1.0366, empirical efficiency ratio 0.9647 to 1.0414, reported efficiency ratio 0.9986 to 1.0012	pass
interval_calibration	v0_ey0__noise_control	control	mean under no treatment in stratum V = 0: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8238 to 0.8623, SE ratio 0.6808 to 0.7369, empirical efficiency ratio 1.3571 to 1.4689, reported efficiency ratio 0.9986 to 1.0011	pass
interval_calibration	v0_ey0__shrunken_se_control	control	mean under no treatment in stratum V = 0: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7933 to 0.8346, SE ratio 0.6728 to 0.7268, empirical efficiency ratio 0.9635 to 1.0406, reported efficiency ratio 0.6991 to 0.7008	pass
interval_calibration	v0_ey1__correctly_specified	positive	mean under treatment in stratum V = 0: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9324 to 0.9567, SE ratio 0.9448 to 1.0165, empirical efficiency ratio 0.9836 to 1.0585, reported efficiency ratio 0.9984 to 1.0010	pass
interval_calibration	v0_ey1__noise_control	control	mean under treatment in stratum V = 0: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.7994 to 0.8402, SE ratio 0.6707 to 0.7215, empirical efficiency ratio 1.3851 to 1.4909, reported efficiency ratio 0.9984 to 1.0009	pass
interval_calibration	v0_ey1__shrunken_se_control	control	mean under treatment in stratum V = 0: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8050 to 0.8453, SE ratio 0.6619 to 0.7124, empirical efficiency ratio 0.9823 to 1.0570, reported efficiency ratio 0.6989 to 0.7007	pass
interval_calibration	v0_par__correctly_specified	positive	population attributable risk in stratum V = 0: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9346 to 0.9585, SE ratio 0.9444 to 1.0161, empirical efficiency ratio 0.9853 to 1.0603, reported efficiency ratio 0.9995 to 1.0033	pass
interval_calibration	v0_par__noise_control	control	population attributable risk in stratum V = 0: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8294 to 0.8675, SE ratio 0.6847 to 0.7395, empirical efficiency ratio 1.3538 to 1.4622, reported efficiency ratio 0.9995 to 1.0033	pass
interval_calibration	v0_par__shrunken_se_control	control	population attributable risk in stratum V = 0: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7894 to 0.8310, SE ratio 0.6607 to 0.7108, empirical efficiency ratio 0.9860 to 1.0606, reported efficiency ratio 0.6997 to 0.7023	pass
interval_calibration	v1_atc__correctly_specified	positive	average effect on the untreated in stratum V = 1: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9374 to 0.9608, SE ratio 0.9626 to 1.0407, empirical efficiency ratio 0.9602 to 1.0379, reported efficiency ratio 0.9965 to 1.0018	pass
interval_calibration	v1_atc__noise_control	control	average effect on the untreated in stratum V = 1: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8137 to 0.8532, SE ratio 0.6912 to 0.7447, empirical efficiency ratio 1.3419 to 1.4453, reported efficiency ratio 0.9966 to 1.0018	pass
interval_calibration	v1_atc__shrunken_se_control	control	average effect on the untreated in stratum V = 1: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8133 to 0.8529, SE ratio 0.6733 to 0.7274, empirical efficiency ratio 0.9614 to 1.0388, reported efficiency ratio 0.6976 to 0.7013	pass
interval_calibration	v1_ate__correctly_specified	positive	average treatment effect in stratum V = 1: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9328 to 0.9570, SE ratio 0.9598 to 1.0366, empirical efficiency ratio 0.9633 to 1.0409, reported efficiency ratio 0.9970 to 1.0006	pass
interval_calibration	v1_ate__noise_control	control	average treatment effect in stratum V = 1: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8190 to 0.8580, SE ratio 0.6882 to 0.7396, empirical efficiency ratio 1.3505 to 1.4514, reported efficiency ratio 0.9970 to 1.0007	pass
interval_calibration	v1_ate__shrunken_se_control	control	average treatment effect in stratum V = 1: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8142 to 0.8536, SE ratio 0.6724 to 0.7242, empirical efficiency ratio 0.9652 to 1.0401, reported efficiency ratio 0.6979 to 0.7005	pass
interval_calibration	v1_ate_crossfit__correctly_specified	positive	average treatment effect in stratum V = 1, from the cross-fitted fit: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9346 to 0.9585, SE ratio 0.9702 to 1.0450, empirical efficiency ratio 0.9577 to 1.0317, reported efficiency ratio 0.9991 to 1.0028	pass
interval_calibration	v1_ate_crossfit__noise_control	control	average treatment effect in stratum V = 1, from the cross-fitted fit: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8042 to 0.8445, SE ratio 0.6703 to 0.7232, empirical efficiency ratio 1.3844 to 1.4932, reported efficiency ratio 0.9991 to 1.0028	pass
interval_calibration	v1_ate_crossfit__shrunken_se_control	control	average treatment effect in stratum V = 1, from the cross-fitted fit: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8072 to 0.8473, SE ratio 0.6796 to 0.7323, empirical efficiency ratio 0.9562 to 1.0312, reported efficiency ratio 0.6994 to 0.7019	pass
interval_calibration	v1_att__correctly_specified	positive	average effect on the treated in stratum V = 1: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9369 to 0.9604, SE ratio 0.9637 to 1.0389, empirical efficiency ratio 0.9653 to 1.0406, reported efficiency ratio 0.9999 to 1.0055	pass
interval_calibration	v1_att__noise_control	control	average effect on the treated in stratum V = 1: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8116 to 0.8513, SE ratio 0.6806 to 0.7340, empirical efficiency ratio 1.3663 to 1.4739, reported efficiency ratio 0.9998 to 1.0056	pass
interval_calibration	v1_att__shrunken_se_control	control	average effect on the treated in stratum V = 1: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8137 to 0.8532, SE ratio 0.6733 to 0.7285, empirical efficiency ratio 0.9640 to 1.0428, reported efficiency ratio 0.6999 to 0.7039	pass
interval_calibration	v1_ey0__correctly_specified	positive	mean under no treatment in stratum V = 1: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9337 to 0.9578, SE ratio 0.9594 to 1.0352, empirical efficiency ratio 0.9659 to 1.0424, reported efficiency ratio 0.9981 to 1.0018	pass
interval_calibration	v1_ey0__noise_control	control	mean under no treatment in stratum V = 1: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8225 to 0.8612, SE ratio 0.6853 to 0.7392, empirical efficiency ratio 1.3522 to 1.4590, reported efficiency ratio 0.9981 to 1.0018	pass
interval_calibration	v1_ey0__shrunken_se_control	control	mean under no treatment in stratum V = 1: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8046 to 0.8449, SE ratio 0.6713 to 0.7250, empirical efficiency ratio 0.9660 to 1.0422, reported efficiency ratio 0.6987 to 0.7012	pass
interval_calibration	v1_ey1__correctly_specified	positive	mean under treatment in stratum V = 1: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9241 to 0.9499, SE ratio 0.9588 to 1.0342, empirical efficiency ratio 0.9634 to 1.0385, reported efficiency ratio 0.9923 to 0.9995	pass
interval_calibration	v1_ey1__noise_control	control	mean under treatment in stratum V = 1: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8046 to 0.8449, SE ratio 0.6733 to 0.7247, empirical efficiency ratio 1.3737 to 1.4788, reported efficiency ratio 0.9923 to 0.9994	pass
interval_calibration	v1_ey1__shrunken_se_control	control	mean under treatment in stratum V = 1: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7994 to 0.8402, SE ratio 0.6709 to 0.7238, empirical efficiency ratio 0.9638 to 1.0384, reported efficiency ratio 0.6946 to 0.6996	pass
interval_calibration	v1_par__correctly_specified	positive	population attributable risk in stratum V = 1: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9374 to 0.9608, SE ratio 0.9601 to 1.0378, empirical efficiency ratio 0.9643 to 1.0422, reported efficiency ratio 0.9980 to 1.0028	pass
interval_calibration	v1_par__noise_control	control	population attributable risk in stratum V = 1: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8085 to 0.8485, SE ratio 0.6765 to 0.7285, empirical efficiency ratio 1.3732 to 1.4788, reported efficiency ratio 0.9980 to 1.0029	pass
interval_calibration	v1_par__shrunken_se_control	control	population attributable risk in stratum V = 1: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8116 to 0.8513, SE ratio 0.6721 to 0.7275, empirical efficiency ratio 0.9627 to 1.0420, reported efficiency ratio 0.6986 to 0.7020	pass
interval_calibration	v2_atc__correctly_specified	positive	average effect on the untreated in stratum V = 2: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9255 to 0.9511, SE ratio 0.9344 to 1.0090, empirical efficiency ratio 0.9874 to 1.0663, reported efficiency ratio 0.9908 to 1.0016	pass
interval_calibration	v2_atc__noise_control	control	average effect on the untreated in stratum V = 2: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.7994 to 0.8402, SE ratio 0.6611 to 0.7123, empirical efficiency ratio 1.3986 to 1.5076, reported efficiency ratio 0.9912 to 1.0018	pass
interval_calibration	v2_atc__shrunken_se_control	control	average effect on the untreated in stratum V = 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7985 to 0.8394, SE ratio 0.6543 to 0.7063, empirical efficiency ratio 0.9876 to 1.0657, reported efficiency ratio 0.6938 to 0.7010	pass
interval_calibration	v2_ate__correctly_specified	positive	average treatment effect in stratum V = 2: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9250 to 0.9507, SE ratio 0.9355 to 1.0108, empirical efficiency ratio 0.9847 to 1.0647, reported efficiency ratio 0.9910 to 1.0000	pass
interval_calibration	v2_ate__noise_control	control	average treatment effect in stratum V = 2: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8007 to 0.8413, SE ratio 0.6654 to 0.7169, empirical efficiency ratio 1.3881 to 1.4954, reported efficiency ratio 0.9911 to 1.0000	pass
interval_calibration	v2_ate__shrunken_se_control	control	average treatment effect in stratum V = 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8024 to 0.8429, SE ratio 0.6546 to 0.7074, empirical efficiency ratio 0.9846 to 1.0653, reported efficiency ratio 0.6937 to 0.7000	pass
interval_calibration	v2_ate_crossfit__correctly_specified	positive	average treatment effect in stratum V = 2, from the cross-fitted fit: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9273 to 0.9526, SE ratio 0.9324 to 1.0031, empirical efficiency ratio 0.9998 to 1.0762, reported efficiency ratio 0.9986 to 1.0078	pass
interval_calibration	v2_ate_crossfit__noise_control	control	average treatment effect in stratum V = 2, from the cross-fitted fit: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8129 to 0.8525, SE ratio 0.6783 to 0.7290, empirical efficiency ratio 1.3763 to 1.4784, reported efficiency ratio 0.9985 to 1.0078	pass
interval_calibration	v2_ate_crossfit__shrunken_se_control	control	average treatment effect in stratum V = 2, from the cross-fitted fit: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7855 to 0.8274, SE ratio 0.6523 to 0.7009, empirical efficiency ratio 1.0013 to 1.0771, reported efficiency ratio 0.6989 to 0.7054	pass
interval_calibration	v2_att__correctly_specified	positive	average effect on the treated in stratum V = 2: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9324 to 0.9567, SE ratio 0.9478 to 1.0249, empirical efficiency ratio 0.9722 to 1.0515, reported efficiency ratio 0.9922 to 1.0015	pass
interval_calibration	v2_att__noise_control	control	average effect on the treated in stratum V = 2: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8059 to 0.8461, SE ratio 0.6781 to 0.7297, empirical efficiency ratio 1.3667 to 1.4695, reported efficiency ratio 0.9923 to 1.0016	pass
interval_calibration	v2_att__shrunken_se_control	control	average effect on the treated in stratum V = 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8055 to 0.8457, SE ratio 0.6633 to 0.7171, empirical efficiency ratio 0.9733 to 1.0518, reported efficiency ratio 0.6946 to 0.7010	pass
interval_calibration	v2_ey0__correctly_specified	positive	mean under no treatment in stratum V = 2: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9356 to 0.9593, SE ratio 0.9507 to 1.0255, empirical efficiency ratio 0.9711 to 1.0488, reported efficiency ratio 0.9923 to 0.9999	pass
interval_calibration	v2_ey0__noise_control	control	mean under no treatment in stratum V = 2: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.7955 to 0.8366, SE ratio 0.6742 to 0.7241, empirical efficiency ratio 1.3759 to 1.4771, reported efficiency ratio 0.9926 to 1.0000	pass
interval_calibration	v2_ey0__shrunken_se_control	control	mean under no treatment in stratum V = 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8103 to 0.8501, SE ratio 0.6639 to 0.7182, empirical efficiency ratio 0.9712 to 1.0493, reported efficiency ratio 0.6947 to 0.6999	pass
interval_calibration	v2_ey1__correctly_specified	positive	mean under treatment in stratum V = 2: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9056 to 0.9344, SE ratio 0.9315 to 1.0094, empirical efficiency ratio 0.9753 to 1.0552, reported efficiency ratio 0.9742 to 0.9931	fail
interval_calibration	v2_ey1__noise_control	control	mean under treatment in stratum V = 2: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.7972 to 0.8382, SE ratio 0.6667 to 0.7212, empirical efficiency ratio 1.3655 to 1.4744, reported efficiency ratio 0.9744 to 0.9932	pass
interval_calibration	v2_ey1__shrunken_se_control	control	mean under treatment in stratum V = 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7955 to 0.8366, SE ratio 0.6517 to 0.7058, empirical efficiency ratio 0.9769 to 1.0558, reported efficiency ratio 0.6821 to 0.6954	pass
interval_calibration	v2_par__correctly_specified	positive	population attributable risk in stratum V = 2: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9356 to 0.9593, SE ratio 0.9525 to 1.0279, empirical efficiency ratio 0.9704 to 1.0476, reported efficiency ratio 0.9926 to 1.0026	pass
interval_calibration	v2_par__noise_control	control	population attributable risk in stratum V = 2: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8007 to 0.8413, SE ratio 0.6634 to 0.7141, empirical efficiency ratio 1.3974 to 1.5047, reported efficiency ratio 0.9926 to 1.0027	pass
interval_calibration	v2_par__shrunken_se_control	control	population attributable risk in stratum V = 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8085 to 0.8485, SE ratio 0.6668 to 0.7195, empirical efficiency ratio 0.9695 to 1.0471, reported efficiency ratio 0.6949 to 0.7018	pass
simultaneous_coverage	crossfit_strata__pointwise_joint_control	control	the three marginal and nine stratum parameters of the cross-fitted fit: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.5999 to 0.6512	pass
simultaneous_coverage	crossfit_strata__simultaneous_band	positive	the three marginal and nine stratum parameters of the cross-fitted fit: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9038 to 0.9329	fail
simultaneous_coverage	strata__pointwise_joint_control	control	the six marginal and eighteen stratum parameters of the in-sample fit: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.5688 to 0.6208	pass
simultaneous_coverage	strata__simultaneous_band	positive	the six marginal and eighteen stratum parameters of the in-sample fit: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.8881 to 0.9194	fail
stratum_targeting_necessity	v0_ate__marginal_fluctuation	control	average treatment effect in stratum V = 0: the same outcome regression with one marginal fluctuation per arm, averaged inside each stratum	bias interval must fall entirely outside the margin	bias -0.0371 to -0.0341, margin 0.0052	pass
stratum_targeting_necessity	v0_ate__stratified	positive	average treatment effect in stratum V = 0: the stratified fit with an outcome regression that omits the stratum, so the per-stratum score blocks do all the adjusting	bias interval inside the equivalence margin	bias -0.0023 to 0.0023, margin 0.0077	pass
stratum_targeting_necessity	v2_ate__marginal_fluctuation	control	average treatment effect in stratum V = 2: the same outcome regression with one marginal fluctuation per arm, averaged inside each stratum	bias interval must fall entirely outside the margin	bias 0.0758 to 0.0784, margin 0.0044	pass
stratum_targeting_necessity	v2_ate__stratified	positive	average treatment effect in stratum V = 2: the stratified fit with an outcome regression that omits the stratum, so the per-stratum score blocks do all the adjusting	bias interval inside the equivalence margin	bias -0.0021 to 0.0026, margin 0.0079	pass

Result

The study publishes under the reporting policy. The declared run had five red verdicts, and the red-cell ledger names strata-boundary-mean as their owner. Every other primary test, paired comparison and property cell passed.

verdict	result	reading
paired comparison with tmle3	9 of 9 equivalent	the stratum arm means and ATEs agree with tmle_stratified
primary truth test of ey[1][V=2], both implementations	red. Coverage 0.9170 for each, with the lower 99% endpoint below the 0.90 floor	the bias is inside its margin and the SE ratio is 0.985. The treated mean of stratum 2 is 0.9358. At n = 2,000 the stratum holds about 157 treated rows and about 9 expected non-events, so its Wald interval under-covers, and tmle3 shows the same coverage on the same draws
v2_ey1 calibration cell	red. Coverage 0.9208	the same mean, in the property sample
strata and crossfit_strata bands	red. Joint coverage 0.9046 and 0.9192	the declared diagnostic read the same rows at the design critical values, 2.846 and 2.778. That oracle band covers 0.9121 and 0.9258, so it also under-covers, and the multiplier is not the main cause. The package critical values average 2.816 and 2.750, which account for the 0.0075 and 0.0066 between the two coverages. Each band inherits the shortfall of the pointwise interval above
the other 17 calibration cells, three cross-fitted cells, and their controls	pass	every stratum parameter, ATT, ATC and PAR included, is calibrated at its efficiency bound
double robustness and stratum targeting	pass	the marginal-fluctuation control moves at least 1.1515 empirical SDs in each outer stratum, and the stratified fit stays inside its margin

The route is the finite-sample one. The default band stays on, because nothing in the band’s construction failed. The study module records the diagnostic, and tests/unit/test_band_shortfall_reading.py rebuilds every number of it from the committed rows. strata-boundary-mean owns the five red verdicts.

Refusals

refusal	pinning test
cv_evaluation=True or targeting_scheme="fold"	tests/unit/test_natural_course_crossfit.py::test_a_complete_outcome_fit_with_strata_meets_the_generic_strata_gate
an incremental stratum without a treatment arm, an MSM singular inside a stratum, or a DRTMLE stratum with no trainable rows	tests/unit/test_stratified_incremental_exact.py, tests/unit/test_stratified_msm_exact.py, tests/unit/test_refusals_before_the_nuisance_fit.py
the cross-fitted arm-indexed missing-outcome contract	tests/unit/test_stratified_refusals.py
a stratum parameter in an omitted-variable or missingness sensitivity analysis	tests/unit/test_stratified_targets.py

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
n	2000	observations per primary replication
independent_tests_total	18	primary tests against truth
independent_tests_passed	16	of those, passing
paired_tests_total	9	external comparisons declared
paired_tests_passed	9	external comparisons passing
property_cells_total	83	repeated-sampling property cells
property_cells_passed	80	cells whose own and family verdicts pass
max_standardized_bias	0.0626	largest absolute primary bias in empirical standard deviations
min_coverage	0.9170	lowest measured primary-study coverage
min_se_ratio_ci_lower	0.9160	lowest bootstrap primary SE-ratio endpoint
max_se_ratio_ci_upper	1.0844	highest bootstrap primary SE-ratio endpoint
properties[simultaneous_coverage/strata__simultaneous_band]:coverage	0.9046	joint coverage of the in-sample band over 24 parameters
properties[simultaneous_coverage/strata__simultaneous_band]:coverage_ci_upper	0.9194	its 99% upper endpoint
properties[simultaneous_coverage/strata__pointwise_joint_control]:coverage	0.5950	joint coverage of the pointwise intervals of the same fits
properties[simultaneous_coverage/crossfit_strata__simultaneous_band]:coverage	0.9192	joint coverage of the cross-fitted band over 12 parameters
properties[simultaneous_coverage/crossfit_strata__simultaneous_band]:coverage_ci_upper	0.9329	its 99% upper endpoint
properties[simultaneous_coverage/crossfit_strata__pointwise_joint_control]:coverage	0.6258	joint coverage of the cross-fitted pointwise intervals
properties[interval_calibration/v2_ey1__correctly_specified]:coverage	0.9208	coverage of the treated mean in the smallest stratum
properties[stratum_targeting_necessity/v0_ate__stratified]:targeting_displacement	1.1515	displacement of the marginal-fluctuation control, the less displaced outer stratum
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 and joint-coverage band, lower limit
margin:calibration_coverage_upper	0.9800	calibration and joint-coverage band, upper limit
margin:type_i_ceiling	0.1000	largest supported type-I rate. No cell of this study reads it
margin:paired_difference	0.1500	paired similarity margin, in pooled empirical standard deviations
margin:rmse_noninferiority	1.1000	largest external-comparison RMSE ratio bound
margin:coverage_noninferiority	-0.0250	smallest external-comparison coverage difference bound
margin:calibration_noninferiority	0.0500	largest external-comparison calibration excess bound
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. No cell of this study reads it
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
margin:union_model_se_lower	0.1000	union-model SE-ratio screen, lower limit
margin:union_model_se_upper	10	union-model SE-ratio screen, upper limit
margin:shrunken_se_factor	0.7000	factor the shrunken-SE control multiplies the standard error by
margin:efficiency_ratio_lower	0.9000	efficiency-ratio band, lower limit
margin:efficiency_ratio_upper	1.1000	efficiency-ratio band, upper limit
margin:targeting_displacement	0.2500	smallest displacement of the marginal-fluctuation control, in empirical SDs
bound:ate[V=0]_standard_error	0.0308	exact efficiency bound on the standard error of ate[V=0] at this n
bound:ate[V=1]_standard_error	0.0347	exact efficiency bound on the standard error of ate[V=1] at this n
bound:ate[V=2]_standard_error	0.0309	exact efficiency bound on the standard error of ate[V=2] at this n
bound:ey[0][V=0]_standard_error	0.0226	exact efficiency bound on the standard error of ey[0][V=0] at this n
bound:ey[0][V=1]_standard_error	0.0259	exact efficiency bound on the standard error of ey[0][V=1] at this n
bound:ey[0][V=2]_standard_error	0.0228	exact efficiency bound on the standard error of ey[0][V=2] at this n
bound:ey[1][V=0]_standard_error	0.0216	exact efficiency bound on the standard error of ey[1][V=0] at this n
bound:ey[1][V=1]_standard_error	0.0235	exact efficiency bound on the standard error of ey[1][V=1] at this n
bound:ey[1][V=2]_standard_error	0.0212	exact efficiency bound on the standard error of ey[1][V=2] at this n

Limitations

limitation	what it means for use
One law with three strata and a binary treatment and outcome	A continuous outcome, more strata, or a multi-arm treatment is not measured
Main-terms logistic learners only	A flexible learner is not covered
No weights, clusters, missing outcomes or repeats	Each composition with strata is a separate study
ATT, ATC and PAR have no comparator	They are measured against the exact truth only
The stratum-targeting control reads the outer strata	The middle stratum’s control could not fail. The exact-law test checks that stratum’s score block

Reproduction

The fixture README gives the regeneration command. The manifest records the seeds, margins, laws, source hashes, and result hashes.