Parametric g-formula#

This study validates ParametricGFormula (NICE), the parametric g-formula of Robins (1986). It simulates forward in time from node-specific main-terms models and averages the simulated outcome under each plan. The page Parametric g-formula states the estimator, its stacked interval, and the way it differs from gformula and pygformula.

The study draws from five exact laws, G1 to G5, and a sixth law, G4Q, for the report of a misspecified fit. Every law of the primary phase is the main-terms model that the estimator fits, so the estimator is correctly specified on it. Every truth is a sum over the branches of the law, with Gauss-Hermite nodes for a Gaussian variable, or a closed form. tests/studies/parametric_gformula_laws.py states each one. The study module tests/studies/canonical_parametric_gformula.py declares the laws, the plans and the reading rule before the run.

No canonical implementation is compared on the study laws. The pygformula package, version 1.2.0, cannot fit node-specific models. So it runs on four separate fixtures where both model classes are correct. All 63 coefficient rows and all 21 estimate rows of those fixtures pass. The fixtures test agreement of the point estimate only. They are not evidence for the interval.

What was compared#

setting	`cleverly`	`pygformula` 1.2.0
status	run and published on this page	run on the fixtures. The results are in `tests/canonical/parametric_gformula_study/pygformula-*.csv`
datasets	1,000 samples of 8,000 rows of each of five laws	one panel of 2,000 units for each of four fixtures, fitted by both packages
models	one main-terms `GLM` for each covariate, treatment, censoring and outcome node, in the full-history design	bare column names with a pooled residual SD over time, so only laws where pooled and node-specific models agree can pair
simulation	`n_draws = 10` histories for each unit, Philox streams keyed by scenario and replicate	`n_simul = n`, with at least 20 seeds for the Monte Carlo SE
intervals	stacked estimating equation with the chain rule and the simulation term, pointwise 95% Wald	none exists. The fixture gate compares the estimate against four combined Monte Carlo SE

The fixture runs use their own environment (tests/canonical/parametric_gformula_study/Dockerfile and requirements.txt), and never a package extra. The README of that directory lists the fixtures.

The study has two phases. The primary phase fits each law once for every replicate and reads the bias, the coverage and the SE ratio against the exact truth. The property phase reads calibration, the root-n ladder, the Monte Carlo accounting, and the necessity of the parametric g-formula against a main-terms ICE fit.

Accuracy against known truth#

law	estimand	what was tested	implementation	bias (99% interval)	coverage	SE ratio	result
law G1: three nodes, a binary covariate, censoring and a binary end-of-study outcome	`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` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.0014 to 0.0018	0.9580	0.9941	pass
law G1: three nodes, a binary covariate, censoring and a binary end-of-study outcome	`ey_regimen[odds x2]`	mean outcome under the plan multiply the treatment odds by two	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.000833 to 0.000317	0.9540	1.0030	pass
law G1: three nodes, a binary covariate, censoring and a binary end-of-study outcome	`ey_regimen[rule]`	mean outcome under the plan follow the covariate-dependent rule	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.000893 to 0.000307	0.9360	0.9596	pass
law G1: three nodes, a binary covariate, censoring and a binary end-of-study outcome	`ey_regimen[treat_all]`	mean outcome under the plan treat at each of the three times	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.000954 to 0.000519	0.9570	1.0256	pass
law G1: three nodes, a binary covariate, censoring and a binary end-of-study outcome	`ey_regimen[treat_none]`	mean outcome under the plan treat at none of the three times	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.0016 to 0.000803	0.9380	0.9614	pass
law G2: three nodes, a Gaussian then a binary covariate per node and a continuous outcome	`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` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.0144 to 0.0047	0.9470	0.9872	pass
law G2: three nodes, a Gaussian then a binary covariate per node and a continuous outcome	`ey_regimen[policy_b]`	mean outcome under the plan treat with probability 0.3 + 0.4 B_t at each of the three times	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.000406 to 0.0104	0.9460	0.9998	pass
law G2: three nodes, a Gaussian then a binary covariate per node and a continuous outcome	`ey_regimen[treat_all]`	mean outcome under the plan treat at each of the three times	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.0044 to 0.0098	0.9420	0.9912	pass
law G2: three nodes, a Gaussian then a binary covariate per node and a continuous outcome	`ey_regimen[treat_none]`	mean outcome under the plan treat at none of the three times	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.000333 to 0.0155	0.9510	0.9978	pass
law G3: four nodes, a binary covariate, censoring and two competing causes	`ate_regimen[treat_all_4 vs treat_none_4, relapse @ t=4]`	difference in cumulative incidence of relapse between the plans “treat at each of the four times” against “treat at none of the four times” at horizon t = 4	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.0013 to 0.0017	0.9520	1.0197	pass
law G3: four nodes, a binary covariate, censoring and two competing causes	`cif_regimen[treat_all_4, death @ t=4]`	cumulative incidence of death under the plan treat at each of the four times at horizon t = 4	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.000597 to 0.000555	0.9480	1.0118	pass
law G3: four nodes, a binary covariate, censoring and two competing causes	`cif_regimen[treat_all_4, relapse @ t=2]`	cumulative incidence of relapse under the plan treat at each of the four times at horizon t = 2	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.000410 to 0.000615	0.9460	1.0020	pass
law G3: four nodes, a binary covariate, censoring and two competing causes	`cif_regimen[treat_all_4, relapse @ t=4]`	cumulative incidence of relapse under the plan treat at each of the four times at horizon t = 4	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.000695 to 0.000793	0.9420	1.0033	pass
law G4: three nodes, a Gaussian covariate and a continuous dose per node, and a continuous outcome	`ate_regimen[shift_half vs natural course]`	difference in mean outcome between the plans “add 0.5 to the dose at each of the three times” against “leave the observed treatment mechanism unchanged”	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.000706 to 0.0015	0.9520	0.9908	pass
law G4: three nodes, a Gaussian covariate and a continuous dose per node, and a continuous outcome	`ey_regimen[dose_half]`	mean outcome under the plan assign the fixed dose 0.5 at each of the three times	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.0021 to 0.0012	0.9530	0.9929	pass
law G4: three nodes, a Gaussian covariate and a continuous dose per node, and a continuous outcome	`ey_regimen[rule_dose]`	mean outcome under the plan assign the dose 0.5 + 0.5 L_t at each of the three times	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.0032 to 0.0015	0.9500	0.9948	pass
law G4: three nodes, a Gaussian covariate and a continuous dose per node, and a continuous outcome	`ey_regimen[shift_half]`	mean outcome under the plan add 0.5 to the dose at each of the three times	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.0052 to 0.0019	0.9570	1.0089	pass
law G5: three nodes, a binary and a three-level categorical covariate, a binary treatment and a continuous outcome	`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` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.000804 to 0.0064	0.9450	0.9950	pass
law G5: three nodes, a binary and a three-level categorical covariate, a binary treatment and a continuous outcome	`ey_regimen[odds x2]`	mean outcome under the plan multiply the treatment odds by two	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.0033 to 0.0014	0.9470	0.9929	pass
law G5: three nodes, a binary and a three-level categorical covariate, a binary treatment and a continuous outcome	`ey_regimen[treat_all]`	mean outcome under the plan treat at each of the three times	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.0019 to 0.0024	0.9530	0.9903	pass
law G5: three nodes, a binary and a three-level categorical covariate, a binary treatment and a continuous outcome	`ey_regimen[treat_none]`	mean outcome under the plan treat at none of the three times	`cleverly` parametric g-formula (NICE), a forward simulation of node-specific GLMs	-0.0056 to 0.000534	0.9400	0.9600	pass

All 21 implementation-estimand tests pass. They read the four or five estimands of each law at n = 8,000. No primary replicate was lost to a fitting failure.

Theory properties#

property	cell	role	what was tested	what must hold	measured	result
`extrapolation_report`	`g4q_dose__main_terms`	diagnostic	parametric g-formula with main-terms models: law G4Q, mean under the fixed dose 0.5, where the outcome carries a quadratic dose term: a main-terms model of a law with a quadratic dose term, fitted and extrapolated to a fixed dose	reported only	bias 1.4840 to 1.4970, coverage 0 to 0.0053, SE ratio 0.9796	reported
`ice_necessity`	`pair_g2_contrast__ice`	control	parametric g-formula against main-terms ICE: law G2, treatment at all three times against none: the main-terms ICE fit on the same draws	bias outside the margin, and displaced from the parametric g-formula by the declared threshold	bias 0.0258 to 0.0374, margin 0.0195, coverage 0.9088 to 0.9476, SE ratio 1.0181	pass
`ice_necessity`	`pair_g2_contrast__nice`	positive	parametric g-formula against main-terms ICE: law G2, treatment at all three times against none: the parametric g-formula with main-terms models	bias inside the margin	bias -0.0039 to 0.0045, margin 0.0141, coverage 0.9402 to 0.9711, SE ratio 1.0243	pass
`ice_necessity`	`pair_g2_treat_all__ice`	control	parametric g-formula against main-terms ICE: law G2, mean under treatment at all three times: the main-terms ICE fit on the same draws	bias outside the margin, and displaced from the parametric g-formula by the declared threshold	bias 0.0706 to 0.0779, margin 0.0123, coverage 0.6204 to 0.6917, SE ratio 0.9885	pass
`ice_necessity`	`pair_g2_treat_all__nice`	positive	parametric g-formula against main-terms ICE: law G2, mean under treatment at all three times: the parametric g-formula with main-terms models	bias inside the margin	bias -0.0038 to 0.0026, margin 0.0107, coverage 0.9421 to 0.9725, SE ratio 1.0026	pass
`ice_necessity`	`pair_g2_treat_none__ice`	control	parametric g-formula against main-terms ICE: law G2, mean under no treatment: the main-terms ICE fit on the same draws	bias outside the margin, and displaced from the parametric g-formula by the declared threshold	bias 0.0373 to 0.0481, margin 0.0182, coverage 0.8830 to 0.9271, SE ratio 1.0133	pass
`ice_necessity`	`pair_g2_treat_none__nice`	positive	parametric g-formula against main-terms ICE: law G2, mean under no treatment: the parametric g-formula with main-terms models	bias inside the margin	bias -0.0045 to 0.0028, margin 0.0123, coverage 0.9306 to 0.9641, SE ratio 0.9852	pass
`ice_reported`	`pair_g1_contrast__ice`	diagnostic	parametric g-formula against main-terms ICE: law G1, treatment at all three times against none: the main-terms ICE fit on the same draws	reported only	bias 0.000863 to 0.0093, coverage 0.9124 to 0.9505, SE ratio 0.9619	reported
`ice_reported`	`pair_g1_contrast__nice`	diagnostic	parametric g-formula against main-terms ICE: law G1, treatment at all three times against none: the parametric g-formula with main-terms models	reported only	bias -0.0012 to 0.0048, coverage 0.9162 to 0.9534, SE ratio 0.9711	reported
`ice_reported`	`pair_g1_treat_all__ice`	diagnostic	parametric g-formula against main-terms ICE: law G1, mean under treatment at all three times: the main-terms ICE fit on the same draws	reported only	bias -0.000408 to 0.0029, coverage 0.9238 to 0.9591, SE ratio 0.9553	reported
`ice_reported`	`pair_g1_treat_all__nice`	diagnostic	parametric g-formula against main-terms ICE: law G1, mean under treatment at all three times: the parametric g-formula with main-terms models	reported only	bias -0.0010 to 0.0018, coverage 0.9228 to 0.9584, SE ratio 0.9701	reported
`ice_reported`	`pair_g1_treat_none__ice`	diagnostic	parametric g-formula against main-terms ICE: law G1, mean under no treatment: the main-terms ICE fit on the same draws	reported only	bias -0.0078 to 0.000093, coverage 0.9031 to 0.9432, SE ratio 0.9591	reported
`ice_reported`	`pair_g1_treat_none__nice`	diagnostic	parametric g-formula against main-terms ICE: law G1, mean under no treatment: the parametric g-formula with main-terms models	reported only	bias -0.0035 to 0.000751, coverage 0.9200 to 0.9562, SE ratio 0.9856	reported
`interval_calibration`	`nice_g1_contrast__correctly_specified`	positive	parametric g-formula: law G1, treatment at all three times against none: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9264 to 0.9518, SE ratio 0.9451 to 1.0165	pass
`interval_calibration`	`nice_g1_contrast__noise_control`	control	parametric g-formula: law G1, 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 0.8146 to 0.8540, SE ratio 0.6861 to 0.7379	pass
`interval_calibration`	`nice_g1_contrast__shrunken_se_control`	control	parametric g-formula: law G1, 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 0.7981 to 0.8390, SE ratio 0.6605 to 0.7115	pass
`interval_calibration`	`nice_g1_odds_x2__correctly_specified`	positive	parametric g-formula: law G1, mean under the odds tilt of two: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9319 to 0.9563, SE ratio 0.9347 to 1.0127	pass
`interval_calibration`	`nice_g1_odds_x2__noise_control`	control	parametric g-formula: law G1, mean under the odds tilt of two: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8172 to 0.8564, SE ratio 0.6831 to 0.7368	pass
`interval_calibration`	`nice_g1_odds_x2__shrunken_se_control`	control	parametric g-formula: law G1, mean under the odds tilt of two: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7998 to 0.8406, SE ratio 0.6548 to 0.7071	pass
`interval_calibration`	`nice_g1_rule__correctly_specified`	positive	parametric g-formula: law G1, mean under the rule A_t = L_t: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9328 to 0.9570, SE ratio 0.9567 to 1.0320	pass
`interval_calibration`	`nice_g1_rule__noise_control`	control	parametric g-formula: law G1, mean under the rule A_t = L_t: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8090 to 0.8489, SE ratio 0.6738 to 0.7249	pass
`interval_calibration`	`nice_g1_rule__shrunken_se_control`	control	parametric g-formula: law G1, mean under the rule A_t = L_t: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8059 to 0.8461, SE ratio 0.6699 to 0.7217	pass
`interval_calibration`	`nice_g1_treat_all__correctly_specified`	positive	parametric g-formula: law G1, mean under treatment at all three times: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9278 to 0.9529, SE ratio 0.9259 to 1.0000	fail
`interval_calibration`	`nice_g1_treat_all__noise_control`	control	parametric g-formula: law G1, 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 0.8203 to 0.8592, SE ratio 0.6762 to 0.7292	pass
`interval_calibration`	`nice_g1_treat_all__shrunken_se_control`	control	parametric g-formula: law G1, 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 0.7959 to 0.8370, SE ratio 0.6482 to 0.6991	pass
`interval_calibration`	`nice_g1_treat_none__correctly_specified`	positive	parametric g-formula: law G1, mean under no treatment: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9305 to 0.9552, SE ratio 0.9554 to 1.0311	pass
`interval_calibration`	`nice_g1_treat_none__noise_control`	control	parametric g-formula: law G1, 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 0.8164 to 0.8556, SE ratio 0.6671 to 0.7205	pass
`interval_calibration`	`nice_g1_treat_none__shrunken_se_control`	control	parametric g-formula: law G1, 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 0.8007 to 0.8413, SE ratio 0.6700 to 0.7218	pass
`interval_calibration`	`nice_g2_contrast__correctly_specified`	positive	parametric g-formula: law G2, treatment at all three times against none: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9351 to 0.9589, SE ratio 0.9651 to 1.0384	pass
`interval_calibration`	`nice_g2_contrast__noise_control`	control	parametric g-formula: law G2, 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 0.8159 to 0.8552, SE ratio 0.6829 to 0.7356	pass
`interval_calibration`	`nice_g2_contrast__shrunken_se_control`	control	parametric g-formula: law G2, 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 0.8150 to 0.8544, SE ratio 0.6747 to 0.7275	pass
`interval_calibration`	`nice_g2_policy_b__correctly_specified`	positive	parametric g-formula: law G2, mean under the known policy that treats with probability 0.3 + 0.4 B_t: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9319 to 0.9563, SE ratio 0.9503 to 1.0258	pass
`interval_calibration`	`nice_g2_policy_b__noise_control`	control	parametric g-formula: law G2, mean under the known policy that treats with probability 0.3 + 0.4 B_t: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8185 to 0.8576, SE ratio 0.6915 to 0.7445	pass
`interval_calibration`	`nice_g2_policy_b__shrunken_se_control`	control	parametric g-formula: law G2, mean under the known policy that treats with probability 0.3 + 0.4 B_t: 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 0.6654 to 0.7189	pass
`interval_calibration`	`nice_g2_treat_all__correctly_specified`	positive	parametric g-formula: law G2, mean under treatment at all three times: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9365 to 0.9600, SE ratio 0.9622 to 1.0434	pass
`interval_calibration`	`nice_g2_treat_all__noise_control`	control	parametric g-formula: law G2, 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 0.8238 to 0.8623, SE ratio 0.6922 to 0.7500	pass
`interval_calibration`	`nice_g2_treat_all__shrunken_se_control`	control	parametric g-formula: law G2, 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 0.8120 to 0.8517, SE ratio 0.6743 to 0.7303	pass
`interval_calibration`	`nice_g2_treat_none__correctly_specified`	positive	parametric g-formula: law G2, mean under no treatment: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9383 to 0.9615, SE ratio 0.9497 to 1.0237	pass
`interval_calibration`	`nice_g2_treat_none__noise_control`	control	parametric g-formula: law G2, 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 0.8029 to 0.8433, SE ratio 0.6618 to 0.7131	pass
`interval_calibration`	`nice_g2_treat_none__shrunken_se_control`	control	parametric g-formula: law G2, 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 0.8037 to 0.8441, SE ratio 0.6665 to 0.7172	pass
`interval_calibration`	`nice_g3_contrast_h4__correctly_specified`	positive	parametric g-formula: law G3, relapse incidence by t = 4, treatment at all four times against none: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9337 to 0.9578, SE ratio 0.9743 to 1.0479	pass
`interval_calibration`	`nice_g3_contrast_h4__noise_control`	control	parametric g-formula: law G3, relapse incidence by t = 4, treatment at all four 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 0.8037 to 0.8441, SE ratio 0.6713 to 0.7230	pass
`interval_calibration`	`nice_g3_contrast_h4__shrunken_se_control`	control	parametric g-formula: law G3, relapse incidence by t = 4, treatment at all four 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 0.8116 to 0.8513, SE ratio 0.6816 to 0.7328	pass
`interval_calibration`	`nice_g3_death_h4__correctly_specified`	positive	parametric g-formula: law G3, death incidence by t = 4 under treatment at all four times: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9374 to 0.9608, SE ratio 0.9533 to 1.0291	pass
`interval_calibration`	`nice_g3_death_h4__noise_control`	control	parametric g-formula: law G3, death incidence by t = 4 under treatment at all four times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.7968 to 0.8378, SE ratio 0.6643 to 0.7143	pass
`interval_calibration`	`nice_g3_death_h4__shrunken_se_control`	control	parametric g-formula: law G3, death incidence by t = 4 under treatment at all four times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7990 to 0.8398, SE ratio 0.6676 to 0.7202	pass
`interval_calibration`	`nice_g3_relapse_h2__correctly_specified`	positive	parametric g-formula: law G3, relapse incidence by t = 2 under treatment at all four times: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9369 to 0.9604, SE ratio 0.9691 to 1.0409	pass
`interval_calibration`	`nice_g3_relapse_h2__noise_control`	control	parametric g-formula: law G3, relapse incidence by t = 2 under treatment at all four times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8055 to 0.8457, SE ratio 0.6721 to 0.7251	pass
`interval_calibration`	`nice_g3_relapse_h2__shrunken_se_control`	control	parametric g-formula: law G3, relapse incidence by t = 2 under treatment at all four times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8024 to 0.8429, SE ratio 0.6787 to 0.7284	pass
`interval_calibration`	`nice_g3_relapse_h4__correctly_specified`	positive	parametric g-formula: law G3, relapse incidence by t = 4 under treatment at all four times: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9416 to 0.9641, SE ratio 0.9886 to 1.0647	pass
`interval_calibration`	`nice_g3_relapse_h4__noise_control`	control	parametric g-formula: law G3, relapse incidence by t = 4 under treatment at all four times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8216 to 0.8604, SE ratio 0.6802 to 0.7332	pass
`interval_calibration`	`nice_g3_relapse_h4__shrunken_se_control`	control	parametric g-formula: law G3, relapse incidence by t = 4 under treatment at all four times: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8116 to 0.8513, SE ratio 0.6912 to 0.7455	pass
`interval_calibration`	`nice_g4_contrast__correctly_specified`	positive	parametric g-formula: law G4, the raised dose against the natural course: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9333 to 0.9574, SE ratio 0.9735 to 1.0501	pass
`interval_calibration`	`nice_g4_contrast__noise_control`	control	parametric g-formula: law G4, the raised 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 0.8177 to 0.8568, SE ratio 0.6897 to 0.7445	pass
`interval_calibration`	`nice_g4_contrast__shrunken_se_control`	control	parametric g-formula: law G4, the raised 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 0.8098 to 0.8497, SE ratio 0.6813 to 0.7361	pass
`interval_calibration`	`nice_g4_dose__correctly_specified`	positive	parametric g-formula: law G4, mean under the fixed dose 0.5 at each of the three times: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9333 to 0.9574, SE ratio 0.9655 to 1.0425	pass
`interval_calibration`	`nice_g4_dose__noise_control`	control	parametric g-formula: law G4, mean under the fixed dose 0.5 at each of the three times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8142 to 0.8536, SE ratio 0.6785 to 0.7343	pass
`interval_calibration`	`nice_g4_dose__shrunken_se_control`	control	parametric g-formula: law G4, mean under the fixed dose 0.5 at each of the 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 0.8103 to 0.8501, SE ratio 0.6762 to 0.7292	pass
`interval_calibration`	`nice_g4_rule_dose__correctly_specified`	positive	parametric g-formula: law G4, mean under the dose 0.5 + 0.5 L_t set by a rule at each time: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9342 to 0.9582, SE ratio 0.9622 to 1.0378	pass
`interval_calibration`	`nice_g4_rule_dose__noise_control`	control	parametric g-formula: law G4, mean under the dose 0.5 + 0.5 L_t set by a rule at each time: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8120 to 0.8517, SE ratio 0.6915 to 0.7433	pass
`interval_calibration`	`nice_g4_rule_dose__shrunken_se_control`	control	parametric g-formula: law G4, mean under the dose 0.5 + 0.5 L_t set by a rule at each time: 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 0.6730 to 0.7262	pass
`interval_calibration`	`nice_g4_shift__correctly_specified`	positive	parametric g-formula: law G4, mean under a dose raised by 0.5 at each of the three times: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9379 to 0.9611, SE ratio 0.9719 to 1.0468	pass
`interval_calibration`	`nice_g4_shift__noise_control`	control	parametric g-formula: law G4, mean under a dose raised by 0.5 at each of the three times: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8116 to 0.8513, SE ratio 0.6706 to 0.7224	pass
`interval_calibration`	`nice_g4_shift__shrunken_se_control`	control	parametric g-formula: law G4, mean under a dose raised by 0.5 at each of the 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 0.8085 to 0.8485, SE ratio 0.6812 to 0.7331	pass
`interval_calibration`	`nice_g5_contrast__correctly_specified`	positive	parametric g-formula: law G5, treatment at all three times against none: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9393 to 0.9622, SE ratio 0.9760 to 1.0523	pass
`interval_calibration`	`nice_g5_contrast__noise_control`	control	parametric g-formula: law G5, 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 0.8281 to 0.8663, SE ratio 0.7054 to 0.7608	pass
`interval_calibration`	`nice_g5_contrast__shrunken_se_control`	control	parametric g-formula: law G5, 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 0.8177 to 0.8568, SE ratio 0.6833 to 0.7363	pass
`interval_calibration`	`nice_g5_odds_x2__correctly_specified`	positive	parametric g-formula: law G5, mean under the odds tilt of two: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9346 to 0.9585, SE ratio 0.9651 to 1.0402	pass
`interval_calibration`	`nice_g5_odds_x2__noise_control`	control	parametric g-formula: law G5, mean under the odds tilt of two: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8068 to 0.8469, SE ratio 0.6822 to 0.7333	pass
`interval_calibration`	`nice_g5_odds_x2__shrunken_se_control`	control	parametric g-formula: law G5, mean under the odds tilt of two: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8150 to 0.8544, SE ratio 0.6764 to 0.7279	pass
`interval_calibration`	`nice_g5_treat_all__correctly_specified`	positive	parametric g-formula: law G5, mean under treatment at all three times: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9388 to 0.9619, SE ratio 0.9780 to 1.0537	pass
`interval_calibration`	`nice_g5_treat_all__noise_control`	control	parametric g-formula: law G5, 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 0.8242 to 0.8627, SE ratio 0.6927 to 0.7457	pass
`interval_calibration`	`nice_g5_treat_all__shrunken_se_control`	control	parametric g-formula: law G5, 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 0.8164 to 0.8556, SE ratio 0.6845 to 0.7395	pass
`interval_calibration`	`nice_g5_treat_none__correctly_specified`	positive	parametric g-formula: law G5, mean under no treatment: all three required nuisance functions are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9328 to 0.9570, SE ratio 0.9638 to 1.0379	pass
`interval_calibration`	`nice_g5_treat_none__noise_control`	control	parametric g-formula: law G5, 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 0.8242 to 0.8627, SE ratio 0.6994 to 0.7521	pass
`interval_calibration`	`nice_g5_treat_none__shrunken_se_control`	control	parametric g-formula: law G5, 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 0.8050 to 0.8453, SE ratio 0.6747 to 0.7261	pass
`monte_carlo_accounting`	`nice_g2_treat_all__mc_removed`	diagnostic	parametric g-formula: law G2, mean under treatment at all three times: the estimate of the one-history fit, with the standard error of an independent fit of 500 histories per unit, so the simulation term is absent from the curve	reported only: the SE-ratio interval, with no verdict	SE ratio 0.8658 to 0.9309	reported
`monte_carlo_accounting`	`nice_g2_treat_all__n_draws_1`	positive	parametric g-formula: law G2, mean under treatment at all three times: one simulated history per unit behind the estimate	bias inside the margin, SE-ratio and coverage intervals inside their calibration bands	SE ratio 0.9688 to 1.0415	pass
`monte_carlo_accounting`	`nice_g2_treat_none__mc_removed`	diagnostic	parametric g-formula: law G2, mean under no treatment: the estimate of the one-history fit, with the standard error of an independent fit of 500 histories per unit, so the simulation term is absent from the curve	reported only: the SE-ratio interval, with no verdict	SE ratio 0.8764 to 0.9448	reported
`monte_carlo_accounting`	`nice_g2_treat_none__n_draws_1`	positive	parametric g-formula: law G2, mean under no treatment: one simulated history per unit behind the estimate	bias inside the margin, SE-ratio and coverage intervals inside their calibration bands	SE ratio 0.9585 to 1.0332	pass
`monte_carlo_accounting`	`nice_g4_dose__mc_removed`	diagnostic	parametric g-formula: law G4, mean under the fixed dose 0.5 at each of the three times: the estimate of the one-history fit, with the standard error of an independent fit of 500 histories per unit, so the simulation term is absent from the curve	reported only: the SE-ratio interval, with no verdict	SE ratio 0.9292 to 1.0026	reported
`monte_carlo_accounting`	`nice_g4_dose__n_draws_1`	positive	parametric g-formula: law G4, mean under the fixed dose 0.5 at each of the three times: one simulated history per unit behind the estimate	bias inside the margin, SE-ratio and coverage intervals inside their calibration bands	SE ratio 0.9730 to 1.0492	pass
`monte_carlo_accounting`	`nice_g4_shift__mc_removed`	diagnostic	parametric g-formula: law G4, mean under a dose raised by 0.5 at each of the three times: the estimate of the one-history fit, with the standard error of an independent fit of 500 histories per unit, so the simulation term is absent from the curve	reported only: the SE-ratio interval, with no verdict	SE ratio 0.9116 to 0.9797	reported
`monte_carlo_accounting`	`nice_g4_shift__n_draws_1`	positive	parametric g-formula: law G4, mean under a dose raised by 0.5 at each of the three times: one simulated history per unit behind the estimate	bias inside the margin, SE-ratio and coverage intervals inside their calibration bands	SE ratio 0.9738 to 1.0470	pass
`monte_carlo_accounting`	`nice_g5_odds_x2__n_draws_1`	positive	parametric g-formula: law G5, mean under the odds tilt of two: one simulated history per unit behind the estimate	bias inside the margin, SE-ratio and coverage intervals inside their calibration bands	SE ratio 0.9488 to 1.0214	pass
`monte_carlo_accounting`	`nice_g5_treat_all__n_draws_1`	positive	parametric g-formula: law G5, mean under treatment at all three times: one simulated history per unit behind the estimate	bias inside the margin, SE-ratio and coverage intervals inside their calibration bands	SE ratio 0.9492 to 1.0237	pass
`monte_carlo_accounting`	`nice_g5_treat_none__n_draws_1`	positive	parametric g-formula: law G5, mean under no treatment: one simulated history per unit behind the estimate	bias inside the margin, SE-ratio and coverage intervals inside their calibration bands	SE ratio 0.9649 to 1.0401	pass
`root_n_and_efficiency`	`nice_g1_contrast__n_2000`	positive	parametric g-formula: law G1, 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 -0.0014, coverage 0.9342 to 0.9694, SE ratio 1.0207	pass
`root_n_and_efficiency`	`nice_g1_contrast__n_4000`	positive	parametric g-formula: law G1, 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 0.000402, coverage 0.9249 to 0.9627, SE ratio 0.9860	pass
`root_n_and_efficiency`	`nice_g1_contrast__n_8000`	positive	parametric g-formula: law G1, 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 0.000653, coverage 0.9283 to 0.9652, SE ratio 1.0058	pass
`root_n_and_efficiency`	`nice_g2_contrast__n_2000`	positive	parametric g-formula: law G2, 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 -0.0075, coverage 0.9249 to 0.9627, SE ratio 0.9824	pass
`root_n_and_efficiency`	`nice_g2_contrast__n_4000`	positive	parametric g-formula: law G2, 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 -0.0016, coverage 0.9295 to 0.9661, SE ratio 1.0042	pass
`root_n_and_efficiency`	`nice_g2_contrast__n_8000`	positive	parametric g-formula: law G2, 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 -0.0044, coverage 0.9400 to 0.9734, SE ratio 1.0320	pass
`root_n_and_efficiency`	`nice_g3_contrast_h4__n_2000`	positive	parametric g-formula: law G3, relapse incidence by t = 4, treatment at all four 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 -0.000326, coverage 0.9307 to 0.9669, SE ratio 0.9928	pass
`root_n_and_efficiency`	`nice_g3_contrast_h4__n_4000`	positive	parametric g-formula: law G3, relapse incidence by t = 4, treatment at all four 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 -0.000556, coverage 0.9249 to 0.9627, SE ratio 0.9944	pass
`root_n_and_efficiency`	`nice_g3_contrast_h4__n_8000`	positive	parametric g-formula: law G3, relapse incidence by t = 4, treatment at all four 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 -0.000263, coverage 0.9365 to 0.9710, SE ratio 0.9963	pass
`root_n_and_efficiency`	`nice_g4_contrast__n_2000`	positive	parametric g-formula: law G4, the raised dose against the natural course: bias, coverage and SE calibration at n = 2,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.0013, coverage 0.9318 to 0.9677, SE ratio 1.0097	pass
`root_n_and_efficiency`	`nice_g4_contrast__n_4000`	positive	parametric g-formula: law G4, the raised dose against the natural course: bias, coverage and SE calibration at n = 4,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias -0.000864, coverage 0.9283 to 0.9652, SE ratio 1.0130	pass
`root_n_and_efficiency`	`nice_g4_contrast__n_8000`	positive	parametric g-formula: law G4, the raised dose against the natural course: bias, coverage and SE calibration at n = 8,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias -0.000069, coverage 0.9295 to 0.9661, SE ratio 0.9952	pass
`root_n_rate`	`nice_g1_contrast__empirical_sd`	positive	parametric g-formula: law G1, 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 -0.5483 to -0.4295	pass
`root_n_rate`	`nice_g1_contrast__reported_se`	positive	parametric g-formula: law G1, 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 -0.5014 to -0.4966	pass
`root_n_rate`	`nice_g2_contrast__empirical_sd`	positive	parametric g-formula: law G2, 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 -0.5913 to -0.4772	pass
`root_n_rate`	`nice_g2_contrast__reported_se`	positive	parametric g-formula: law G2, 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 -0.5013 to -0.4980	pass
`root_n_rate`	`nice_g3_contrast_h4__empirical_sd`	positive	parametric g-formula: law G3, relapse incidence by t = 4, treatment at all four 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 -0.5625 to -0.4442	pass
`root_n_rate`	`nice_g3_contrast_h4__reported_se`	positive	parametric g-formula: law G3, relapse incidence by t = 4, treatment at all four 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 -0.5009 to -0.4970	pass
`root_n_rate`	`nice_g4_contrast__empirical_sd`	positive	parametric g-formula: law G4, the raised dose against the natural course: 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 -0.5489 to -0.4293	pass
`root_n_rate`	`nice_g4_contrast__reported_se`	positive	parametric g-formula: law G4, the raised dose against the natural course: the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5013 to -0.4978	pass
`shared_target`	`target_g1_contrast__ltmle`	diagnostic	parametric g-formula beside the targeted estimator: law G1, treatment at all three times against none: `LTMLE` with GLM nuisances on the same draws, which targets the same parameter	reported only	bias -0.0025 to 0.0067, coverage 0.9007 to 0.9414, SE ratio 0.9405	reported
`shared_target`	`target_g1_contrast__nice`	diagnostic	parametric g-formula beside the targeted estimator: law G1, treatment at all three times against none: the parametric g-formula with main-terms models	reported only	bias -0.0028 to 0.0031, coverage 0.9224 to 0.9582, SE ratio 0.9820	reported
`shared_target`	`target_g1_odds_x2__ipsi`	diagnostic	parametric g-formula beside the targeted estimator: law G1, mean under the odds tilt of two: `IPSI` with GLM nuisances on the same draws, which targets the same parameter	reported only	bias -0.0015 to 0.000614, coverage 0.9339 to 0.9667, SE ratio 1.0184	reported
`shared_target`	`target_g1_odds_x2__nice`	diagnostic	parametric g-formula beside the targeted estimator: law G1, mean under the odds tilt of two: the parametric g-formula with main-terms models	reported only	bias -0.0014 to 0.000733, coverage 0.9320 to 0.9653, SE ratio 1.0118	reported
`shared_target`	`target_g1_rule__ltmle`	diagnostic	parametric g-formula beside the targeted estimator: law G1, mean under the rule A_t = L_t: `LTMLE` with GLM nuisances on the same draws, which targets the same parameter	reported only	bias -0.0017 to 0.0025, coverage 0.9301 to 0.9639, SE ratio 0.9872	reported
`shared_target`	`target_g1_rule__nice`	diagnostic	parametric g-formula beside the targeted estimator: law G1, mean under the rule A_t = L_t: the parametric g-formula with main-terms models	reported only	bias -0.0014 to 0.000654, coverage 0.9398 to 0.9709, SE ratio 1.0166	reported
`shared_target`	`target_g1_treat_all__ltmle`	diagnostic	parametric g-formula beside the targeted estimator: law G1, mean under treatment at all three times: `LTMLE` with GLM nuisances on the same draws, which targets the same parameter	reported only	bias -0.0018 to 0.0015, coverage 0.9320 to 0.9653, SE ratio 1.0005	reported
`shared_target`	`target_g1_treat_all__nice`	diagnostic	parametric g-formula beside the targeted estimator: law G1, mean under treatment at all three times: the parametric g-formula with main-terms models	reported only	bias -0.0018 to 0.000915, coverage 0.9301 to 0.9639, SE ratio 1.0022	reported
`shared_target`	`target_g2_contrast__ltmle`	diagnostic	parametric g-formula beside the targeted estimator: law G2, treatment at all three times against none: `LTMLE` with GLM nuisances on the same draws, which targets the same parameter	reported only	bias -0.0298 to -0.0050, coverage 0.8866 to 0.9300, SE ratio 0.8754	reported
`shared_target`	`target_g2_contrast__nice`	diagnostic	parametric g-formula beside the targeted estimator: law G2, treatment at all three times against none: the parametric g-formula with main-terms models	reported only	bias -0.0066 to 0.0108, coverage 0.9220 to 0.9577, SE ratio 0.9908	reported
`shared_target`	`target_g2_treat_all__ltmle`	diagnostic	parametric g-formula beside the targeted estimator: law G2, mean under treatment at all three times: `LTMLE` with GLM nuisances on the same draws, which targets the same parameter	reported only	bias -0.0088 to 0.0066, coverage 0.9258 to 0.9606, SE ratio 0.9741	reported
`shared_target`	`target_g2_treat_all__nice`	diagnostic	parametric g-formula beside the targeted estimator: law G2, mean under treatment at all three times: the parametric g-formula with main-terms models	reported only	bias -0.0053 to 0.0080, coverage 0.9154 to 0.9527, SE ratio 0.9662	reported

The study has 119 property cells. Of these, 96 carry a verdict and 23 report a value only. 95 of the 96 pass, and one is red. properties.csv has 119 rows.

family	cells	what it reads	control that must fail
`interval_calibration`	21 labels at n = 2,000 and 2,400 replications on `G1` to `G5`	the SE ratio inside 0.93 to 1.07, the coverage inside 0.92 to 0.98, and the bias inside its margin	the standard error scaled by 0.7, and added noise of one pilot sampling SD
`root_n_and_efficiency`	four contrasts at n = 2,000, 4,000 and 8,000	the bias, the coverage floor, and the SE ratio screen	none. The next family reads the rate
`root_n_rate`	the empirical SD and the reported SE of the same four contrasts	the slope of each against n, in the band for a root-n rate	none. The slope interval must exclude -0.25
`monte_carlo_accounting`	seven cells at `n_draws = 1`, and four `mc_removed` cells	the interval that includes the simulation term passes the calibration rule	the `mc_removed` cells report the same estimate with the standard error of 500 histories, and carry no verdict
`ice_necessity`	three plans on `G2` at n = 32,000	the NICE bias inside its margin	the main-terms ICE fit on the same draws, which must leave the margin
`ice_reported`	the paired ICE and NICE fits on `G1`	none. The cells report	none
`shared_target`	`LTMLE` and `IPSI` beside NICE on `G1` and `G2`	none. The cells report	none
`extrapolation_report`	the main-terms fit of `G4Q` at a fixed dose	none. The cell reports a bias of 1.49	none

One red cell. The cell interval_calibration/nice_g1_treat_all__correctly_specified (n = 2,000, 2,400 replications) has an SE ratio of 0.9619. Its 99% interval, 0.9259 to 1.0000, leaves the band 0.93 to 1.07. Its coverage is 0.9413, with a 99% interval of 0.9278 to 0.9529 inside the band 0.92 to 0.98. Its bias is 0.000158 with a standard error of 0.000393.

The study declares the reading of a red cell before the run. A calibration cell reads finite-sample only when three conditions hold. Its 99% SE-ratio interval contains 1. Its coverage is consistent with 0.95. The diagnosis finds no defect.

The study expects 1.26 such reds over 114 gated cells, and the chance of at least one is 0.72. This cell meets the first two conditions. The witnesses below support the third.

witness	SE ratio	replications
the same law, plan and size in `shared_target/target_g1_treat_all__nice`	1.0022	1,192
the same law, plan and size in `ice_reported/pair_g1_treat_all__nice`	0.9701	1,198
the other `G1` calibration cells	0.972 to 0.993	2,400 each
the `G1` contrast ladder at n = 2,000, 4,000 and 8,000	1.021, 0.986 and 1.006	the ladder size

The independent draws of the same law, plan and size read 1.0022 and 0.9701. Every other G1 calibration cell passes, and the ladder reads close to one. No defect shows, so the cell reads as a finite-sample red. The roadmap owner X45-finite-sample holds it, and the red-cell ledger lists it.

Fitting failures. The property phase recorded ten fitting failures in property-failures.csv. Two of 1,200 replicates were lost in the paired G1 fit set, and eight of 1,200 in the shared G1 fit set. Each failure is a GLM with a singular information matrix. Both rates are under the declared bound of 0.01.

A rerun of paired_g1/293 and shared_g1/248 fits ParametricGFormula without error. The failing fit is the sequential outcome GLM of the comparator in the same fit set. The comparator is SequentialGComputation with method="ice" in the paired set and LTMLE in the shared set. These cells carry no verdict, so no gate reads the lost replicates. property-failure-accounting.csv has no rows.

Measured values#

quantity	value	source
`replicates`	1000	primary replications per scenario
`n`	8000	observations per primary replication
`independent_tests_total`	21	implementation-estimand tests against the truth
`independent_tests_passed`	21	of those, passing
`property_cells_total`	96	repeated-sampling property cells
`property_cells_passed`	95	cells whose own and family verdicts pass
`property_cells_reported`	23	cells that report a value and carry no verdict
`max_standardized_bias`	0.0782	largest absolute primary bias in empirical standard deviations
`min_coverage`	0.9360	lowest measured primary-study coverage
`min_se_ratio_ci_lower`	0.9088	lowest bootstrap primary SE-ratio endpoint
`max_se_ratio_ci_upper`	1.0865	highest bootstrap primary SE-ratio endpoint
`subject_failures`	0	primary replicates of `cleverly` lost to a recorded fitting failure
`margin:subject_failure_bound`	0.0100	share of replicates one primary cell may lose
`margin:subject_failures_allowed`	10	replicates one primary cell may lose
`margin:alpha`	0.0500	nominal size of the reported intervals, and the family level of the rule
`margin:bootstrap_replicates`	10000	resamples behind every bootstrap interval
`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:calibration_noninferiority`	0.0500	largest external-comparison calibration excess bound
`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:confidence_level`	0.9900	confidence level of every Monte Carlo interval
`margin:coverage_floor`	0.9000	validity floor the coverage lower endpoint must clear
`margin:coverage_noninferiority`	-0.0250	smallest external-comparison coverage difference bound
`margin:excluded_slope`	-0.2500	slower rate a root-n interval must exclude
`margin:minimum_power`	0.8000	rejection lower bound a power cell must clear
`margin:nominal_coverage`	0.9500	nominal coverage those intervals claim
`margin:over_coverage_ceiling`	0.9900	above this, coverage is conservative rather than invalid
`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: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:se_ratio_sanity_lower`	0.8000	SE-ratio screen, lower limit
`margin:se_ratio_sanity_upper`	1.2000	SE-ratio screen, upper limit
`margin:shrunken_se_factor`	0.7000	negative-control SE multiplier
`margin:standardized_bias`	0.2500	bias equivalence margin, in empirical standard deviations
`margin:type_i_ceiling`	0.1000	the rate a positive cell must bound and a control must exceed

Limitations#

limit	what it means for use
no comparator on the study laws	`pygformula` runs on four fixtures, not on the study laws. The fixtures compare coefficients and point estimates, not intervals
correctly specified laws	every law but `G4Q` is the main-terms model that the estimator fits. The study does not show coverage under misspecification. The `G4Q` cell reports a bias of 1.49
one red cell	the `G1` treat-all calibration cell reads as finite-sample under a declared reading. A repeat run under a fresh declaration would test the reading
GLM learners only	the estimator ships with `GLM` models. A flexible learner is outside the evidence
node-specific models	`pygformula` pools residual SD over time, so its fixtures use laws where pooled and node-specific models agree. The fixtures do not cover node-specific laws
no published variance	no published analytic variance exists for the simulation form. The interval is a natural extension, and its calibration here is the evidence for it
lost replicates	ten property replicates were lost to comparator fits. They carry no verdict, so no gate reads them

Reproduction#

The manifest records the seeds, the margins, the estimator configuration, the source hashes and the result hashes. It records no comparator. Run python -m tests.canonical.parametric_gformula_study.regenerate to regenerate the artifacts. Run python -m tests.canonical.parametric_gformula_study.compare_pygformula to repeat the pygformula fixtures. That command needs Docker. The replications and the property results carry every published row.