Sequentially doubly robust estimation

This study validates SDR, the sequentially doubly robust estimator of Díaz, Williams, Hoffman and Schenck (2023), Equation (4) and Section 5.3. The sequentially doubly robust estimator section states the estimator, its conditions and its exact-law evidence.

The study pairs each fit with pinned lmtp 1.5.4: cf_sdr and theta_dr(is_sdr = TRUE). Both sides read the same shifted values, per-node ratios and fold assignment. The study writes them beside each replicate, so lmtp fits no ratio.

What was compared

scenario	law and plans	pairing
sdr_end_of_study	the censored two-node law; never, always and a dynamic plan	one fold
sdr_end_of_study_crossfit	the same law and plans at five folds	five folds, identical fold assignment
sdr_survival	the two-node survival law; the same three plans at horizons 1 and 2	one fold
sdr_mtp	a truncated-normal dose at both nodes; up, scale at 2 and up then history	one fold, exact
sdr_policy	a categorical treatment under three known stochastic policies, through four copies of each unit	one fold; mix is exact

setting	cleverly	R lmtp
datasets	1,000 samples of 2,000 rows per scenario	the identical rows
per-node ratio	the generating mechanism, and the oracle binned density of the longitudinal modified-treatment-policy study at a continuous node	the same ratio array, read from the replicate data
node regressions	a quasibinomial GLM at the last node and least squares at the earlier node, unclipped	SL.glm on the same columns
cross-fitting	the training-fold recursion: fold \(k\) fits every regression on its training rows	cf_sdr on the same folds
intervals	pointwise 95% Wald from the influence curve	the same, from lmtp’s influence curve

At five folds the two constructions differ. This package composes each fold’s transforms from that fold’s own regressions. lmtp stitches each row’s later transform from the fold that holds the row out. The pairing gates (gates.csv) therefore hold each scenario to one of two rules. The sdr_mtp rows and ey_regimen[mix] are exact pairs, and their largest estimate gap is 3.2e-12. Every other row is a margins pair. All 180 gate rows pass.

Accuracy against known truth

law	estimand	what was tested	implementation	bias (99% interval)	coverage	SE ratio	result
two-node law with monotone censoring, three plans, one fold	ate_regimen[always vs never]	difference in mean outcome between the plans “treat at both times” against “treat at neither time”	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0014 to 0.0038	0.9460	0.9826	pass
two-node law with monotone censoring, three plans, one fold	ate_regimen[always vs never]	difference in mean outcome between the plans “treat at both times” against “treat at neither time”	R lmtp	-0.0016 to 0.0036	0.9470	0.9872	pass
two-node law with monotone censoring, three plans, one fold	ate_regimen[treat then continue if l2 positive vs never]	difference in mean outcome between the plans “treat, then continue only if L2 is positive” against “treat at neither time”	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.000346 to 0.0049	0.9420	0.9981	pass
two-node law with monotone censoring, three plans, one fold	ate_regimen[treat then continue if l2 positive vs never]	difference in mean outcome between the plans “treat, then continue only if L2 is positive” against “treat at neither time”	R lmtp	-0.000724 to 0.0045	0.9510	1.0046	pass
two-node law with monotone censoring, three plans, one fold	ey_regimen[always]	mean outcome under the plan treat at both times	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.000780 to 0.0023	0.9410	1.0122	pass
two-node law with monotone censoring, three plans, one fold	ey_regimen[always]	mean outcome under the plan treat at both times	R lmtp	-0.000814 to 0.0022	0.9450	1.0155	pass
two-node law with monotone censoring, three plans, one fold	ey_regimen[never]	mean outcome under the plan treat at neither time	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0025 to 0.0016	0.9510	0.9909	pass
two-node law with monotone censoring, three plans, one fold	ey_regimen[never]	mean outcome under the plan treat at neither time	R lmtp	-0.0024 to 0.0017	0.9570	0.9973	pass
two-node law with monotone censoring, three plans, one fold	ey_regimen[treat then continue if l2 positive]	mean outcome under the plan treat, then continue only if L2 is positive	cleverly sequentially doubly robust (SDR) longitudinal estimator	0.000113 to 0.0035	0.9410	0.9723	pass
two-node law with monotone censoring, three plans, one fold	ey_regimen[treat then continue if l2 positive]	mean outcome under the plan treat, then continue only if L2 is positive	R lmtp	-0.000117 to 0.0032	0.9450	0.9795	pass
the same law and plans, five folds	ate_regimen[always vs never]	difference in mean outcome between the plans “treat at both times” against “treat at neither time”	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0036 to 0.0017	0.9410	0.9603	pass
the same law and plans, five folds	ate_regimen[always vs never]	difference in mean outcome between the plans “treat at both times” against “treat at neither time”	R lmtp	-0.0034 to 0.0019	0.9400	0.9655	pass
the same law and plans, five folds	ate_regimen[treat then continue if l2 positive vs never]	difference in mean outcome between the plans “treat, then continue only if L2 is positive” against “treat at neither time”	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0035 to 0.0020	0.9410	0.9616	pass
the same law and plans, five folds	ate_regimen[treat then continue if l2 positive vs never]	difference in mean outcome between the plans “treat, then continue only if L2 is positive” against “treat at neither time”	R lmtp	-0.0034 to 0.0021	0.9460	0.9681	pass
the same law and plans, five folds	ey_regimen[always]	mean outcome under the plan treat at both times	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0016 to 0.0017	0.9370	0.9435	pass
the same law and plans, five folds	ey_regimen[always]	mean outcome under the plan treat at both times	R lmtp	-0.0015 to 0.0019	0.9360	0.9384	pass
the same law and plans, five folds	ey_regimen[never]	mean outcome under the plan treat at neither time	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0012 to 0.0031	0.9390	0.9659	pass
the same law and plans, five folds	ey_regimen[never]	mean outcome under the plan treat at neither time	R lmtp	-0.0012 to 0.0031	0.9410	0.9691	pass
the same law and plans, five folds	ey_regimen[treat then continue if l2 positive]	mean outcome under the plan treat, then continue only if L2 is positive	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0014 to 0.0019	0.9500	0.9950	pass
the same law and plans, five folds	ey_regimen[treat then continue if l2 positive]	mean outcome under the plan treat, then continue only if L2 is positive	R lmtp	-0.0014 to 0.0020	0.9480	0.9922	pass
two-node law with a truncated-normal dose at both nodes and four plans	ate_regimen[scale at 2 vs natural]	difference in mean outcome between the plans “multiply the second dose by 1.25, capped at 5.5” against “leave the observed dose unchanged at both times”	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.000357 to 0.0012	0.9520	1.0253	pass
two-node law with a truncated-normal dose at both nodes and four plans	ate_regimen[scale at 2 vs natural]	difference in mean outcome between the plans “multiply the second dose by 1.25, capped at 5.5” against “leave the observed dose unchanged at both times”	R lmtp	-0.000357 to 0.0012	0.9520	1.0253	pass
two-node law with a truncated-normal dose at both nodes and four plans	ate_regimen[up then history vs natural]	difference in mean outcome between the plans “add 0.5 to the first dose, then add 0.5 to the second where the first exceeds 3” against “leave the observed dose unchanged at both times”	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.000551 to 0.000799	0.9340	1.0070	pass
two-node law with a truncated-normal dose at both nodes and four plans	ate_regimen[up then history vs natural]	difference in mean outcome between the plans “add 0.5 to the first dose, then add 0.5 to the second where the first exceeds 3” against “leave the observed dose unchanged at both times”	R lmtp	-0.000551 to 0.000799	0.9340	1.0070	pass
two-node law with a truncated-normal dose at both nodes and four plans	ate_regimen[up vs natural]	difference in mean outcome between the plans “add 0.5 to the dose at both times, capped at 5.5” against “leave the observed dose unchanged at both times”	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.000398 to 0.0010	0.9420	1.0169	pass
two-node law with a truncated-normal dose at both nodes and four plans	ate_regimen[up vs natural]	difference in mean outcome between the plans “add 0.5 to the dose at both times, capped at 5.5” against “leave the observed dose unchanged at both times”	R lmtp	-0.000398 to 0.0010	0.9420	1.0169	pass
two-node law with a truncated-normal dose at both nodes and four plans	ey_regimen[natural]	mean outcome under the plan leave the observed dose unchanged at both times	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.000841 to 0.000981	0.9590	0.9974	pass
two-node law with a truncated-normal dose at both nodes and four plans	ey_regimen[natural]	mean outcome under the plan leave the observed dose unchanged at both times	R lmtp	-0.000841 to 0.000981	0.9590	0.9974	pass
two-node law with a truncated-normal dose at both nodes and four plans	ey_regimen[scale at 2]	mean outcome under the plan multiply the second dose by 1.25, capped at 5.5	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.000689 to 0.0017	0.9540	1.0287	pass
two-node law with a truncated-normal dose at both nodes and four plans	ey_regimen[scale at 2]	mean outcome under the plan multiply the second dose by 1.25, capped at 5.5	R lmtp	-0.000689 to 0.0017	0.9540	1.0287	pass
two-node law with a truncated-normal dose at both nodes and four plans	ey_regimen[up then history]	mean outcome under the plan add 0.5 to the first dose, then add 0.5 to the second where the first exceeds 3	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.000914 to 0.0013	0.9590	1.0270	pass
two-node law with a truncated-normal dose at both nodes and four plans	ey_regimen[up then history]	mean outcome under the plan add 0.5 to the first dose, then add 0.5 to the second where the first exceeds 3	R lmtp	-0.000914 to 0.0013	0.9590	1.0270	pass
two-node law with a truncated-normal dose at both nodes and four plans	ey_regimen[up]	mean outcome under the plan add 0.5 to the dose at both times, capped at 5.5	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.000748 to 0.0015	0.9580	1.0315	pass
two-node law with a truncated-normal dose at both nodes and four plans	ey_regimen[up]	mean outcome under the plan add 0.5 to the dose at both times, capped at 5.5	R lmtp	-0.000748 to 0.0015	0.9580	1.0315	pass
the three-level law with the plans low, mix and taper	ate_regimen[mix vs low]	difference in mean outcome between the plans “draw each arm from a known policy at both times” against “assign the low arm at both times”	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0025 to 0.0032	0.9350	0.9815	pass
the three-level law with the plans low, mix and taper	ate_regimen[mix vs low]	difference in mean outcome between the plans “draw each arm from a known policy at both times” against “assign the low arm at both times”	R lmtp	-0.0025 to 0.0033	0.9410	0.9923	pass
the three-level law with the plans low, mix and taper	ate_regimen[taper vs low]	difference in mean outcome between the plans “assign the high arm first, then draw from a known policy” against “assign the low arm at both times”	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0037 to 0.0031	0.9420	0.9809	pass
the three-level law with the plans low, mix and taper	ate_regimen[taper vs low]	difference in mean outcome between the plans “assign the high arm first, then draw from a known policy” against “assign the low arm at both times”	R lmtp	-0.0034 to 0.0035	0.9510	0.9926	pass
the three-level law with the plans low, mix and taper	ey_regimen[low]	mean outcome under the plan assign the low arm at both times	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0035 to 0.0020	0.9350	0.9868	pass
the three-level law with the plans low, mix and taper	ey_regimen[low]	mean outcome under the plan assign the low arm at both times	R lmtp	-0.0037 to 0.0020	0.9370	0.9948	pass
the three-level law with the plans low, mix and taper	ey_regimen[mix]	mean outcome under the plan draw each arm from a known policy at both times	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0016 to 0.000747	0.9530	1.0011	pass
the three-level law with the plans low, mix and taper	ey_regimen[mix]	mean outcome under the plan draw each arm from a known policy at both times	R lmtp	-0.0016 to 0.000747	0.9530	1.0011	pass
the three-level law with the plans low, mix and taper	ey_regimen[taper]	mean outcome under the plan assign the high arm first, then draw from a known policy	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0030 to 0.000884	0.9520	0.9944	pass
the three-level law with the plans low, mix and taper	ey_regimen[taper]	mean outcome under the plan assign the high arm first, then draw from a known policy	R lmtp	-0.0027 to 0.0011	0.9520	1.0043	pass
censored survival law, risks at horizons 1 and 2, one fold	ate_regimen[always vs never @ t=1]	difference in cumulative risk between the plans “treat at both times” against “treat at neither time” at horizon t = 1	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0012 to 0.0019	0.9580	1.0086	pass
censored survival law, risks at horizons 1 and 2, one fold	ate_regimen[always vs never @ t=1]	difference in cumulative risk between the plans “treat at both times” against “treat at neither time” at horizon t = 1	R lmtp	-0.0012 to 0.0019	0.9580	1.0078	pass
censored survival law, risks at horizons 1 and 2, one fold	ate_regimen[always vs never @ t=2]	difference in cumulative risk between the plans “treat at both times” against “treat at neither time” at horizon t = 2	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0013 to 0.0035	0.9410	0.9714	pass
censored survival law, risks at horizons 1 and 2, one fold	ate_regimen[always vs never @ t=2]	difference in cumulative risk between the plans “treat at both times” against “treat at neither time” at horizon t = 2	R lmtp	-0.0012 to 0.0035	0.9450	0.9817	pass
censored survival law, risks at horizons 1 and 2, one fold	ate_regimen[treat then continue if l2 positive vs never @ t=2]	difference in cumulative risk between the plans “treat, then continue only if L2 is positive” against “treat at neither time” at horizon t = 2	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0012 to 0.0036	0.9460	0.9799	pass
censored survival law, risks at horizons 1 and 2, one fold	ate_regimen[treat then continue if l2 positive vs never @ t=2]	difference in cumulative risk between the plans “treat, then continue only if L2 is positive” against “treat at neither time” at horizon t = 2	R lmtp	-0.0011 to 0.0037	0.9470	0.9910	pass
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[always @ t=1]	cumulative risk under the plan treat at both times at horizon t = 1	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0013 to 0.000623	0.9500	1.0081	pass
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[always @ t=1]	cumulative risk under the plan treat at both times at horizon t = 1	R lmtp	-0.0013 to 0.000617	0.9520	1.0099	pass
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[always @ t=2]	cumulative risk under the plan treat at both times at horizon t = 2	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.000840 to 0.0021	0.9440	0.9797	pass
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[always @ t=2]	cumulative risk under the plan treat at both times at horizon t = 2	R lmtp	-0.000805 to 0.0021	0.9480	0.9830	pass
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[never @ t=1]	cumulative risk under the plan treat at neither time at horizon t = 1	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0020 to 0.000503	0.9450	1.0029	pass
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[never @ t=1]	cumulative risk under the plan treat at neither time at horizon t = 1	R lmtp	-0.0020 to 0.000509	0.9470	1.0023	pass
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[never @ t=2]	cumulative risk under the plan treat at neither time at horizon t = 2	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.0024 to 0.0014	0.9450	0.9780	pass
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[never @ t=2]	cumulative risk under the plan treat at neither time at horizon t = 2	R lmtp	-0.0024 to 0.0014	0.9480	0.9945	pass
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[treat then continue if l2 positive @ t=2]	cumulative risk under the plan treat, then continue only if L2 is positive at horizon t = 2	cleverly sequentially doubly robust (SDR) longitudinal estimator	-0.000754 to 0.0022	0.9470	1.0169	pass
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[treat then continue if l2 positive @ t=2]	cumulative risk under the plan treat, then continue only if L2 is positive at horizon t = 2	R lmtp	-0.000714 to 0.0022	0.9510	1.0210	pass

Agreement with the canonical implementation

Comparator-backed: a paired comparison with lmtp 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
two-node law with monotone censoring, three plans, one fold	ate_regimen[always vs never]	difference in mean outcome between the plans “treat at both times” against “treat at neither time”	0.000180	0.0379	1.0077	-0.0010	matching implementation	0.0047 vs 0.0500	equivalent
two-node law with monotone censoring, three plans, one fold	ate_regimen[treat then continue if l2 positive vs never]	difference in mean outcome between the plans “treat, then continue only if L2 is positive” against “treat at neither time”	0.000396	0.0829	1.0160	-0.0090	matching implementation	0.0148 vs 0.0500	equivalent
two-node law with monotone censoring, three plans, one fold	ey_regimen[always]	mean outcome under the plan treat at both times	0.000036	0.0129	1.0085	-0.0040	matching implementation	0.0114 vs 0.0500	equivalent
two-node law with monotone censoring, three plans, one fold	ey_regimen[never]	mean outcome under the plan treat at neither time	-0.000144	0.0380	1.0093	-0.0060	matching implementation	0.0050 vs 0.0500	equivalent
two-node law with monotone censoring, three plans, one fold	ey_regimen[treat then continue if l2 positive]	mean outcome under the plan treat, then continue only if L2 is positive	0.000252	0.0816	1.0252	-0.0040	matching implementation	0.0102 vs 0.0500	equivalent
the same law and plans, five folds	ate_regimen[always vs never]	difference in mean outcome between the plans “treat at both times” against “treat at neither time”	-0.000219	0.0447	1.0164	0.0010	different estimator	0.0067 vs 0.0500	equivalent
the same law and plans, five folds	ate_regimen[treat then continue if l2 positive vs never]	difference in mean outcome between the plans “treat, then continue only if L2 is positive” against “treat at neither time”	-0.000092	0.0183	1.0208	-0.0050	different estimator	0.0070 vs 0.0500	equivalent
the same law and plans, five folds	ey_regimen[always]	mean outcome under the plan treat at both times	-0.000165	0.0544	1.0052	0.0010	different estimator	0.0070 vs 0.0500	equivalent
the same law and plans, five folds	ey_regimen[never]	mean outcome under the plan treat at neither time	0.000054	0.0138	1.0126	-0.0020	different estimator	0.0056 vs 0.0500	equivalent
the same law and plans, five folds	ey_regimen[treat then continue if l2 positive]	mean outcome under the plan treat, then continue only if L2 is positive	-0.000038	0.0123	1.0191	0.0020	different estimator	0.0140 vs 0.0500	equivalent
two-node law with a truncated-normal dose at both nodes and four plans	ate_regimen[scale at 2 vs natural]	difference in mean outcome between the plans “multiply the second dose by 1.25, capped at 5.5” against “leave the observed dose unchanged at both times”	-3.687e-16	2.577e-13	1.0000	0	matching implementation	3.175e-14 vs 0.0500	equivalent
two-node law with a truncated-normal dose at both nodes and four plans	ate_regimen[up then history vs natural]	difference in mean outcome between the plans “add 0.5 to the first dose, then add 0.5 to the second where the first exceeds 3” against “leave the observed dose unchanged at both times”	-2.780e-16	2.241e-13	1.0000	0	matching implementation	2.764e-14 vs 0.0500	equivalent
two-node law with a truncated-normal dose at both nodes and four plans	ate_regimen[up vs natural]	difference in mean outcome between the plans “add 0.5 to the dose at both times, capped at 5.5” against “leave the observed dose unchanged at both times”	-2.735e-16	2.091e-13	1.0000	0	matching implementation	2.265e-14 vs 0.0500	equivalent
two-node law with a truncated-normal dose at both nodes and four plans	ey_regimen[natural]	mean outcome under the plan leave the observed dose unchanged at both times	0	0	1	0	matching implementation	3.331e-16 vs 0.0500	equivalent
two-node law with a truncated-normal dose at both nodes and four plans	ey_regimen[scale at 2]	mean outcome under the plan multiply the second dose by 1.25, capped at 5.5	-3.920e-16	1.806e-13	1.0000	0	matching implementation	2.021e-14 vs 0.0500	equivalent
two-node law with a truncated-normal dose at both nodes and four plans	ey_regimen[up then history]	mean outcome under the plan add 0.5 to the first dose, then add 0.5 to the second where the first exceeds 3	-2.846e-16	1.397e-13	1.0000	0	matching implementation	1.554e-14 vs 0.0500	equivalent
two-node law with a truncated-normal dose at both nodes and four plans	ey_regimen[up]	mean outcome under the plan add 0.5 to the dose at both times, capped at 5.5	-2.820e-16	1.355e-13	1.0000	0	matching implementation	1.643e-14 vs 0.0500	equivalent
the three-level law with the plans low, mix and taper	ate_regimen[mix vs low]	difference in mean outcome between the plans “draw each arm from a known policy at both times” against “assign the low arm at both times”	-0.000080	0.0152	0.9893	-0.0060	matching implementation	0.0182 vs 0.0500	equivalent
the three-level law with the plans low, mix and taper	ate_regimen[taper vs low]	difference in mean outcome between the plans “assign the high arm first, then draw from a known policy” against “assign the low arm at both times”	-0.000324	0.0515	0.9955	-0.0090	matching implementation	0.0164 vs 0.0500	equivalent
the three-level law with the plans low, mix and taper	ey_regimen[low]	mean outcome under the plan assign the low arm at both times	0.000080	0.0155	0.9763	-0.0020	matching implementation	0.0194 vs 0.0500	equivalent
the three-level law with the plans low, mix and taper	ey_regimen[mix]	mean outcome under the plan draw each arm from a known policy at both times	-1.272e-13	5.993e-11	1.0000	0	matching implementation	6.405e-11 vs 0.0500	equivalent
the three-level law with the plans low, mix and taper	ey_regimen[taper]	mean outcome under the plan assign the high arm first, then draw from a known policy	-0.000244	0.0693	1.0243	0	matching implementation	0.0150 vs 0.0500	equivalent
censored survival law, risks at horizons 1 and 2, one fold	ate_regimen[always vs never @ t=1]	difference in cumulative risk between the plans “treat at both times” against “treat at neither time” at horizon t = 1	0.000010	0.0034	1.0004	0	matching implementation	0.0013 vs 0.0500	equivalent
censored survival law, risks at horizons 1 and 2, one fold	ate_regimen[always vs never @ t=2]	difference in cumulative risk between the plans “treat at both times” against “treat at neither time” at horizon t = 2	-0.000046	0.0104	1.0135	-0.0040	matching implementation	0.0053 vs 0.0500	equivalent
censored survival law, risks at horizons 1 and 2, one fold	ate_regimen[treat then continue if l2 positive vs never @ t=2]	difference in cumulative risk between the plans “treat, then continue only if L2 is positive” against “treat at neither time” at horizon t = 2	-0.000051	0.0114	1.0151	-0.0010	matching implementation	0.0054 vs 0.0500	equivalent
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[always @ t=1]	cumulative risk under the plan treat at both times at horizon t = 1	0.000005	0.0027	1.0033	-0.0020	matching implementation	0.0049 vs 0.0500	equivalent
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[always @ t=2]	cumulative risk under the plan treat at both times at horizon t = 2	-0.000030	0.0112	1.0060	-0.0040	matching implementation	0.0028 vs 0.0500	equivalent
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[never @ t=1]	cumulative risk under the plan treat at neither time at horizon t = 1	-0.000005	0.0021	1.0011	-0.0020	matching implementation	0.0019 vs 0.0500	equivalent
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[never @ t=2]	cumulative risk under the plan treat at neither time at horizon t = 2	0.000016	0.0045	1.0208	-0.0030	matching implementation	0.0066 vs 0.0500	equivalent
censored survival law, risks at horizons 1 and 2, one fold	risk_regimen[treat then continue if l2 positive @ t=2]	cumulative risk under the plan treat, then continue only if L2 is positive at horizon t = 2	-0.000035	0.0129	1.0091	-0.0040	matching implementation	0.0115 vs 0.0500	equivalent

Theory properties

property	cell	role	what was tested	what must hold	measured	result
clustered_calibration	clusters_200__known_ratio	positive	contrast of always against never, 200 clusters of 10 rows: grouped folds, the known ratio and GLM outcome regressions	SE ratio and coverage intervals both inside their calibration bands	SE ratio 0.9699 to 1.0249, coverage 0.9348 to 0.9536	pass
clustered_calibration	clusters_200__noise_control	control	contrast of always against never, 200 clusters of 10 rows: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	SE ratio 0.6845 to 0.7254, coverage 0.8075 to 0.8388	pass
clustered_calibration	clusters_200__shrunken_se_control	control	contrast of always against never, 200 clusters of 10 rows: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	SE ratio 0.6777 to 0.7172, coverage 0.8067 to 0.8380	pass
clustered_calibration	clusters_20__known_ratio	positive	contrast of always against never, 20 clusters of 100 rows: grouped folds, the known ratio and GLM outcome regressions	SE ratio and coverage intervals both inside their calibration bands	SE ratio 0.9511 to 1.0091, coverage 0.9375 to 0.9559	pass
clustered_calibration	clusters_20__noise_control	control	contrast of always against never, 20 clusters of 100 rows: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	SE ratio 0.6950 to 0.7389, coverage 0.8204 to 0.8508	pass
clustered_calibration	clusters_20__shrunken_se_control	control	contrast of always against never, 20 clusters of 100 rows: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	SE ratio 0.6660 to 0.7063, coverage 0.7969 to 0.8289	pass
construction_diagnostic	estimated_flexible_mechanism	diagnostic	the shipped construction with a tree mechanism estimated in each fold, under the default bounds (0.01, 1)	reported only	bias -0.0034 to 0.0015, coverage 0.9650, SE ratio 1.0441	reported
construction_diagnostic	stitched_cross_fit	diagnostic	the stitched construction: each row’s node 2 transform comes from the fold that holds it out, and node 1 regresses the stitched transforms	reported only	bias -0.0029 to 0.0013, coverage 0.9483, SE ratio 0.9856	reported
crossfit_overfitting	cross_fitted_sdr	positive	five-fold SDR with fully grown outcome trees and the known mechanism	SE ratio clears the overfitting floor and stays inside the sanity band	SE ratio 0.9739 to 1.0132	pass
crossfit_overfitting	in_sample_control	control	the same flexible learner fitted in sample, with no cross-fitting	SE ratio must fall below the overfitting ceiling	SE ratio 0.3477 to 0.3622	pass
interval_calibration	competing_h2__correctly_specified	positive	difference of always and never in the death incidence at t = 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 0.9307 to 0.9502, SE ratio 0.9617 to 1.0199, empirical efficiency ratio 1.0135 to 1.0732, reported efficiency ratio 1.0297 to 1.0359	pass
interval_calibration	competing_h2__noise_control	control	difference of always and never in the death incidence at t = 2: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8235 to 0.8537, SE ratio 0.7040 to 0.7453, empirical efficiency ratio 1.3863 to 1.4659, reported efficiency ratio 1.0297 to 1.0360	pass
interval_calibration	competing_h2__shrunken_se_control	control	difference of always and never in the death incidence at t = 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8059 to 0.8373, SE ratio 0.6736 to 0.7140, empirical efficiency ratio 1.0129 to 1.0727, reported efficiency ratio 0.7207 to 0.7252	pass
interval_calibration	dynamic__correctly_specified	positive	dynamic plan: 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 0.9396 to 0.9578, SE ratio 0.9806 to 1.0394, empirical efficiency ratio 0.9686 to 1.0263, reported efficiency ratio 1.0049 to 1.0077	pass
interval_calibration	dynamic__noise_control	control	dynamic plan: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8217 to 0.8520, SE ratio 0.6934 to 0.7357, empirical efficiency ratio 1.3679 to 1.4513, reported efficiency ratio 1.0049 to 1.0077	pass
interval_calibration	dynamic__shrunken_se_control	control	dynamic plan: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8139 to 0.8448, SE ratio 0.6863 to 0.7281, empirical efficiency ratio 0.9675 to 1.0261, reported efficiency ratio 0.7034 to 0.7054	pass
interval_calibration	msm_identity__correctly_specified	positive	the duration coefficient of the identity-link working model: 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 0.9350 to 0.9539, SE ratio 0.9683 to 1.0276, empirical efficiency ratio 0.9923 to 1.0523, reported efficiency ratio 1.0170 to 1.0217	pass
interval_calibration	msm_identity__noise_control	control	the duration coefficient of the identity-link working model: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8245 to 0.8546, SE ratio 0.6990 to 0.7413, empirical efficiency ratio 1.3757 to 1.4584, reported efficiency ratio 1.0171 to 1.0218	pass
interval_calibration	msm_identity__shrunken_se_control	control	the duration coefficient of the identity-link working model: 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 0.8457, SE ratio 0.6777 to 0.7196, empirical efficiency ratio 0.9919 to 1.0527, reported efficiency ratio 0.7119 to 0.7152	pass
interval_calibration	msm_logit__correctly_specified	positive	the duration coefficient of the logit-link working model: 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 0.9386 to 0.9569, SE ratio 0.9692 to 1.0294, empirical efficiency ratio 1.0011 to 1.0634, reported efficiency ratio 1.0282 to 1.0326	pass
interval_calibration	msm_logit__noise_control	control	the duration coefficient of the logit-link working model: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8240 to 0.8542, SE ratio 0.6950 to 0.7376, empirical efficiency ratio 1.3970 to 1.4825, reported efficiency ratio 1.0282 to 1.0327	pass
interval_calibration	msm_logit__shrunken_se_control	control	the duration coefficient of the logit-link working model: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8163 to 0.8469, SE ratio 0.6786 to 0.7201, empirical efficiency ratio 1.0020 to 1.0632, reported efficiency ratio 0.7198 to 0.7228	pass
interval_calibration	mtp_up__correctly_specified	positive	the shift up at both nodes against the natural course, continuous dose: 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 0.9359 to 0.9546, SE ratio 0.9676 to 1.0238, empirical efficiency ratio 1.0026 to 1.0606, reported efficiency ratio 1.0232 to 1.0296	pass
interval_calibration	mtp_up__noise_control	control	the shift up at both nodes against the natural course, continuous dose: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8276 to 0.8575, SE ratio 0.7004 to 0.7431, empirical efficiency ratio 1.3815 to 1.4652, reported efficiency ratio 1.0232 to 1.0296	pass
interval_calibration	mtp_up__shrunken_se_control	control	the shift up at both nodes against the natural course, continuous dose: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8090 to 0.8402, SE ratio 0.6767 to 0.7169, empirical efficiency ratio 1.0016 to 1.0619, reported efficiency ratio 0.7162 to 0.7208	pass
interval_calibration	policy_mix__correctly_specified	positive	contrast of the known policy mix against low, three-level law: 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 0.9440 to 0.9614, SE ratio 0.9921 to 1.0521, empirical efficiency ratio 0.9617 to 1.0194, reported efficiency ratio 1.0098 to 1.0131	pass
interval_calibration	policy_mix__noise_control	control	contrast of the known policy mix against low, three-level law: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8219 to 0.8522, SE ratio 0.6949 to 0.7358, empirical efficiency ratio 1.3750 to 1.4555, reported efficiency ratio 1.0098 to 1.0131	pass
interval_calibration	policy_mix__shrunken_se_control	control	contrast of the known policy mix against low, three-level law: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8230 to 0.8532, SE ratio 0.6945 to 0.7363, empirical efficiency ratio 0.9619 to 1.0193, reported efficiency ratio 0.7069 to 0.7092	pass
interval_calibration	static__correctly_specified	positive	static plan: 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 0.9318 to 0.9511, SE ratio 0.9637 to 1.0208, empirical efficiency ratio 1.0005 to 1.0589, reported efficiency ratio 1.0189 to 1.0233	pass
interval_calibration	static__noise_control	control	static plan: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8227 to 0.8530, SE ratio 0.6903 to 0.7336, empirical efficiency ratio 1.3921 to 1.4787, reported efficiency ratio 1.0189 to 1.0233	pass
interval_calibration	static__shrunken_se_control	control	static plan: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8077 to 0.8390, SE ratio 0.6742 to 0.7144, empirical efficiency ratio 1.0011 to 1.0598, reported efficiency ratio 0.7132 to 0.7163	pass
interval_calibration	survival_h2__correctly_specified	positive	difference of always and never in the risk at t = 2, survival law: 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 0.9377 to 0.9562, SE ratio 0.9772 to 1.0353, empirical efficiency ratio 1.0022 to 1.0608, reported efficiency ratio 1.0342 to 1.0402	pass
interval_calibration	survival_h2__noise_control	control	difference of always and never in the risk at t = 2, survival law: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8178 to 0.8484, SE ratio 0.7041 to 0.7451, empirical efficiency ratio 1.3925 to 1.4726, reported efficiency ratio 1.0340 to 1.0401	pass
interval_calibration	survival_h2__shrunken_se_control	control	difference of always and never in the risk at t = 2, survival law: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8095 to 0.8407, SE ratio 0.6847 to 0.7251, empirical efficiency ratio 1.0021 to 1.0603, reported efficiency ratio 0.7239 to 0.7281	pass
power	static__alternative	positive	static plan: the same test applied to a law with a real effect	rejection lower bound clears the minimum power	rejection 0.9637, 0.9431 to 0.9786	pass
root_n_and_efficiency	static__n_1000	positive	static plan: bias, coverage and SE calibration at n = 1,000	bias inside the margin, coverage clears the floor, SE ratio inside the band	bias -0.000706, coverage 0.9282 to 0.9711, SE ratio 1.0228	pass
root_n_and_efficiency	static__n_2000	positive	static plan: bias, coverage and SE calibration at n = 2,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias -0.000667, coverage 0.9214 to 0.9665, SE ratio 0.9922	pass
root_n_and_efficiency	static__n_8000	positive	static plan: bias, coverage and SE calibration at n = 8,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.0011, coverage 0.9214 to 0.9665, SE ratio 1.0002	pass
root_n_rate	static__empirical_sd	positive	static plan: 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 -0.5565 to -0.4633	pass
root_n_rate	static__reported_se	positive	static plan: the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5221 to -0.5150	pass
sdr_tmle_agreement	static	diagnostic	the absolute difference of SDR and LTMLE over the SE of SDR, for always against never, on the calibration draws	reported only	mean absolute difference / SE 0.0087	reported
sequential_double_robustness	P_A__n_2000	positive	both outcome regressions are correct and both mechanisms are wrong, at n = 2,000	absolute bias + 2 MCSE at n = 8,000 below 0.01 and below its value at n = 2,000, SE ratio inside the union-model band	absolute bias + 2 MCSE 0.0069, SE ratio 0.7200, coverage 0.8420	pass
sequential_double_robustness	P_A__n_8000	positive	both outcome regressions are correct and both mechanisms are wrong, at n = 8,000	absolute bias + 2 MCSE at n = 8,000 below 0.01 and below its value at n = 2,000, SE ratio inside the union-model band	absolute bias + 2 MCSE 0.0023, SE ratio 0.7498, coverage 0.8730	pass
sequential_double_robustness	P_B__n_2000	positive	node 1 outcome regression wrong, node 2 mechanism wrong, at n = 2,000	absolute bias + 2 MCSE at n = 8,000 below 0.01 and below its value at n = 2,000, SE ratio inside the union-model band	absolute bias + 2 MCSE 0.0073, SE ratio 0.6910, coverage 0.8160	pass
sequential_double_robustness	P_B__n_8000	positive	node 1 outcome regression wrong, node 2 mechanism wrong, at n = 8,000	absolute bias + 2 MCSE at n = 8,000 below 0.01 and below its value at n = 2,000, SE ratio inside the union-model band	absolute bias + 2 MCSE 0.0023, SE ratio 0.6722, coverage 0.8260	pass
sequential_double_robustness	P_C__n_2000	positive	both mechanisms are correct and both outcome regressions are wrong, at n = 2,000	bias inside the margin, SE ratio inside the union-model band, coverage clears the floor	bias -0.0064 to 0.0074, margin 0.0210, coverage 0.9100 to 0.9518, SE ratio 0.9868	pass
sequential_double_robustness	P_C__n_8000	positive	both mechanisms are correct and both outcome regressions are wrong, at n = 8,000	bias inside the margin, SE ratio inside the union-model band, coverage clears the floor	bias -0.0014 to 0.0053, margin 0.0103, coverage 0.9307 to 0.9669, SE ratio 1.0106	pass
sequential_double_robustness	P_D__n_2000	positive	node 1 mechanism wrong, node 2 outcome regression wrong, the pattern LTMLE misses, at n = 2,000	absolute bias + 2 MCSE at n = 8,000 below 0.01 and below its value at n = 2,000, SE ratio inside the union-model band	absolute bias + 2 MCSE 0.0083, SE ratio 0.6023, coverage 0.7620	pass
sequential_double_robustness	P_D__n_8000	positive	node 1 mechanism wrong, node 2 outcome regression wrong, the pattern LTMLE misses, at n = 8,000	absolute bias + 2 MCSE at n = 8,000 below 0.01 and below its value at n = 2,000, SE ratio inside the union-model band	absolute bias + 2 MCSE 0.0036, SE ratio 0.5927, coverage 0.7650	pass
sequential_double_robustness	both_correct__n_2000	positive	every outcome regression and mechanism is correct, at n = 2,000	bias inside the margin, SE ratio inside the union-model band, coverage clears the floor	bias 0.000011 to 0.0112, margin 0.0172, coverage 0.8853 to 0.9327, SE ratio 0.9459	fail
sequential_double_robustness	both_correct__n_8000	positive	every outcome regression and mechanism is correct, at n = 8,000	bias inside the margin, SE ratio inside the union-model band, coverage clears the floor	bias -0.0018 to 0.0033, margin 0.0077, coverage 0.9295 to 0.9661, SE ratio 0.9994	pass
sequential_double_robustness	ltmle_P_D_control	control	LTMLE in pattern P_D, where its recursion needs the node 2 outcome regression	bias interval at least 3 empirical standard deviations from zero, SE ratio inside the union-model band	bias 0.2158 to 0.2235, empirical SD 0.0468, SE ratio 1.0199	pass
sequential_double_robustness	node2_both_wrong_control	control	SDR with the outcome regression and the mechanism both wrong at node 2	bias interval at least 3 empirical standard deviations from zero, SE ratio inside the union-model band	bias 0.2158 to 0.2233, empirical SD 0.0456, SE ratio 1.0690	pass
simultaneous_coverage	six_regimens__pointwise_joint_control	control	the six regimen means and five contrasts of the two-node law: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.6739 to 0.7271	pass
simultaneous_coverage	six_regimens__simultaneous_band	positive	the six regimen means and five contrasts of the two-node law: 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 0.9085 to 0.9394	fail
type_i_error	static__sharp_null	positive	static plan: a confounded law whose true contrast is exactly zero	one-sided rejection bound stays under the declared type-I ceiling	rejection 0.0600, 0.0404 to 0.0850	pass
weighted_calibration	selection_weighted__correctly_specified	positive	contrast of always against never on the selected law, with weights: every nuisance is correct; no efficiency ratio is claimed (RM18-fixed-weights)	SE ratio and coverage intervals both inside their calibration bands	SE ratio 0.9681 to 1.0272, coverage 0.9273 to 0.9472	pass
weighted_calibration	selection_weighted__noise_control	control	contrast of always against never on the selected law, with weights: one efficiency-bound unit of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	SE ratio 0.6900 to 0.7323, coverage 0.8093 to 0.8404	pass
weighted_calibration	selection_weighted__shrunken_se_control	control	contrast of always against never on the selected law, with weights: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	SE ratio 0.6777 to 0.7180, coverage 0.8038 to 0.8354	pass

The sequential_double_robustness family reads the two-node law of tests/discrete_law_longitudinal_sdr.py. Each of the patterns P_A to P_D makes one nuisance wrong at each node, and the pattern both_correct makes none wrong. The patterns both_correct and P_C keep the ratios exact, so they gate the bias and the coverage at both sizes. The patterns P_A, P_B and P_D gate the absolute bias at n = 2,000 and n = 8,000, and report their coverage only. Theorem 4 needs the rate product for their intervals. Both controls make the same nuisances wrong at one node, and their bias clears the floor of 3 empirical SDs.

The construction_diagnostic and sdr_tmle_agreement cells state no verdict. The stitched cell fits Step 2 of Section 5.3 as printed. The tree cell estimates the mechanism with trees of at least 50 rows a leaf, under the default bounds (0.01, 1).

Two property cells fail their own rule, and the diagnosis finds no defect in SDR. The X4-finite-sample owner holds the coverage cell. The band-finite-sample owner holds the band.

cell	measured	reading
sequential_double_robustness/both_correct__n_2000	coverage 0.911, 99% interval 0.885 to 0.933, against a floor of 0.90; SE ratio 0.946	finite-sample, shared with LTMLE
simultaneous_coverage/six_regimens__simultaneous_band	joint coverage 0.925, 99% interval 0.909 to 0.939, against a band of 0.92 to 0.98	finite-sample, pointwise shortfall inherited

The both_correct cell at n = 2,000. The law’s smallest path probability is near 0.012, so an inverse weight can reach about 85. At n = 2,000 the standard error then varies with the error it measures. A diagnostic refitted the cell’s own fit and LTMLE with the same learners on the same 1,000 fresh draws (tests/diagnostics/x4_both_correct/).

engine	coverage	SE ratio	coefficient of variation of the SE	correlation of SE and error
SDR	0.903	0.918	0.186	0.301
LTMLE	0.903	0.917	0.187	0.321

The two engines cover equally on the same draws. The same cell at n = 8,000 covers 0.950, with an SE ratio of 0.999. A defect in the SDR curve would not be shared with LTMLE, and would not disappear as \(n\) grows.

The band. The band reads every regimen mean and contrast of the six-plan law. The oracle band at the exact-law critical value of 2.693 covers 0.931 on the same replications. The package band covers 0.925 at a mean critical value of 2.683. The shortfall therefore comes from the pointwise intervals. The other cells that the band-finite-sample owner holds read the same way. tests/unit/test_sdr_shortfall_reading.py rebuilds the coverage reading from the committed rows. tests/unit/test_band_shortfall_reading.py rebuilds the band reading.

Measured values and declared margins

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	paired replications
n	2000	observations per paired replication
independent_tests_passed	60	truth tests passing
independent_tests_total	60	truth tests reported
paired_tests_passed	30	paired comparisons passing
paired_tests_total	30	paired comparisons reported
property_cells_passed	54	property cells passing
property_cells_total	56	property cells reported
property_cells_reported	3	diagnostic cells with no verdict
max_standardized_bias	0.0871	largest primary standardized bias
min_coverage	0.9340	lowest primary coverage
max_margin_utilization	0.0829	largest paired similarity-margin share
margin:confidence_level	0.9900	Monte Carlo confidence level
margin:alpha	0.0500	test size
margin:bootstrap_replicates	10000	bootstrap replications
margin:nominal_coverage	0.9500	nominal interval coverage
margin:over_coverage_ceiling	0.9900	descriptive overcoverage threshold
margin:se_ratio_sanity_lower	0.8000	primary SE-ratio lower screen
margin:se_ratio_sanity_upper	1.2000	primary SE-ratio upper screen
margin:coverage_noninferiority	-0.0250	coverage-difference noninferiority bound
margin:rmse_noninferiority	1.1000	RMSE-ratio noninferiority bound
margin:calibration_noninferiority	0.0500	calibration-excess noninferiority bound
margin:root_n_slope	-0.5000	expected root-n slope
margin:root_n_slope_lower	-0.6250	root-n slope lower bound
margin:root_n_slope_upper	-0.3750	root-n slope upper bound
margin:excluded_slope	-0.2500	slower rate the interval must exclude
margin:overfit_coverage_gain	0.1500	minimum paired coverage gain
margin:standardized_bias	0.2500	standardized-bias margin
margin:coverage_floor	0.9000	primary coverage floor
margin:calibration_se_ratio_lower	0.9300	calibration SE-ratio lower bound
margin:calibration_se_ratio_upper	1.0700	calibration SE-ratio upper bound
margin:calibration_coverage_lower	0.9200	calibration coverage lower bound
margin:calibration_coverage_upper	0.9800	calibration coverage upper bound
margin:paired_difference	0.1500	paired similarity margin in pooled SDs
margin:efficiency_ratio_lower	0.9000	exact-EIF ratio lower bound
margin:efficiency_ratio_upper	1.1000	exact-EIF ratio upper bound
margin:shrunken_se_factor	0.7000	negative-control SE multiplier
margin:overfit_se_floor	0.8500	cross-fitted tree SE-ratio lower bound
margin:overfit_control_ceiling	0.7500	in-sample tree SE-ratio upper bound
margin:type_i_ceiling	0.1000	type-I upper bound
margin:minimum_power	0.8000	power lower bound

Limits

limit	what it means for use
finite-support laws with two nodes, and one continuous-dose law	the evidence covers these laws, with plans and policies fixed before the run
the mechanism is known in every primary scenario	both sides read the generating ratio. An estimated mechanism appears in the tree diagnostic cell only, which states no verdict
parametric node regressions in the primary scenarios	a quasibinomial GLM and least squares. The overfitting family adds fully grown trees with a known mechanism
the cross-fitted pairs compare two constructions	lmtp stitches Step 2 across folds, and this package runs the training-fold recursion. The pairs are margins pairs, not exactness checks
the one-correct patterns report coverage only	an interval under P_A, P_B or P_D needs the Theorem 4 rate product, which a wrong nuisance does not meet
two property cells are red under reporting	a finite-sample coverage cell at n = 2,000 shared with LTMLE, and a band that inherits its pointwise shortfall. The X4-finite-sample and band-finite-sample owners hold them
clusters, weights and an MSM are calibration cells only	the clustered_calibration, weighted_calibration and msm_* cells have no lmtp pairing
no multiply robust interval	page 854 of the source states that neither SDR nor TMLE gives one