Point-treatment survival

This study validates longitudinal TMLE on a held design. The design has one baseline treatment, held over every visit, and it reads one follow-up time and one event code per unit (TimeToEvent). The sections one baseline treatment held over the nodes and time-to-event input state the estimator and its exact-law evidence.

The law is make_point_survival. W1 is Bernoulli(0.5), W2 is uniform on 0..3, and the arm is binary. The discrete-time hazards depend on the visit, the arm and W, and dropout at each visit depends on the arm and W. Every truth is an exact finite sum. Every efficiency bound is the exact standard deviation of the efficient influence function over the law’s support.

The study pairs each fit with R survtmle 1.1.1, method = "mean" (Benkeser, Carone and Gilbert 2018), on the same samples.

What was compared

setting	cleverly	R survtmle
datasets	1,600 samples of 2,000 rows for each scenario	the identical rows
scenarios	survival: five visits, the risks of both arms and their difference at visits 1, 3 and 5. competing: four visits and two causes, the incidences and their differences at visits 2 and 4	the same
treatment model	a logistic regression on W1 + W2	glm.trt = "W1 + W2"
censoring model	a logistic regression on the arm, W1 and W2 at each visit	one pooled glm with one intercept and three slopes for each visit, which factorises by visit into the same model
sequential regressions	a quasibinomial regression on W1 + W2 for each arm. The hazard is logistic in the visit, the arm and W, so the iterated means are misspecified on purpose	glm.ftime = "trt * (W1 + W2)"
targeting	the intercept of each node, with the clever covariate in the loss weight	one logistic fluctuation for each cause, with the clever covariates of both arms
intervals	pointwise 95% Wald from the influence curve	the same, from the survtmle influence curve

The two targeting submodels differ. The arms have disjoint support, so the scores separate by arm and the two solve the same equations along different paths. The paired rows therefore read under the default margins.

The initial_estimate column is not one quantity on the two sides. Here it is the mean of the node-1 regression, which is fitted on pseudo-outcomes that the later nodes already targeted. The survtmle value is a second call with Gcomp = TRUE, which is the fully untargeted recursion. No verdict reads the column.

Four replications of competing (189, 1,008, 1,302 and 1,398) have one sequential regression with quasi-complete separation. One W1 cell has no event of one cause at one node, so the coefficient diverges while the deviance settles. The quasibinomial learner keeps the last iterate with a warning, as R’s glm does. The first declared run stopped on replication 189 and published nothing, and the study re-ran under a fresh declaration.

Accuracy against known truth

law	estimand	what was tested	implementation	bias (99% interval)	coverage	SE ratio	result
four visits, two competing causes, a held binary treatment, visit dropout	ate_regimen[arm1 vs arm0, death @ t=2]	difference in cumulative incidence of death between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 2	cleverly	-0.000917 to 0.000859	0.9387	0.9816	pass
four visits, two competing causes, a held binary treatment, visit dropout	ate_regimen[arm1 vs arm0, death @ t=2]	difference in cumulative incidence of death between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 2	R survtmle, method="mean"	-0.000917 to 0.000859	0.9381	0.9783	pass
four visits, two competing causes, a held binary treatment, visit dropout	ate_regimen[arm1 vs arm0, death @ t=4]	difference in cumulative incidence of death between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 4	cleverly	-0.000931 to 0.0014	0.9463	0.9951	pass
four visits, two competing causes, a held binary treatment, visit dropout	ate_regimen[arm1 vs arm0, death @ t=4]	difference in cumulative incidence of death between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 4	R survtmle, method="mean"	-0.000930 to 0.0014	0.9406	0.9837	pass
four visits, two competing causes, a held binary treatment, visit dropout	ate_regimen[arm1 vs arm0, relapse @ t=2]	difference in cumulative incidence of relapse between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 2	cleverly	-0.0012 to 0.000758	0.9481	0.9765	pass
four visits, two competing causes, a held binary treatment, visit dropout	ate_regimen[arm1 vs arm0, relapse @ t=2]	difference in cumulative incidence of relapse between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 2	R survtmle, method="mean"	-0.0012 to 0.000759	0.9469	0.9710	pass
four visits, two competing causes, a held binary treatment, visit dropout	ate_regimen[arm1 vs arm0, relapse @ t=4]	difference in cumulative incidence of relapse between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 4	cleverly	-0.0023 to 0.000375	0.9463	0.9869	pass
four visits, two competing causes, a held binary treatment, visit dropout	ate_regimen[arm1 vs arm0, relapse @ t=4]	difference in cumulative incidence of relapse between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 4	R survtmle, method="mean"	-0.0023 to 0.000373	0.9375	0.9696	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm0, death @ t=2]	cumulative incidence of death under the plan assign arm 0 at baseline and hold it at horizon t = 2	cleverly	-0.000915 to 0.000567	0.9394	0.9781	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm0, death @ t=2]	cumulative incidence of death under the plan assign arm 0 at baseline and hold it at horizon t = 2	R survtmle, method="mean"	-0.000913 to 0.000568	0.9400	0.9781	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm0, death @ t=4]	cumulative incidence of death under the plan assign arm 0 at baseline and hold it at horizon t = 4	cleverly	-0.0017 to 0.000157	0.9444	0.9888	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm0, death @ t=4]	cumulative incidence of death under the plan assign arm 0 at baseline and hold it at horizon t = 4	R survtmle, method="mean"	-0.0017 to 0.000158	0.9444	0.9889	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm0, relapse @ t=2]	cumulative incidence of relapse under the plan assign arm 0 at baseline and hold it at horizon t = 2	cleverly	-0.000655 to 0.000749	0.9481	0.9940	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm0, relapse @ t=2]	cumulative incidence of relapse under the plan assign arm 0 at baseline and hold it at horizon t = 2	R survtmle, method="mean"	-0.000654 to 0.000750	0.9487	0.9939	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm0, relapse @ t=4]	cumulative incidence of relapse under the plan assign arm 0 at baseline and hold it at horizon t = 4	cleverly	-0.000362 to 0.0015	0.9487	0.9831	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm0, relapse @ t=4]	cumulative incidence of relapse under the plan assign arm 0 at baseline and hold it at horizon t = 4	R survtmle, method="mean"	-0.000360 to 0.0015	0.9481	0.9832	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm1, death @ t=2]	cumulative incidence of death under the plan assign arm 1 at baseline and hold it at horizon t = 2	cleverly	-0.000686 to 0.000279	0.9444	1.0083	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm1, death @ t=2]	cumulative incidence of death under the plan assign arm 1 at baseline and hold it at horizon t = 2	R survtmle, method="mean"	-0.000684 to 0.000281	0.9387	0.9969	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm1, death @ t=4]	cumulative incidence of death under the plan assign arm 1 at baseline and hold it at horizon t = 4	cleverly	-0.0012 to 0.000112	0.9525	1.0267	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm1, death @ t=4]	cumulative incidence of death under the plan assign arm 1 at baseline and hold it at horizon t = 4	R survtmle, method="mean"	-0.0012 to 0.000114	0.9456	0.9924	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm1, relapse @ t=2]	cumulative incidence of relapse under the plan assign arm 1 at baseline and hold it at horizon t = 2	cleverly	-0.000883 to 0.000491	0.9431	0.9975	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm1, relapse @ t=2]	cumulative incidence of relapse under the plan assign arm 1 at baseline and hold it at horizon t = 2	R survtmle, method="mean"	-0.000882 to 0.000492	0.9419	0.9863	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm1, relapse @ t=4]	cumulative incidence of relapse under the plan assign arm 1 at baseline and hold it at horizon t = 4	cleverly	-0.0013 to 0.000554	0.9537	0.9992	pass
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm1, relapse @ t=4]	cumulative incidence of relapse under the plan assign arm 1 at baseline and hold it at horizon t = 4	R survtmle, method="mean"	-0.0013 to 0.000554	0.9450	0.9649	pass
five visits, a binary baseline treatment held over every node, visit dropout	ate_regimen[arm1 vs arm0 @ t=1]	difference in cumulative risk between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 1	cleverly	-0.0010 to 0.000776	0.9619	1.0251	pass
five visits, a binary baseline treatment held over every node, visit dropout	ate_regimen[arm1 vs arm0 @ t=1]	difference in cumulative risk between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 1	R survtmle, method="mean"	-0.0010 to 0.000776	0.9619	1.0248	pass
five visits, a binary baseline treatment held over every node, visit dropout	ate_regimen[arm1 vs arm0 @ t=3]	difference in cumulative risk between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 3	cleverly	-0.0015 to 0.0013	0.9463	0.9948	pass
five visits, a binary baseline treatment held over every node, visit dropout	ate_regimen[arm1 vs arm0 @ t=3]	difference in cumulative risk between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 3	R survtmle, method="mean"	-0.0015 to 0.0013	0.9450	0.9837	pass
five visits, a binary baseline treatment held over every node, visit dropout	ate_regimen[arm1 vs arm0 @ t=5]	difference in cumulative risk between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 5	cleverly	-0.0026 to 0.000558	0.9450	0.9824	pass
five visits, a binary baseline treatment held over every node, visit dropout	ate_regimen[arm1 vs arm0 @ t=5]	difference in cumulative risk between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 5	R survtmle, method="mean"	-0.0026 to 0.000559	0.9381	0.9568	pass
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm0 @ t=1]	cumulative risk under the plan assign arm 0 at baseline and hold it at horizon t = 1	cleverly	-0.000572 to 0.000792	0.9637	1.0474	pass
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm0 @ t=1]	cumulative risk under the plan assign arm 0 at baseline and hold it at horizon t = 1	R survtmle, method="mean"	-0.000572 to 0.000792	0.9637	1.0471	pass
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm0 @ t=3]	cumulative risk under the plan assign arm 0 at baseline and hold it at horizon t = 3	cleverly	-0.0010 to 0.0011	0.9569	0.9999	pass
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm0 @ t=3]	cumulative risk under the plan assign arm 0 at baseline and hold it at horizon t = 3	R survtmle, method="mean"	-0.0010 to 0.0010	0.9569	1.0000	pass
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm0 @ t=5]	cumulative risk under the plan assign arm 0 at baseline and hold it at horizon t = 5	cleverly	-0.000624 to 0.0015	0.9506	1.0061	pass
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm0 @ t=5]	cumulative risk under the plan assign arm 0 at baseline and hold it at horizon t = 5	R survtmle, method="mean"	-0.000628 to 0.0015	0.9506	1.0065	pass
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm1 @ t=1]	cumulative risk under the plan assign arm 1 at baseline and hold it at horizon t = 1	cleverly	-0.000622 to 0.000589	0.9406	0.9728	pass
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm1 @ t=1]	cumulative risk under the plan assign arm 1 at baseline and hold it at horizon t = 1	R survtmle, method="mean"	-0.000622 to 0.000588	0.9406	0.9725	pass
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm1 @ t=3]	cumulative risk under the plan assign arm 1 at baseline and hold it at horizon t = 3	cleverly	-0.0011 to 0.000850	0.9475	0.9878	pass
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm1 @ t=3]	cumulative risk under the plan assign arm 1 at baseline and hold it at horizon t = 3	R survtmle, method="mean"	-0.0011 to 0.000850	0.9406	0.9639	pass
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm1 @ t=5]	cumulative risk under the plan assign arm 1 at baseline and hold it at horizon t = 5	cleverly	-0.0017 to 0.000572	0.9469	0.9879	pass
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm1 @ t=5]	cumulative risk under the plan assign arm 1 at baseline and hold it at horizon t = 5	R survtmle, method="mean"	-0.0017 to 0.000569	0.9287	0.9378	pass

Agreement with the canonical implementation

Comparator-backed: a paired comparison with survtmle 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
four visits, two competing causes, a held binary treatment, visit dropout	ate_regimen[arm1 vs arm0, death @ t=2]	difference in cumulative incidence of death between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 2	-1.396e-07	0.000068	1.0005	0.000625	different estimator	0.0069 vs 0.0500	equivalent
four visits, two competing causes, a held binary treatment, visit dropout	ate_regimen[arm1 vs arm0, death @ t=4]	difference in cumulative incidence of death between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 4	-6.531e-07	0.000241	1.0005	0.0056	different estimator	0.0233 vs 0.0500	superior
four visits, two competing causes, a held binary treatment, visit dropout	ate_regimen[arm1 vs arm0, relapse @ t=2]	difference in cumulative incidence of relapse between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 2	-3.299e-07	0.000142	1.0003	0.0012	different estimator	0.0113 vs 0.0500	equivalent
four visits, two competing causes, a held binary treatment, visit dropout	ate_regimen[arm1 vs arm0, relapse @ t=4]	difference in cumulative incidence of relapse between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 4	0.000001	0.000395	1.0004	0.0088	different estimator	0.0353 vs 0.0500	superior
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm0, death @ t=2]	cumulative incidence of death under the plan assign arm 0 at baseline and hold it at horizon t = 2	-0.000002	0.000896	1.0004	-0.000625	different estimator	0.000153 vs 0.0500	equivalent
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm0, death @ t=4]	cumulative incidence of death under the plan assign arm 0 at baseline and hold it at horizon t = 4	-0.000001	0.000496	1.0005	0	different estimator	0.000195 vs 0.0500	equivalent
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm0, relapse @ t=2]	cumulative incidence of relapse under the plan assign arm 0 at baseline and hold it at horizon t = 2	-7.538e-07	0.000462	1.0003	-0.000625	different estimator	0.000291 vs 0.0500	equivalent
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm0, relapse @ t=4]	cumulative incidence of relapse under the plan assign arm 0 at baseline and hold it at horizon t = 4	-0.000002	0.000877	1.0004	0.000625	different estimator	0.000205 vs 0.0500	equivalent
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm1, death @ t=2]	cumulative incidence of death under the plan assign arm 1 at baseline and hold it at horizon t = 2	-0.000002	0.0015	1.0003	0.0056	different estimator	0.0069 vs 0.0500	superior
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm1, death @ t=4]	cumulative incidence of death under the plan assign arm 1 at baseline and hold it at horizon t = 4	-0.000002	0.0011	1.0004	0.0069	different estimator	0.0168 vs 0.0500	superior
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm1, relapse @ t=2]	cumulative incidence of relapse under the plan assign arm 1 at baseline and hold it at horizon t = 2	-0.000001	0.000678	1.0004	0.0012	different estimator	0.0232 vs 0.0500	equivalent
four visits, two competing causes, a held binary treatment, visit dropout	cif_regimen[arm1, relapse @ t=4]	cumulative incidence of relapse under the plan assign arm 1 at baseline and hold it at horizon t = 4	-6.768e-07	0.000311	1.0004	0.0088	different estimator	0.0702 vs 0.0500 >	superior
five visits, a binary baseline treatment held over every node, visit dropout	ate_regimen[arm1 vs arm0 @ t=1]	difference in cumulative risk between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 1	4.393e-08	0.000021	1.0000	0	different estimator	0.000019 vs 0.0500	equivalent
five visits, a binary baseline treatment held over every node, visit dropout	ate_regimen[arm1 vs arm0 @ t=3]	difference in cumulative risk between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 3	2.294e-07	0.000070	1.0004	0.0013	different estimator	0.0227 vs 0.0500	equivalent
five visits, a binary baseline treatment held over every node, visit dropout	ate_regimen[arm1 vs arm0 @ t=5]	difference in cumulative risk between the plans “assign arm 1 at baseline and hold it” against “assign arm 0 at baseline and hold it” at horizon t = 5	-0.000001	0.000384	1.0005	0.0069	different estimator	0.0471 vs 0.0500	superior
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm0 @ t=1]	cumulative risk under the plan assign arm 0 at baseline and hold it at horizon t = 1	1.189e-09	7.490e-07	1.0000	0	different estimator	0.000023 vs 0.0500	equivalent
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm0 @ t=3]	cumulative risk under the plan assign arm 0 at baseline and hold it at horizon t = 3	4.474e-07	0.000186	1.0004	0	different estimator	0.000215 vs 0.0500	equivalent
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm0 @ t=5]	cumulative risk under the plan assign arm 0 at baseline and hold it at horizon t = 5	0.000004	0.0016	1.0006	0	different estimator	0.000894 vs 0.0500	equivalent
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm1 @ t=1]	cumulative risk under the plan assign arm 1 at baseline and hold it at horizon t = 1	4.512e-08	0.000032	1.0000	0	different estimator	0.000510 vs 0.0500	equivalent
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm1 @ t=3]	cumulative risk under the plan assign arm 1 at baseline and hold it at horizon t = 3	6.768e-07	0.000301	1.0004	0.0069	different estimator	0.0490 vs 0.0500	superior
five visits, a binary baseline treatment held over every node, visit dropout	risk_regimen[arm1 @ t=5]	cumulative risk under the plan assign arm 1 at baseline and hold it at horizon t = 5	0.000003	0.000982	1.0003	0.0181	different estimator	0.0579 vs 0.0500 >	superior

Theory properties

property	cell	role	what was tested	what must hold	measured	result
clustered_inference	clustered_t5__cluster_robust	positive	arm-0 risk at visit 5, 25 clusters of 80 that share W: five-fold point-treatment TMLE with cluster-robust ATE inference	SE-ratio and coverage intervals both stay inside their calibration bands	coverage 0.9385 to 0.9662, SE ratio 0.9560 to 1.0478, paired coverage gain 0.0838 to 0.1237	pass
clustered_inference	clustered_t5__iid_control	control	arm-0 risk at visit 5, 25 clusters of 80 that share W: the identical rows, point estimates, and influence curves treated as independent	the SE-ratio upper endpoint must not exceed the declared IID-control ceiling	coverage 0.8263 to 0.8728, SE ratio 0.7084 to 0.7747, paired coverage gain 0.0838 to 0.1237	pass
double_robustness	survival_t5__both_correct	positive	difference of arm 1 and arm 0 at visit 5, five-visit held law: both the outcome regression and the treatment mechanism are correctly specified	bias interval inside the equivalence margin, with the reported standard error on the scale of the empirical spread	bias -0.0011 to 0.0026, margin 0.0062, SE ratio 0.9769	pass
double_robustness	survival_t5__both_wrong	control	difference of arm 1 and arm 0 at visit 5, five-visit held law: both nuisances are misspecified	bias interval must fall entirely outside the margin, with the reported standard error still on the scale of the empirical spread	bias 0.0316 to 0.0352, margin 0.0061, SE ratio 0.9909	pass
double_robustness	survival_t5__mechanism_correct	positive	difference of arm 1 and arm 0 at visit 5, five-visit held law: only the treatment and censoring mechanisms are correctly specified	bias interval inside the equivalence margin, with the reported standard error on the scale of the empirical spread	bias -0.0016 to 0.0020, margin 0.0061, SE ratio 1.0083	pass
double_robustness	survival_t5__outcome_correct	positive	difference of arm 1 and arm 0 at visit 5, five-visit held law: only the outcome regression is correctly specified	bias interval inside the equivalence margin, with the reported standard error on the scale of the empirical spread	bias -0.0024 to 0.0012, margin 0.0062, SE ratio 0.9626	pass
interval_calibration	competing_t4__correctly_specified	positive	difference in the death incidence at visit 4, two causes: 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 0.9421 to 0.9689, SE ratio 0.9662 to 1.0596, empirical efficiency ratio 0.9429 to 1.0341, reported efficiency ratio 0.9976 to 1.0008	pass
interval_calibration	competing_t4__noise_control	control	difference in the death incidence at visit 4, two causes: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8039 to 0.8529, SE ratio 0.6808 to 0.7449, empirical efficiency ratio 1.3415 to 1.4677, reported efficiency ratio 0.9976 to 1.0008	pass
interval_calibration	competing_t4__shrunken_se_control	control	difference in the death incidence at visit 4, two causes: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8078 to 0.8564, SE ratio 0.6775 to 0.7423, empirical efficiency ratio 0.9421 to 1.0325, reported efficiency ratio 0.6983 to 0.7005	pass
interval_calibration	continuous_t4__correctly_specified	positive	difference at grid time 3, exponential event time, visit dropout: 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 0.9293 to 0.9592, SE ratio 0.9411 to 1.0294, empirical efficiency ratio 0.9708 to 1.0618, reported efficiency ratio 0.9986 to 1.0000	pass
interval_calibration	continuous_t4__noise_control	control	difference at grid time 3, exponential event time, visit dropout: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8012 to 0.8505, SE ratio 0.6567 to 0.7199, empirical efficiency ratio 1.3880 to 1.5217, reported efficiency ratio 0.9986 to 1.0000	pass
interval_calibration	continuous_t4__shrunken_se_control	control	difference at grid time 3, exponential event time, visit dropout: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7888 to 0.8393, SE ratio 0.6588 to 0.7212, empirical efficiency ratio 0.9702 to 1.0616, reported efficiency ratio 0.6990 to 0.7000	pass
interval_calibration	end_of_study__correctly_specified	positive	held end-of-study difference after two censoring nodes: 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 0.9603, SE ratio 0.9306 to 1.0218, empirical efficiency ratio 0.9786 to 1.0746, reported efficiency ratio 0.9993 to 1.0005	pass
interval_calibration	end_of_study__noise_control	control	held end-of-study difference after two censoring nodes: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8111 to 0.8594, SE ratio 0.6739 to 0.7385, empirical efficiency ratio 1.3542 to 1.4837, reported efficiency ratio 0.9993 to 1.0005	pass
interval_calibration	end_of_study__shrunken_se_control	control	held end-of-study difference after two censoring nodes: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7914 to 0.8417, SE ratio 0.6516 to 0.7139, empirical efficiency ratio 0.9805 to 1.0742, reported efficiency ratio 0.6995 to 0.7004	pass
interval_calibration	rmst_5__correctly_specified	positive	RMST difference up to visit 5, five-visit held 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 0.9429 to 0.9546, SE ratio 0.9842 to 1.0206, empirical efficiency ratio 0.9795 to 1.0156, reported efficiency ratio 0.9993 to 1.0001	pass
interval_calibration	rmst_5__noise_control	control	RMST difference up to visit 5, five-visit held law: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8262 to 0.8458, SE ratio 0.6983 to 0.7248, empirical efficiency ratio 1.3793 to 1.4316, reported efficiency ratio 0.9993 to 1.0002	pass
interval_calibration	rmst_5__shrunken_se_control	control	RMST difference up to visit 5, five-visit held law: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8226 to 0.8423, SE ratio 0.6885 to 0.7144, empirical efficiency ratio 0.9794 to 1.0164, reported efficiency ratio 0.6995 to 0.7001	pass
interval_calibration	survival_t5__correctly_specified	positive	difference of arm 1 and arm 0 at visit 5, five-visit held 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 0.9416 to 0.9534, SE ratio 0.9774 to 1.0144, empirical efficiency ratio 0.9857 to 1.0229, reported efficiency ratio 0.9996 to 1.0002	pass
interval_calibration	survival_t5__noise_control	control	difference of arm 1 and arm 0 at visit 5, five-visit held law: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8181 to 0.8380, SE ratio 0.6835 to 0.7098, empirical efficiency ratio 1.4086 to 1.4628, reported efficiency ratio 0.9996 to 1.0002	pass
interval_calibration	survival_t5__shrunken_se_control	control	difference of arm 1 and arm 0 at visit 5, five-visit held law: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8196 to 0.8395, SE ratio 0.6840 to 0.7097, empirical efficiency ratio 0.9862 to 1.0231, reported efficiency ratio 0.6997 to 0.7001	pass
interval_calibration	three_arm_t3__correctly_specified	positive	difference of arm 2 and arm 0 at visit 3, three arms with L_t: 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 0.9314 to 0.9608, SE ratio 0.9513 to 1.0400, empirical efficiency ratio 0.9610 to 1.0509, reported efficiency ratio 0.9986 to 1.0004	pass
interval_calibration	three_arm_t3__noise_control	control	difference of arm 2 and arm 0 at visit 3, three arms with L_t: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8045 to 0.8535, SE ratio 0.6770 to 0.7410, empirical efficiency ratio 1.3486 to 1.4764, reported efficiency ratio 0.9986 to 1.0004	pass
interval_calibration	three_arm_t3__shrunken_se_control	control	difference of arm 2 and arm 0 at visit 3, three arms with 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 0.7888 to 0.8393, SE ratio 0.6661 to 0.7270, empirical efficiency ratio 0.9627 to 1.0506, reported efficiency ratio 0.6990 to 0.7003	pass
interval_calibration	weighted_t5__correctly_specified	positive	difference at visit 5 under the weight 1 + W1 / 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 0.9421 to 0.9689, SE ratio 0.9807 to 1.0762, empirical efficiency ratio 0.9300 to 1.0204, reported efficiency ratio 1.0000 to 1.0015	fail
interval_calibration	weighted_t5__noise_control	control	difference at visit 5 under the weight 1 + W1 / 2: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8085 to 0.8570, SE ratio 0.6797 to 0.7429, empirical efficiency ratio 1.3471 to 1.4722, reported efficiency ratio 0.9999 to 1.0014	pass
interval_calibration	weighted_t5__shrunken_se_control	control	difference at visit 5 under the weight 1 + W1 / 2: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8197 to 0.8670, SE ratio 0.6875 to 0.7533, empirical efficiency ratio 0.9299 to 1.0187, reported efficiency ratio 0.7000 to 0.7010	pass
power	survival_t5__alternative	positive	difference of arm 1 and arm 0 at visit 5, five-visit held law: the same test applied to a law with a real effect	rejection lower bound clears the minimum power	rejection 1, 0.9934 to 1	pass
root_n_and_efficiency	survival_t5__n_1000	control	difference of arm 1 and arm 0 at visit 5, five-visit held law: bias, coverage and SE calibration at n = 1,000	coverage interval lies below nominal or clears the declared floor	bias -0.0010, coverage 0.9462 to 0.9805, SE ratio 1.0472	pass
root_n_and_efficiency	survival_t5__n_2000	positive	difference of arm 1 and arm 0 at visit 5, five-visit held law: bias, coverage and SE calibration at n = 2,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias -0.000173, coverage 0.9311 to 0.9708, SE ratio 0.9952	pass
root_n_and_efficiency	survival_t5__n_8000	positive	difference of arm 1 and arm 0 at visit 5, five-visit held law: bias, coverage and SE calibration at n = 8,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias -0.000019, coverage 0.9401 to 0.9767, SE ratio 1.0043	pass
root_n_rate	survival_t5__empirical_sd	positive	difference of arm 1 and arm 0 at visit 5, five-visit held law: 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 -0.5236 to -0.4440	pass
root_n_rate	survival_t5__reported_se	positive	difference of arm 1 and arm 0 at visit 5, five-visit held law: the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5007 to -0.4993	pass
simultaneous_coverage	all_reported__pointwise_joint_control	control	every parameter the calibration fit reports: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.6526 to 0.6775	pass
simultaneous_coverage	all_reported__simultaneous_band	positive	every parameter the calibration fit reports: 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 0.9400 to 0.9520	pass

The positive cells fit the saturated cell means, which are correct on these finite laws. Each calibration label reads one estimand on one law.

label	estimand
survival_t5	the difference of the two arm risks at visit 5
rmst_5	the difference of the restricted mean survival times at visit 5, on the survival_t5 fits
competing_t4	the difference of the death incidences at visit 4
three_arm_t3	arm 2 against arm 0 at visit 3, with a binary covariate measured at each visit, on the wide layout
continuous_t4	the difference at grid time 3, with an exponential event time binned onto the grid
end_of_study	the difference of the held end-of-study means after two censoring nodes
weighted_t5	the visit-5 difference on the law tilted by the weight 1 + W1 / 2
clustered_t5	the arm-0 risk at visit 5 on 25 clusters of 80 rows that share W

The weighted_t5__correctly_specified calibration cell is red on its SE-ratio band. The SE ratio is 1.027, and its 99% interval is 0.981 to 1.076 against an upper bound of 1.07. The coverage is 0.957. The reported standard error is the weighted efficiency bound to 0.07% (ratio 1.0007). The empirical spread is 2.5% below the bound, and its interval, 0.930 to 1.020, contains the bound.

The diagnostic tests/diagnostics/x13_weighted_calibration/ refits the cell on 1,000 fresh draws, and its module records the seeds and the command. It reads an SE ratio of 1.022, inside the band, an empirical efficiency ratio of 0.979, a reported efficiency ratio of 1.000 and a coverage of 0.957. The diagnosis finds no defect: at 1,600 replications the interval reaches past the band from a point of 1.027. By the declared route the cell stays red under reporting, with the owner row X13-finite-sample.

Measured values

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

quantity	value	source
replicates	1600	primary replications per scenario
n	2000	observations per primary replication
independent_tests_total	42	implementation-estimand tests against the truth
independent_tests_passed	42	of those, passing
paired_tests_total	21	paired comparisons with survtmle
paired_tests_passed	21	of those, passing
property_cells_total	35	repeated-sampling property cells
property_cells_passed	34	cells whose own and family verdicts pass
max_standardized_bias	0.0538	largest absolute primary bias in empirical standard deviations
min_coverage	0.9287	lowest measured primary-study coverage
min_se_ratio_ci_lower	0.8978	lowest bootstrap primary SE-ratio endpoint
max_se_ratio_ci_upper	1.0992	highest bootstrap primary SE-ratio endpoint
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. No cell of this study reads it
margin:calibration_coverage_upper	0.9800	calibration-cell coverage band, upper limit. No cell of this study reads it
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. No cell of this study reads it
margin:calibration_se_ratio_upper	1.0700	calibration-cell SE-ratio band, upper limit. No cell of this study reads it
margin:clustered_coverage_gain	0.0300	paired coverage-gain floor
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:efficiency_ratio_lower	0.9000	efficiency-ratio lower bound
margin:efficiency_ratio_upper	1.1000	efficiency-ratio upper bound
margin:excluded_slope	-0.2500	slower rate a root-n interval must exclude
margin:iid_control_se_ceiling	0.8000	IID-control SE-ratio ceiling
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
margin:union_model_se_lower	0.1000	union-model SE-ratio screen, lower limit
margin:union_model_se_upper	10	union-model SE-ratio screen, upper limit

Limitations

limit	what it means for use
one baseline treatment on finite laws	the evidence covers binary and three-arm baseline treatments on discrete covariates. A continuous dose has fast-tier evidence only
the paired rows are not an exactness check	the targeting submodels differ by construction, so the pairs read under the default margins
per-horizon targeting	each horizon has its own backward pass, so the curve is not constrained to be monotone. Hazard-based survival targeting covers hazard-based and whole-curve targeting
discrete time	a continuous event time is binned onto a declared grid. The continuous_t4 cell measures the binned parameter, not a continuous-time one
one calibration cell is red under reporting	the weighted_t5 SE-ratio interval reaches past its band. The reported standard error equals the efficiency bound. The X13-finite-sample owner holds it
survtmle’s bounds= is not paired	X33 part (h) owns it

Reproduction

The manifest records the seeds, the margins, the estimator configuration, the source hashes and the result hashes. Run python -m tests.canonical.point_survival.regenerate to regenerate the artifacts. The replications and the property results carry every published row.