Point survival hazard

This study validates longitudinal TMLE with survival_model="hazard" and targeting="iterative" 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). Each reported horizon targets the discrete cause-specific hazards of every regimen and cause on its own (Moore and van der Laan 2009, Section 4.1). The section hazard-based survival targeting states the estimator and its exact-law evidence.

The laws are the survival and competing scenarios of point-treatment survival. 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 comparator is R survtmle 1.1.1 with method = "hazard" (Benkeser, Carone and Gilbert 2018). The comparator runs are pending, so this study carries the label “Python property evidence, with comparator runs pending”. The runs are queued as Study queue row 20 in TRACKER.md. The comparison is not acceptance evidence for any claim until that row closes.

What was compared

setting	cleverly	R survtmle
status	run and published on this page	pending. No reference process ran, and equivalence.csv has no rows
datasets	1,600 samples of 2,000 rows for each scenario	the identical rows, once the runs exist
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
hazard model	an unpenalized logistic regression on W1, W2 and the arm at each node and cause	one pooled glm with the same terms for each visit and cause
targeting	targeting="iterative", all causes fluctuated together in a multinomial logistic submodel, stopped at a relative score of 1e-10	one cause at a time in a logistic submodel, stopped at `max
intervals	pointwise 95% Wald from the influence curve	the same

The pending runs read under the default margins. The two targeting loops differ by construction. The runner declares tol = 1/n and maxIter = 100. The survtmle default tol = 1/sqrt(n) stops before any targeting step at the laws of this study.

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	-0.000415 to 0.0013	0.9544	1.0251	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	-0.000787 to 0.0016	0.9519	0.9928	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	-0.000912 to 0.0010	0.9519	1.0157	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	-0.0013 to 0.0014	0.9475	0.9847	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	-0.000980 to 0.000460	0.9494	1.0075	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	-0.0011 to 0.000869	0.9431	0.9768	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	-0.000696 to 0.000665	0.9519	1.0255	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	-0.000883 to 0.000929	0.9500	1.0063	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	-0.000304 to 0.000656	0.9500	1.0170	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	-0.000387 to 0.000968	0.9519	1.0169	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	-0.000655 to 0.000727	0.9487	0.9937	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	-0.000883 to 0.0010	0.9456	0.9692	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	-0.000617 to 0.0012	0.9619	1.0254	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	-0.000543 to 0.0023	0.9506	0.9945	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	-0.0013 to 0.0019	0.9487	1.0009	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	-0.000909 to 0.000506	0.9519	1.0091	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	-0.0019 to 0.000165	0.9537	0.9877	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	-0.0017 to 0.000440	0.9525	1.0147	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	-0.000521 to 0.000688	0.9431	0.9757	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	-0.000956 to 0.000924	0.9594	1.0152	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	-0.0014 to 0.000779	0.9531	1.0188	pass

All 21 implementation-estimand tests pass. No replication raised an error, so no cell lost a replicate.

Theory properties

property	cell	role	what was tested	what must hold	measured	result
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 -0.0024 to 0.0013, margin 0.0062, SE ratio 0.9823	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 0.0330 to 0.0366, margin 0.0060, SE ratio 1.0075	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 -0.0027 to 0.000933, margin 0.0060, SE ratio 1.0206	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 -0.000803 to 0.0028, margin 0.0061, SE ratio 0.9720	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 0.9371 to 0.9541, SE ratio 0.9745 to 1.0264, empirical efficiency ratio 0.9740 to 1.0257, reported efficiency ratio 0.9986 to 1.0004	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 0.9445 to 0.9560, SE ratio 0.9859 to 1.0221, empirical efficiency ratio 0.9803 to 1.0162, reported efficiency ratio 1.0015 to 1.0021	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 0.8268 to 0.8464, SE ratio 0.6965 to 0.7223, empirical efficiency ratio 1.3868 to 1.4384, reported efficiency ratio 1.0015 to 1.0021	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 0.8252 to 0.8448, SE ratio 0.6892 to 0.7157, empirical efficiency ratio 0.9798 to 1.0175, reported efficiency ratio 0.7011 to 0.7015	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 -0.0022, coverage 0.9371 to 0.9747, SE ratio 1.0186	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 -0.000720, coverage 0.9311 to 0.9708, SE ratio 1.0110	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 0.000264, coverage 0.9252 to 0.9667, SE ratio 0.9897	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 -0.5286 to -0.4436	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 -0.5019 to -0.5005	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 0.6522 to 0.6772	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 0.9392 to 0.9512	pass
targeting_necessity	survival_t5__targeted	positive	difference of arm 1 and arm 0 at visit 5, five-visit held law: the estimator fluctuates a misspecified outcome model, so targeting does all the adjusting	bias interval inside the equivalence margin	bias -0.0014 to 0.0025, margin 0.0064	pass
targeting_necessity	survival_t5__untargeted	control	difference of arm 1 and arm 0 at visit 5, five-visit held law: the identical fit with every fluctuation step removed	bias interval must fall entirely outside the margin	bias 0.1405 to 0.1405, margin 0	pass

All 18 property cells pass. Each positive cell has a control that fails the same instrument in the opposite direction.

family	positive cells	control that must fail
interval_calibration	the visit-5 difference on survival, and the death incidence difference at visit 4 on competing	reported standard errors scaled by 0.7, and one efficiency-bound unit of added noise
double_robustness	the hazard correct, the mechanism correct, or both	both wrong
targeting_necessity	the targeted estimate with a wrong hazard and the correct mechanism	the plug-in of the same fit
root_n_and_efficiency	n = 2,000 and 8,000	n = 1,000
root_n_rate	the empirical spread and the reported standard error	none. The slope interval must exclude -0.25
power	the alternative on survival	none
simultaneous_coverage	the band over the fifteen reported parameters	the pointwise intervals read as a joint set

The correct mechanism learners are the saturated cell fits. The correct hazard learner is an additive logistic fit on survival, which targeting moves, and the saturated cell fit on competing. A saturated hazard fitted in sample is the maximum-likelihood estimate, so its initial score is zero and targeting does not move it. The untargeted control predicts one hazard for each node and both arms, so its plug-in contrast is zero in every sample. The necessity verdict rests on the targeted cell and on its displacement from the plug-in.

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	21	implementation-estimand tests against the truth
independent_tests_passed	21	of those, passing
property_cells_total	18	repeated-sampling property cells
property_cells_passed	18	cells whose own and family verdicts pass
max_standardized_bias	0.0543	largest absolute primary bias in empirical standard deviations
min_coverage	0.9431	lowest measured primary-study coverage
min_se_ratio_ci_lower	0.9287	lowest bootstrap primary SE-ratio endpoint
max_se_ratio_ci_upper	1.0758	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: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: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:targeting_displacement	0.2500	least targeting must move the estimate
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
the comparator runs are pending	no survtmle output is compared. The survtmle rows of Study queue row 20 follow, and this page is Python property evidence until then
per-horizon targeting only	targeting="one_step" and the monotone whole-curve estimate are outside this study
finite laws with discrete covariates	the evidence covers correct or misspecified low-dimensional logistic and saturated learners. A flexible learner is outside it
the declared survtmle settings differ	survtmle fluctuates one cause at a time. The pending pairs read under the default margins and not as an exactness check
no cross-fitting, weights or clusters	each is a separate composition and needs its own row

Reproduction

The manifest records the seeds, the margins, the estimator configuration, the source hashes and the result hashes. It records the comparator as pending, with the runner and the image source hashes. Run python -m tests.canonical.point_survival_hazard.regenerate to regenerate the artifacts. The replications and the property results carry every published row.