Cross-fitted competing-risk longitudinal TMLE

This study validates five-fold cumulative-incidence estimation for two competing causes. It covers two horizons, monotone censoring, static plans, and one dynamic plan. The comparison uses R lmtp 1.5.4 with the same realized outer folds.

Each fold runs an untargeted backward regression sequence on its training rows. One pooled fluctuation per node then targets the out-of-fold predictions over every follower. The cross-fitting section of the technical reference gives the construction. The pinned comparator instead fits each fold’s fluctuation on that fold’s training rows and carries it into the fold’s next regression. Upstream lmtp commit 9996b04 classifies that update as a bug. Each paired margin stays as registered.

The study reports each unique parameter once. The dynamic plan equals the always-treated plan at the first horizon. A structural test checks this identity outside repeated sampling.

What was compared

setting	cleverly	R lmtp
datasets	1,600 panels from the same finite-support law	the identical rows
causes	relapse and death	each cause fitted as the event, with the other cause in compete=
folds	one balanced five-fold assignment	the identical serialized assignment
plans	never treat, always treat, and continue when L2 equals one	the same unique plan and horizon combinations
mechanisms	exact treatment and censoring probabilities	the same exact per-node density ratios
sequential regressions	fold-specific untargeted intercept-only regressions	fold-specific SL.mean regressions on the same histories
targeting	one pooled fluctuation per node over every follower	a fluctuation on each fold’s training rows, carried into that fold’s next regression
learner path	scikit-learn estimators, called directly	lmtp’s internal run_ensemble replaced by the same single-learner fit, without SuperLearner’s inner cross-validation. The adapter checks the two agree to 1e-10 before every run
intervals	pointwise 95% Wald intervals from held-out influence curves	the same, after transforming one minus the incidence back to incidence

The outcome regressions are misspecified in this comparison. Therefore, targeting stays nonzero and the competing-event risk mask affects the result. The exact mechanisms and identical folds isolate those steps without making the comparison an oracle-law duplicate.

The two targeting steps now differ, and the paired table shows it. Before the pooled update, both implementations ran the same fold-local update, and the largest paired mean difference was below 2e-9 in absolute value. Under the pooled update, the largest one is -0.000195, for cif_regimen[continue_if_l2, relapse @ t=2], against a margin of 0.004029. Every paired comparison still concludes equivalent.

Accuracy against known truth

law	estimand	what was tested	implementation	bias (99% interval)	coverage	SE ratio	result
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[always vs never, death @ t=1]	difference in cumulative incidence of death between the plans “treat at both times” against “treat at neither time” at horizon t = 1	cleverly cross-fitted competing-risk LTMLE	-0.0014 to 0.000982	0.9463	1.0030	pass
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[always vs never, death @ t=1]	difference in cumulative incidence of death between the plans “treat at both times” against “treat at neither time” at horizon t = 1	R lmtp	-0.0015 to 0.000965	0.9450	1.0027	pass
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[always vs never, death @ t=2]	difference in cumulative incidence of death between the plans “treat at both times” against “treat at neither time” at horizon t = 2	cleverly cross-fitted competing-risk LTMLE	-0.000199 to 0.0039	0.9537	1.0044	pass
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[always vs never, death @ t=2]	difference in cumulative incidence of death between the plans “treat at both times” against “treat at neither time” at horizon t = 2	R lmtp	-0.000189 to 0.0039	0.9537	1.0052	pass
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[always vs never, relapse @ t=1]	difference in cumulative incidence of relapse between the plans “treat at both times” against “treat at neither time” at horizon t = 1	cleverly cross-fitted competing-risk LTMLE	-0.0019 to 0.000525	0.9444	0.9908	pass
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[always vs never, relapse @ t=1]	difference in cumulative incidence of relapse between the plans “treat at both times” against “treat at neither time” at horizon t = 1	R lmtp	-0.0019 to 0.000557	0.9444	0.9909	pass
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[always vs never, relapse @ t=2]	difference in cumulative incidence of relapse between the plans “treat at both times” against “treat at neither time” at horizon t = 2	cleverly cross-fitted competing-risk LTMLE	-0.0037 to 0.000193	0.9475	0.9947	pass
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[always vs never, relapse @ t=2]	difference in cumulative incidence of relapse between the plans “treat at both times” against “treat at neither time” at horizon t = 2	R lmtp	-0.0038 to 0.000153	0.9481	0.9971	pass
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[continue_if_l2 vs never, death @ t=2]	difference in cumulative incidence of death between the plans “treat first, then continue if L2 equals one” against “treat at neither time” at horizon t = 2	cleverly cross-fitted competing-risk LTMLE	-0.000981 to 0.0029	0.9437	0.9946	pass
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[continue_if_l2 vs never, death @ t=2]	difference in cumulative incidence of death between the plans “treat first, then continue if L2 equals one” against “treat at neither time” at horizon t = 2	R lmtp	-0.001000 to 0.0029	0.9444	0.9979	pass
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[continue_if_l2 vs never, relapse @ t=2]	difference in cumulative incidence of relapse between the plans “treat first, then continue if L2 equals one” against “treat at neither time” at horizon t = 2	cleverly cross-fitted competing-risk LTMLE	-0.0031 to 0.000864	0.9481	0.9966	pass
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[continue_if_l2 vs never, relapse @ t=2]	difference in cumulative incidence of relapse between the plans “treat first, then continue if L2 equals one” against “treat at neither time” at horizon t = 2	R lmtp	-0.0029 to 0.0010	0.9500	0.9998	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[always, death @ t=1]	cumulative incidence of death under the plan treat at both times at horizon t = 1	cleverly cross-fitted competing-risk LTMLE	-0.0010 to 0.000955	0.9456	1.0066	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[always, death @ t=1]	cumulative incidence of death under the plan treat at both times at horizon t = 1	R lmtp	-0.0010 to 0.000949	0.9469	1.0063	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[always, death @ t=2]	cumulative incidence of death under the plan treat at both times at horizon t = 2	cleverly cross-fitted competing-risk LTMLE	-0.000165 to 0.0034	0.9431	1.0085	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[always, death @ t=2]	cumulative incidence of death under the plan treat at both times at horizon t = 2	R lmtp	-0.000150 to 0.0034	0.9425	1.0090	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[always, relapse @ t=1]	cumulative incidence of relapse under the plan treat at both times at horizon t = 1	cleverly cross-fitted competing-risk LTMLE	-0.0015 to 0.000674	0.9425	0.9762	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[always, relapse @ t=1]	cumulative incidence of relapse under the plan treat at both times at horizon t = 1	R lmtp	-0.0014 to 0.000704	0.9425	0.9759	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[always, relapse @ t=2]	cumulative incidence of relapse under the plan treat at both times at horizon t = 2	cleverly cross-fitted competing-risk LTMLE	-0.0028 to 0.000726	0.9419	0.9869	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[always, relapse @ t=2]	cumulative incidence of relapse under the plan treat at both times at horizon t = 2	R lmtp	-0.0028 to 0.000714	0.9413	0.9881	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[continue_if_l2, death @ t=2]	cumulative incidence of death under the plan treat first, then continue if L2 equals one at horizon t = 2	cleverly cross-fitted competing-risk LTMLE	-0.000926 to 0.0024	0.9413	1.0000	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[continue_if_l2, death @ t=2]	cumulative incidence of death under the plan treat first, then continue if L2 equals one at horizon t = 2	R lmtp	-0.000938 to 0.0024	0.9413	1.0046	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[continue_if_l2, relapse @ t=2]	cumulative incidence of relapse under the plan treat first, then continue if L2 equals one at horizon t = 2	cleverly cross-fitted competing-risk LTMLE	-0.0021 to 0.0014	0.9431	0.9932	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[continue_if_l2, relapse @ t=2]	cumulative incidence of relapse under the plan treat first, then continue if L2 equals one at horizon t = 2	R lmtp	-0.0019 to 0.0016	0.9463	0.9975	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[never, death @ t=1]	cumulative incidence of death under the plan treat at neither time at horizon t = 1	cleverly cross-fitted competing-risk LTMLE	-0.000532 to 0.000943	0.9437	0.9647	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[never, death @ t=1]	cumulative incidence of death under the plan treat at neither time at horizon t = 1	R lmtp	-0.000521 to 0.000955	0.9437	0.9646	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[never, death @ t=2]	cumulative incidence of death under the plan treat at neither time at horizon t = 2	cleverly cross-fitted competing-risk LTMLE	-0.0012 to 0.000787	0.9469	0.9712	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[never, death @ t=2]	cumulative incidence of death under the plan treat at neither time at horizon t = 2	R lmtp	-0.0012 to 0.000793	0.9469	0.9714	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[never, relapse @ t=1]	cumulative incidence of relapse under the plan treat at neither time at horizon t = 1	cleverly cross-fitted competing-risk LTMLE	-0.000320 to 0.000934	0.9469	0.9959	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[never, relapse @ t=1]	cumulative incidence of relapse under the plan treat at neither time at horizon t = 1	R lmtp	-0.000322 to 0.000932	0.9463	0.9962	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[never, relapse @ t=2]	cumulative incidence of relapse under the plan treat at neither time at horizon t = 2	cleverly cross-fitted competing-risk LTMLE	-0.000210 to 0.0017	0.9363	0.9600	pass
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[never, relapse @ t=2]	cumulative incidence of relapse under the plan treat at neither time at horizon t = 2	R lmtp	-0.000183 to 0.0017	0.9394	0.9607	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-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[always vs never, death @ t=1]	difference in cumulative incidence of death between the plans “treat at both times” against “treat at neither time” at horizon t = 1	0.000018	0.0062	1.0007	0.0013	different estimator	0.000953 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[always vs never, death @ t=2]	difference in cumulative incidence of death between the plans “treat at both times” against “treat at neither time” at horizon t = 2	-0.000010	0.0021	1.0037	0	different estimator	0.0048 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[always vs never, relapse @ t=1]	difference in cumulative incidence of relapse between the plans “treat at both times” against “treat at neither time” at horizon t = 1	-0.000031	0.0110	1.0011	0	different estimator	0.000925 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[always vs never, relapse @ t=2]	difference in cumulative incidence of relapse between the plans “treat at both times” against “treat at neither time” at horizon t = 2	0.000037	0.0081	1.0049	-0.000625	different estimator	0.0027 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[continue_if_l2 vs never, death @ t=2]	difference in cumulative incidence of death between the plans “treat first, then continue if L2 equals one” against “treat at neither time” at horizon t = 2	0.000023	0.0051	1.0051	-0.000625	different estimator	0.0028 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	ate_regimen[continue_if_l2 vs never, relapse @ t=2]	difference in cumulative incidence of relapse between the plans “treat first, then continue if L2 equals one” against “treat at neither time” at horizon t = 2	-0.000169	0.0370	1.0047	-0.0019	different estimator	0.0025 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[always, death @ t=1]	cumulative incidence of death under the plan treat at both times at horizon t = 1	0.000006	0.0028	1.0009	-0.0012	different estimator	0.0011 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[always, death @ t=2]	cumulative incidence of death under the plan treat at both times at horizon t = 2	-0.000016	0.0038	1.0037	0.000625	different estimator	0.0043 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[always, relapse @ t=1]	cumulative incidence of relapse under the plan treat at both times at horizon t = 1	-0.000029	0.0117	1.0009	0	different estimator	0.0012 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[always, relapse @ t=2]	cumulative incidence of relapse under the plan treat at both times at horizon t = 2	0.000011	0.0026	1.0039	0.000625	different estimator	0.0032 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[continue_if_l2, death @ t=2]	cumulative incidence of death under the plan treat first, then continue if L2 equals one at horizon t = 2	0.000017	0.0044	1.0065	0	different estimator	0.0121 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[continue_if_l2, relapse @ t=2]	cumulative incidence of relapse under the plan treat first, then continue if L2 equals one at horizon t = 2	-0.000195	0.0484	1.0057	-0.0031	different estimator	0.0027 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[never, death @ t=1]	cumulative incidence of death under the plan treat at neither time at horizon t = 1	-0.000011	0.0065	1.0004	0	different estimator	0.000557 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[never, death @ t=2]	cumulative incidence of death under the plan treat at neither time at horizon t = 2	-0.000006	0.0026	1.0019	0	different estimator	0.0020 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[never, relapse @ t=1]	cumulative incidence of relapse under the plan treat at neither time at horizon t = 1	0.000002	0.0015	1.0008	0.000625	different estimator	0.000476 vs 0.0500	equivalent
two-time-point, two-cause competing-risk law with monotone censoring	cif_regimen[never, relapse @ t=2]	cumulative incidence of relapse under the plan treat at neither time at horizon t = 2	-0.000026	0.0118	1.0022	-0.0031	different estimator	0.0019 vs 0.0500	equivalent

Theory properties

property	cell	role	what was tested	what must hold	measured	result
competing_risk_recursion_necessity	death_always_t2__all_cause	positive	always-treat death incidence at horizon two: the estimator removes every first-node event from the later risk set	bias interval inside the equivalence margin	bias -0.0041 to 0.000037, margin 0.0070	pass
competing_risk_recursion_necessity	death_always_t2__cause_specific_control	control	always-treat death incidence at horizon two: the same recursion wrongly lets the competing cause remain at risk	bias interval must fall entirely outside the margin	bias 0.1475 to 0.1564, margin 0.0150	pass
competing_risk_recursion_necessity	relapse_always_t2__all_cause	positive	always-treat relapse incidence at horizon two: the estimator removes every first-node event from the later risk set	bias interval inside the equivalence margin	bias -0.000219 to 0.0037, margin 0.0067	pass
competing_risk_recursion_necessity	relapse_always_t2__cause_specific_control	control	always-treat relapse incidence at horizon two: the same recursion wrongly lets the competing cause remain at risk	bias interval must fall entirely outside the margin	bias 0.0621 to 0.0685, margin 0.0108	pass
crossfit_overfitting	cross_fitted_competing_ltmle	positive	five-fold horizon-two competing-risk LTMLE with a fully grown outcome tree	SE ratio clears the overfitting floor and stays inside the sanity band	SE ratio 0.9682 to 1.0094	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 0.3940 to 0.4101	pass
double_robustness	death_static_t2__both_correct	positive	static death contrast at horizon two: 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 -0.0028 to 0.0019, margin 0.0080, SE ratio 0.9861	pass
double_robustness	death_static_t2__both_wrong	control	static death contrast at horizon two: 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 -0.0184 to -0.0139, margin 0.0074, SE ratio 0.7384	pass
double_robustness	death_static_t2__mechanism_correct	positive	static death contrast at horizon two: 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 -0.000715 to 0.0040, margin 0.0079, SE ratio 1.0031	pass
double_robustness	death_static_t2__outcome_correct	positive	static death contrast at horizon two: 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 -0.0027 to 0.0020, margin 0.0079, SE ratio 0.6928	pass
double_robustness	relapse_dynamic_t2__both_correct	positive	dynamic relapse contrast at horizon two: 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 -0.0026 to 0.0018, margin 0.0074, SE ratio 1.0309	pass
double_robustness	relapse_dynamic_t2__both_wrong	control	dynamic relapse contrast at horizon two: 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 0.0279 to 0.0324, margin 0.0075, SE ratio 0.7503	pass
double_robustness	relapse_dynamic_t2__mechanism_correct	positive	dynamic relapse contrast at horizon two: 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 -0.0035 to 0.0012, margin 0.0079, SE ratio 0.9574	pass
double_robustness	relapse_dynamic_t2__outcome_correct	positive	dynamic relapse contrast at horizon two: 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 -0.0023 to 0.0023, margin 0.0076, SE ratio 0.7391	pass
interval_calibration	death_static_t2__correctly_specified	positive	static death contrast at horizon two: 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 0.9539, SE ratio 0.9749 to 1.0124, empirical efficiency ratio 0.9896 to 1.0277, reported efficiency ratio 1.0014 to 1.0023	pass
interval_calibration	death_static_t2__noise_control	control	static death contrast at horizon two: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8265 to 0.8461, SE ratio 0.6958 to 0.7220, empirical efficiency ratio 1.3876 to 1.4398, reported efficiency ratio 1.0014 to 1.0023	pass
interval_calibration	death_static_t2__shrunken_se_control	control	static death contrast at horizon two: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8164 to 0.8364, SE ratio 0.6826 to 0.7083, empirical efficiency ratio 0.9902 to 1.0275, reported efficiency ratio 0.7010 to 0.7016	pass
interval_calibration	relapse_dynamic_t2__correctly_specified	positive	dynamic relapse contrast at horizon two: 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 0.9431 to 0.9548, SE ratio 0.9734 to 1.0097, empirical efficiency ratio 0.9919 to 1.0289, reported efficiency ratio 1.0011 to 1.0020	pass
interval_calibration	relapse_dynamic_t2__noise_control	control	dynamic relapse contrast at horizon two: 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 0.8432, SE ratio 0.6987 to 0.7254, empirical efficiency ratio 1.3807 to 1.4331, reported efficiency ratio 1.0011 to 1.0020	pass
interval_calibration	relapse_dynamic_t2__shrunken_se_control	control	dynamic relapse contrast at horizon two: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8169 to 0.8369, SE ratio 0.6820 to 0.7072, empirical efficiency ratio 0.9914 to 1.0282, reported efficiency ratio 0.7008 to 0.7014	pass
power	death_static_t2__alternative	positive	static death contrast at horizon two: the same test applied to a law with a real effect	rejection lower bound clears the minimum power	rejection 0.9950, 0.9884 to 0.9984	pass
power	relapse_dynamic_t2__alternative	positive	dynamic relapse contrast at horizon two: the same test applied to a law with a real effect	rejection lower bound clears the minimum power	rejection 0.9869, 0.9776 to 0.9931	pass
root_n_and_efficiency	death_static_t2__n_32000	positive	static death contrast at horizon two: bias, coverage and SE calibration at n = 32,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias -0.000006, coverage 0.9336 to 0.9624, SE ratio 1.0121	pass
root_n_and_efficiency	death_static_t2__n_4000	positive	static death contrast at horizon two: bias, coverage and SE calibration at n = 4,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias -0.0011, coverage 0.9210 to 0.9526, SE ratio 0.9947	pass
root_n_and_efficiency	death_static_t2__n_8000	positive	static death contrast at horizon two: bias, coverage and SE calibration at n = 8,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias -0.0012, coverage 0.9357 to 0.9641, SE ratio 1.0091	pass
root_n_and_efficiency	relapse_dynamic_t2__n_32000	positive	dynamic relapse contrast at horizon two: bias, coverage and SE calibration at n = 32,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000064, coverage 0.9350 to 0.9635, SE ratio 1.0298	pass
root_n_and_efficiency	relapse_dynamic_t2__n_4000	positive	dynamic relapse contrast at horizon two: bias, coverage and SE calibration at n = 4,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias -0.000059, coverage 0.9364 to 0.9646, SE ratio 1.0089	pass
root_n_and_efficiency	relapse_dynamic_t2__n_8000	positive	dynamic relapse contrast at horizon two: bias, coverage and SE calibration at n = 8,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000896, coverage 0.9203 to 0.9521, SE ratio 0.9904	pass
root_n_rate	death_static_t2__empirical_sd	positive	static death contrast at horizon two: 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 -0.5445 to -0.4829	pass
root_n_rate	death_static_t2__reported_se	positive	static death contrast at horizon two: the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5073 to -0.5043	pass
root_n_rate	relapse_dynamic_t2__empirical_sd	positive	dynamic relapse contrast at horizon two: 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 -0.5484 to -0.4876	pass
root_n_rate	relapse_dynamic_t2__reported_se	positive	dynamic relapse contrast at horizon two: the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5065 to -0.5035	pass
targeting_necessity	death_static_t2__targeted	positive	static death contrast at horizon two: the estimator fluctuates a misspecified outcome model, so targeting does all the adjusting	bias interval inside the equivalence margin	bias -0.000266 to 0.0044, margin 0.0079	pass
targeting_necessity	death_static_t2__untargeted	control	static death contrast at horizon two: the identical fit with every fluctuation step removed	bias interval must fall entirely outside the margin	bias -0.0155 to -0.0109, margin 0.0077	pass
targeting_necessity	relapse_dynamic_t2__targeted	positive	dynamic relapse contrast at horizon two: the estimator fluctuates a misspecified outcome model, so targeting does all the adjusting	bias interval inside the equivalence margin	bias -0.0025 to 0.0020, margin 0.0074	pass
targeting_necessity	relapse_dynamic_t2__untargeted	control	dynamic relapse contrast at horizon two: the identical fit with every fluctuation step removed	bias interval must fall entirely outside the margin	bias 0.0262 to 0.0304, margin 0.0072	pass
type_i_error	death_static_t2__sharp_null	positive	static death contrast at horizon two: a confounded law whose true contrast is exactly zero	one-sided rejection bound stays under the declared type-I ceiling	rejection 0.0581, 0.0441 to 0.0749	pass
type_i_error	relapse_dynamic_t2__sharp_null	positive	dynamic relapse contrast at horizon two: a confounded law whose true contrast is exactly zero	one-sided rejection bound stays under the declared type-I ceiling	rejection 0.0612, 0.0468 to 0.0784	pass

The property study keeps the ordinary row’s two-cause instruments. It also pairs a fully grown outcome tree with the same fit without cross-fitting. The joint verdict requires cross-fitting to restore standard-error scale and improve coverage. Under the pooled update the cross-fitted ratio is 0.987990, with a 99% interval from 0.968219 to 1.009389. The fold-fluctuated construction gave 1.092332 on the same seeds.

At the second horizon a baseline-only standardisation misses the null by -0.0077 for death and 0.0091 for relapse. The null is therefore one an estimator has to be longitudinal to find. At the first horizon that same analysis returns exactly zero, because no time-varying node precedes the first event node. A crude comparison of arms is biased at both horizons, so the first-horizon cells still test baseline and censoring adjustment.

Measured values

Names beginning margin: are thresholds declared before the run. The other values come from the committed results.

quantity	value	source
replicates	1600	paired replications
n	4000	observations per paired replication
independent_tests_total	32	implementation-estimand truth tests
independent_tests_passed	32	truth tests passing
paired_tests_total	16	paired estimand comparisons
paired_tests_passed	16	paired comparisons passing
property_cells_total	38	independent property cells
property_cells_passed	38	property cells passing
max_standardized_bias	0.0595	largest primary standardized bias
min_coverage	0.9363	lowest primary coverage
min_coverage_ci_lower	0.9189	lowest primary coverage lower endpoint
min_se_ratio_ci_lower	0.9187	lowest primary SE-ratio endpoint
max_se_ratio_ci_upper	1.0576	highest primary SE-ratio endpoint
properties[crossfit_overfitting/cross_fitted_competing_ltmle]:coverage	0.9460	cross-fitted tree coverage
properties[crossfit_overfitting/in_sample_control]:coverage	0.5650	in-sample tree coverage
properties[crossfit_overfitting/cross_fitted_competing_ltmle]:coverage_gain_ci_lower	0.3673	lower bound for the paired coverage gain
properties[crossfit_overfitting/cross_fitted_competing_ltmle]:replicates	8000	paired overfitting replications
properties[targeting_necessity/relapse_dynamic_t2__targeted]:targeting_displacement	0.4859	least paired targeting displacement
properties[competing_risk_recursion_necessity/relapse_always_t2__all_cause]:recursion_displacement	2.3835	least competing-risk recursion displacement
margin:confidence_level	0.9900	Monte Carlo confidence level
margin:alpha	0.0500	test size
margin:nominal_coverage	0.9500	nominal interval coverage
margin:bootstrap_replicates	10000	bootstrap replications
margin:standardized_bias	0.2500	standardized-bias margin
margin:coverage_floor	0.9000	primary coverage floor
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: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:type_i_ceiling	0.1000	type-I upper bound
margin:paired_difference	0.1500	paired similarity margin
margin:rmse_noninferiority	1.1000	RMSE-ratio noninferiority bound
margin:coverage_noninferiority	-0.0250	coverage-difference noninferiority bound
margin:calibration_noninferiority	0.0500	calibration-excess noninferiority bound
margin:minimum_power	0.8000	power lower bound
margin:root_n_slope	-0.5000	expected root-n slope
margin:root_n_slope_lower	-0.6250	accepted slope lower bound
margin:root_n_slope_upper	-0.3750	accepted slope upper bound
margin:excluded_slope	-0.2500	rate the interval must exclude
margin:union_model_se_lower	0.1000	union-model SE-ratio screen, lower limit
margin:union_model_se_upper	10	union-model SE-ratio screen, upper limit
margin: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	deliberate SE mutation factor
margin:targeting_displacement	0.2500	least required targeting displacement
margin:recursion_displacement	0.2500	least required recursion displacement
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:overfit_coverage_gain	0.1500	minimum paired coverage gain

Limitations

limitation	what it means for use
Agreement with lmtp is distributional	The paired claim tests mean similarity and non-inferiority, not rowwise numerical equality. lmtp 1.5.4 targets on each fold’s training rows, and cleverly runs one pooled fluctuation per node
One fixed five-fold assignment is studied	The row does not validate repeated folds or time-respecting splits
The comparison covers two causes and two horizons	Longer event processes and more causes need separate evidence
The first-horizon null is not a longitudinal null	No time-varying node precedes the first event node, so a baseline-only standardisation recovers that null exactly. The first-horizon type-I cells test baseline and censoring adjustment only
The inference is pointwise	The row does not validate simultaneous bands across causes, plans, or horizons. The default-band study measures the default band of this study’s subject fit.
The mechanisms are supplied	The comparison does not test learned-mechanism parity or active truncation
Competing events remain natural	The row does not validate an estimand that eliminates a competing event
The data are independent and unweighted	The row does not validate observation weights or clustering

The causal interpretation requires consistency, sequential exchangeability, longitudinal positivity, conditionally independent censoring, and correct competing-event coding.

Reproduction

The fixture README gives the commands. The manifest records the seeds, configuration, source digests, and artifact hashes.