Cross-fitted survival-curve longitudinal TMLE

This study validates five-fold cumulative-risk estimation under absorbing failure. It covers two horizons, monotone censoring, static plans, and a dynamic plan. 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 canonical comparison uses R lmtp 1.5.4 at commit f04a2b4, on the same panels and the same stored fold assignment, with one fitted prefix per reported horizon. R ltmle has no cross-fitting, so it cannot witness this construction.

The pinned comparator runs a different targeting step. lmtp 1.5.4 fits each fold’s fluctuation on that fold’s training rows and carries the targeted prediction into the fold’s next regression. Upstream commit 9996b04 classifies that update as a bug. Each paired margin stays as registered, so each paired verdict compares two constructions.

Agreement with R is secondary to the finite-support functional and Gateaux EIF in tests/discrete_law_survival.py.

What was compared

setting	cleverly	R lmtp
datasets and folds	1,600 censored survival panels, each with one exact five-fold assignment	the identical rows and the identical assignment
horizons	cumulative risk at times one and two	one fitted prefix per horizon
plans	never treat, always treat, and continue after initial treatment when L2 is positive	the same three, as shifted treatment columns
contrasts	always-minus-never at both horizons and dynamic-minus-never at time two	the same, from rowwise influence-curve differences
treatment and censoring mechanisms	the generating probabilities from the law	the same probabilities, supplied as exact per-node density ratios
sequential regressions	untargeted quasibinomial GLMs within each outer training set	SL.glm, within the same training sets
targeting	one pooled fluctuation per node over every follower	a fluctuation on each fold’s training rows, carried into that fold’s next regression
intervals	pointwise 95% identity-scale Wald intervals	the same, after the horizon-two transformation below

Both implementations receive the mechanism from the law rather than estimating it. lmtp has no gform argument, so the adapter substitutes exact per-node density ratios into it, the same way it substitutes the fold assignment. The substitution is checked on every run against lmtp’s own estimate: the zero pattern must agree cell for cell, and the cumulative ratio must track it.

That choice is what makes the comparison a comparison. An earlier version let each side estimate the mechanism its own way, and the result measured two unrelated pipelines. lmtp fits its ratio with SL.glm, whose linear logit cannot represent the exact classifier log-odds -log g for a deterministic regime, so the ratio came out shrunken. A shrunken clever covariate under-targets and understates the influence curve: that earlier probe measured coverage from 0.75 to 0.91 and an SE ratio from 0.60 to 0.86. No committed artifact holds its rows, because supplying the mechanism retired it. This row’s own committed rows give cleverly coverage from 0.9444 to 0.9525 and an SE ratio from 0.9853 to 1.0063. The sequential regressions stay misspecified on both sides, so targeting still has work to do.

The retained R runner uses the one-node binary mean at horizon one because lmtp requires two event nodes for its survival path. At horizon two, it converts event-free survival to cumulative risk and reverses the influence-curve sign. The registered run invokes that runner, so the transformation is exercised on every regeneration rather than described.

The exact-law structural test repeats every support point in each fold. It checks every unique risk and contrast against the finite functional and Gateaux EIF. Separate mutations check held-out outcome predictions and the first-horizon risk-set boundary.

Accuracy against known truth

law	estimand	what was tested	implementation	bias (99% interval)	coverage	SE ratio	result
two-time-point absorbing-event law with monotone censoring	ate_regimen[always vs never @ t=1]	difference in cumulative risk between the plans “treat at both times” against “treat at neither time” at horizon t = 1	cleverly cross-fitted survival LTMLE	-0.000324 to 0.0022	0.9513	0.9853	pass
two-time-point absorbing-event law with monotone censoring	ate_regimen[always vs never @ t=1]	difference in cumulative risk between the plans “treat at both times” against “treat at neither time” at horizon t = 1	R lmtp	-0.000333 to 0.0022	0.9519	0.9847	pass
two-time-point absorbing-event law with monotone censoring	ate_regimen[always vs never @ t=2]	difference in cumulative risk between the plans “treat at both times” against “treat at neither time” at horizon t = 2	cleverly cross-fitted survival LTMLE	-0.0013 to 0.0024	0.9469	0.9932	pass
two-time-point absorbing-event law with monotone censoring	ate_regimen[always vs never @ t=2]	difference in cumulative risk between the plans “treat at both times” against “treat at neither time” at horizon t = 2	R lmtp	-0.0013 to 0.0025	0.9444	0.9953	pass
two-time-point absorbing-event law with monotone censoring	ate_regimen[treat then continue if l2 positive vs never @ t=2]	difference in cumulative risk between the plans “treat, then continue only if L2 is positive” against “treat at neither time” at horizon t = 2	cleverly cross-fitted survival LTMLE	-0.0012 to 0.0027	0.9463	0.9877	pass
two-time-point absorbing-event law with monotone censoring	ate_regimen[treat then continue if l2 positive vs never @ t=2]	difference in cumulative risk between the plans “treat, then continue only if L2 is positive” against “treat at neither time” at horizon t = 2	R lmtp	-0.0011 to 0.0027	0.9437	0.9892	pass
two-time-point absorbing-event law with monotone censoring	risk_regimen[always @ t=1]	cumulative risk under the plan treat at both times at horizon t = 1	cleverly cross-fitted survival LTMLE	-0.000523 to 0.0010	0.9525	0.9988	pass
two-time-point absorbing-event law with monotone censoring	risk_regimen[always @ t=1]	cumulative risk under the plan treat at both times at horizon t = 1	R lmtp	-0.000505 to 0.0010	0.9544	0.9981	pass
two-time-point absorbing-event law with monotone censoring	risk_regimen[always @ t=2]	cumulative risk under the plan treat at both times at horizon t = 2	cleverly cross-fitted survival LTMLE	-0.000907 to 0.0014	0.9525	0.9912	pass
two-time-point absorbing-event law with monotone censoring	risk_regimen[always @ t=2]	cumulative risk under the plan treat at both times at horizon t = 2	R lmtp	-0.000918 to 0.0014	0.9506	0.9908	pass
two-time-point absorbing-event law with monotone censoring	risk_regimen[never @ t=1]	cumulative risk under the plan treat at neither time at horizon t = 1	cleverly cross-fitted survival LTMLE	-0.0017 to 0.000297	0.9463	0.9995	pass
two-time-point absorbing-event law with monotone censoring	risk_regimen[never @ t=1]	cumulative risk under the plan treat at neither time at horizon t = 1	R lmtp	-0.0016 to 0.000321	0.9475	1.0004	pass
two-time-point absorbing-event law with monotone censoring	risk_regimen[never @ t=2]	cumulative risk under the plan treat at neither time at horizon t = 2	cleverly cross-fitted survival LTMLE	-0.0018 to 0.0012	0.9444	1.0063	pass
two-time-point absorbing-event law with monotone censoring	risk_regimen[never @ t=2]	cumulative risk under the plan treat at neither time at horizon t = 2	R lmtp	-0.0018 to 0.0011	0.9525	1.0122	pass
two-time-point absorbing-event law with monotone censoring	risk_regimen[treat then continue if l2 positive @ t=2]	cumulative risk under the plan treat, then continue only if L2 is positive at horizon t = 2	cleverly cross-fitted survival LTMLE	-0.000760 to 0.0017	0.9481	0.9870	pass
two-time-point absorbing-event law with monotone censoring	risk_regimen[treat then continue if l2 positive @ t=2]	cumulative risk under the plan treat, then continue only if L2 is positive at horizon t = 2	R lmtp	-0.000782 to 0.0016	0.9463	0.9866	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 absorbing-event law with monotone censoring	ate_regimen[always vs never @ t=1]	difference in cumulative risk between the plans “treat at both times” against “treat at neither time” at horizon t = 1	0.000009	0.0029	1.0016	-0.000625	different estimator	0.0026 vs 0.0500	equivalent
two-time-point absorbing-event law with monotone censoring	ate_regimen[always vs never @ t=2]	difference in cumulative risk between the plans “treat at both times” against “treat at neither time” at horizon t = 2	-0.000084	0.0195	1.0097	0.0025	different estimator	0.0047 vs 0.0500	equivalent
two-time-point absorbing-event law with monotone censoring	ate_regimen[treat then continue if l2 positive vs never @ t=2]	difference in cumulative risk between the plans “treat, then continue only if L2 is positive” against “treat at neither time” at horizon t = 2	-0.000072	0.0161	1.0096	0.0025	different estimator	0.0051 vs 0.0500	equivalent
two-time-point absorbing-event law with monotone censoring	risk_regimen[always @ t=1]	cumulative risk under the plan treat at both times at horizon t = 1	-0.000017	0.0096	1.0020	-0.0019	different estimator	0.0034 vs 0.0500	equivalent
two-time-point absorbing-event law with monotone censoring	risk_regimen[always @ t=2]	cumulative risk under the plan treat at both times at horizon t = 2	0.000011	0.0040	1.0035	0.0019	different estimator	0.0040 vs 0.0500	equivalent
two-time-point absorbing-event law with monotone censoring	risk_regimen[never @ t=1]	cumulative risk under the plan treat at neither time at horizon t = 1	-0.000026	0.0114	1.0040	-0.0012	different estimator	0.0030 vs 0.0500	equivalent
two-time-point absorbing-event law with monotone censoring	risk_regimen[never @ t=2]	cumulative risk under the plan treat at neither time at horizon t = 2	0.000095	0.0276	1.0162	-0.0081	different estimator	0.0165 vs 0.0500	equivalent
two-time-point absorbing-event law with monotone censoring	risk_regimen[treat then continue if l2 positive @ t=2]	cumulative risk under the plan treat, then continue only if L2 is positive at horizon t = 2	0.000023	0.0081	1.0051	0.0019	different estimator	0.0048 vs 0.0500	equivalent

Theory properties

property	cell	role	what was tested	what must hold	measured	result
crossfit_overfitting	cross_fitted_survival_ltmle	positive	five-fold horizon-two survival LTMLE with a fully grown outcome tree	SE ratio clears the overfitting floor and stays inside the sanity band	SE ratio 0.9638 to 1.0037	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 0.3963 to 0.4128	pass
double_robustness	dynamic_t2__both_correct	positive	dynamic plan 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 -0.0062 to 0.000382, margin 0.0110, SE ratio 0.9996	pass
double_robustness	dynamic_t2__both_wrong	control	dynamic plan 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 -0.0456 to -0.0388, margin 0.0113, SE ratio 0.7442	pass
double_robustness	dynamic_t2__mechanism_correct	positive	dynamic plan 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 -0.0029 to 0.0038, margin 0.0113, SE ratio 1.0022	pass
double_robustness	dynamic_t2__outcome_correct	positive	dynamic plan 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 -0.0037 to 0.0027, margin 0.0107, SE ratio 0.7597	pass
double_robustness	static_t1__both_correct	positive	static plan at horizon one: 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 0.0017, margin 0.0069, SE ratio 1.0087	pass
double_robustness	static_t1__both_wrong	control	static plan at horizon one: 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 -0.0451 to -0.0411, margin 0.0068, SE ratio 0.9474	pass
double_robustness	static_t1__mechanism_correct	positive	static plan at horizon one: 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 -0.0024 to 0.0019, margin 0.0072, SE ratio 0.9951	pass
double_robustness	static_t1__outcome_correct	positive	static plan at horizon one: 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 0.0018, margin 0.0071, SE ratio 0.8796	pass
double_robustness	static_t2__both_correct	positive	static plan 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 -0.0054 to 0.0012, margin 0.0112, SE ratio 1.0149	pass
double_robustness	static_t2__both_wrong	control	static plan 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 -0.0380 to -0.0309, margin 0.0118, SE ratio 0.6698	pass
double_robustness	static_t2__mechanism_correct	positive	static plan 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 -0.0020 to 0.0048, margin 0.0115, SE ratio 1.0028	pass
double_robustness	static_t2__outcome_correct	positive	static plan 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 -0.0044 to 0.0023, margin 0.0112, SE ratio 0.6830	pass
interval_calibration	dynamic_t2__correctly_specified	positive	dynamic plan 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 0.9381 to 0.9502, SE ratio 0.9845 to 1.0231, empirical efficiency ratio 1.0028 to 1.0414, reported efficiency ratio 1.0236 to 1.0273	pass
interval_calibration	dynamic_t2__noise_control	control	dynamic plan 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 0.8261 to 0.8457, SE ratio 0.6993 to 0.7262, empirical efficiency ratio 1.4119 to 1.4659, reported efficiency ratio 1.0236 to 1.0273	pass
interval_calibration	dynamic_t2__shrunken_se_control	control	dynamic plan 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 0.8219 to 0.8417, SE ratio 0.6889 to 0.7161, empirical efficiency ratio 1.0022 to 1.0415, reported efficiency ratio 0.7165 to 0.7191	pass
interval_calibration	static_t1__correctly_specified	positive	static plan at horizon one: 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 0.9450 to 0.9564, SE ratio 0.9825 to 1.0194, empirical efficiency ratio 0.9828 to 1.0196, reported efficiency ratio 1.0014 to 1.0023	pass
interval_calibration	static_t1__noise_control	control	static plan at horizon one: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8214 to 0.8412, SE ratio 0.6927 to 0.7193, empirical efficiency ratio 1.3927 to 1.4460, reported efficiency ratio 1.0014 to 1.0023	pass
interval_calibration	static_t1__shrunken_se_control	control	static plan at horizon one: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8207 to 0.8405, SE ratio 0.6881 to 0.7134, empirical efficiency ratio 0.9832 to 1.0192, reported efficiency ratio 0.7010 to 0.7016	pass
interval_calibration	static_t2__correctly_specified	positive	static plan 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 0.9414 to 0.9532, SE ratio 0.9876 to 1.0262, empirical efficiency ratio 1.0100 to 1.0486, reported efficiency ratio 1.0340 to 1.0379	pass
interval_calibration	static_t2__noise_control	control	static plan 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 0.8330 to 0.8523, SE ratio 0.7082 to 0.7358, empirical efficiency ratio 1.4084 to 1.4625, reported efficiency ratio 1.0339 to 1.0380	pass
interval_calibration	static_t2__shrunken_se_control	control	static plan 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 0.8204 to 0.8403, SE ratio 0.6911 to 0.7185, empirical efficiency ratio 1.0096 to 1.0490, reported efficiency ratio 0.7237 to 0.7266	pass
power	dynamic_t2__alternative	positive	dynamic plan at horizon two: 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
power	static_t1__alternative	positive	static plan at horizon one: 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
power	static_t2__alternative	positive	static plan at horizon two: 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	dynamic_t2__n_1000	control	dynamic plan at horizon two: bias, coverage and SE calibration at n = 1,000	coverage interval lies below nominal or clears the declared floor	bias -0.0024, coverage 0.9238 to 0.9657, SE ratio 0.9787	pass
root_n_and_efficiency	dynamic_t2__n_2000	positive	dynamic plan at horizon two: bias, coverage and SE calibration at n = 2,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000309, coverage 0.9282 to 0.9688, SE ratio 1.0107	pass
root_n_and_efficiency	dynamic_t2__n_8000	positive	dynamic plan 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 0.000113, coverage 0.9252 to 0.9667, SE ratio 0.9990	pass
root_n_and_efficiency	static_t1__n_1000	control	static plan at horizon one: bias, coverage and SE calibration at n = 1,000	coverage interval lies below nominal or clears the declared floor	bias 0.000974, coverage 0.9416 to 0.9776, SE ratio 1.0202	pass
root_n_and_efficiency	static_t1__n_2000	positive	static plan at horizon one: bias, coverage and SE calibration at n = 2,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000130, coverage 0.9447 to 0.9796, SE ratio 1.0262	pass
root_n_and_efficiency	static_t1__n_8000	positive	static plan at horizon one: bias, coverage and SE calibration at n = 8,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias -0.000040, coverage 0.9267 to 0.9677, SE ratio 0.9791	pass
root_n_and_efficiency	static_t2__n_1000	control	static plan at horizon two: bias, coverage and SE calibration at n = 1,000	coverage interval lies below nominal or clears the declared floor	bias -0.0029, coverage 0.9092 to 0.9554, SE ratio 0.9966	pass
root_n_and_efficiency	static_t2__n_2000	positive	static plan at horizon two: bias, coverage and SE calibration at n = 2,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias -0.000719, coverage 0.9297 to 0.9698, SE ratio 1.0313	pass
root_n_and_efficiency	static_t2__n_8000	positive	static plan 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 0.000150, coverage 0.9297 to 0.9698, SE ratio 1.0122	pass
root_n_rate	dynamic_t2__empirical_sd	positive	dynamic plan 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 -0.5754 to -0.4871	pass
root_n_rate	dynamic_t2__reported_se	positive	dynamic plan 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 -0.5283 to -0.5193	pass
root_n_rate	static_t1__empirical_sd	positive	static plan at horizon one: 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 -0.5243 to -0.4343	pass
root_n_rate	static_t1__reported_se	positive	static plan at horizon one: the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5023 to -0.5003	pass
root_n_rate	static_t2__empirical_sd	positive	static plan 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 -0.5768 to -0.4914	pass
root_n_rate	static_t2__reported_se	positive	static plan 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 -0.5348 to -0.5254	pass
survival_recursion_necessity	always_t2__survival	positive	always-treat risk at horizon two: the survival estimator keeps failures in their event node and removes them afterward	bias interval inside the equivalence margin	bias -0.0030 to 0.0032, margin 0.0105	pass
survival_recursion_necessity	always_t2__survivor_only	control	always-treat risk at horizon two: the same horizon-two outcome analyzed only among first-node survivors	bias interval must fall entirely outside the margin	bias -0.1510 to -0.1413, margin 0.0163	pass
targeting_necessity	dynamic_t2__targeted	positive	dynamic plan at horizon two: the estimator fluctuates a misspecified outcome model, so targeting does all the adjusting	bias interval inside the equivalence margin	bias -0.0040 to 0.0026, margin 0.0111	pass
targeting_necessity	dynamic_t2__untargeted	control	dynamic plan at horizon two: the identical fit with every fluctuation step removed	bias interval must fall entirely outside the margin	bias -0.0456 to -0.0391, margin 0.0109	pass
targeting_necessity	static_t1__targeted	positive	static plan at horizon one: the estimator fluctuates a misspecified outcome model, so targeting does all the adjusting	bias interval inside the equivalence margin	bias -0.0034 to 0.0011, margin 0.0075	pass
targeting_necessity	static_t1__untargeted	control	static plan at horizon one: the identical fit with every fluctuation step removed	bias interval must fall entirely outside the margin	bias -0.0461 to -0.0417, margin 0.0073	pass
targeting_necessity	static_t2__targeted	positive	static plan at horizon two: the estimator fluctuates a misspecified outcome model, so targeting does all the adjusting	bias interval inside the equivalence margin	bias -0.0034 to 0.0035, margin 0.0115	pass
targeting_necessity	static_t2__untargeted	control	static plan at horizon two: the identical fit with every fluctuation step removed	bias interval must fall entirely outside the margin	bias -0.0372 to -0.0303, margin 0.0115	pass
type_i_error	dynamic_t2__sharp_null	positive	dynamic plan at horizon two: a confounded law whose true contrast is exactly zero	one-sided rejection bound stays under the declared type-I ceiling	rejection 0.0600, 0.0404 to 0.0850	pass
type_i_error	static_t1__sharp_null	positive	static plan at horizon one: a confounded law whose true contrast is exactly zero	one-sided rejection bound stays under the declared type-I ceiling	rejection 0.0625, 0.0425 to 0.0879	pass
type_i_error	static_t2__sharp_null	positive	static plan at horizon two: a confounded law whose true contrast is exactly zero	one-sided rejection bound stays under the declared type-I ceiling	rejection 0.0600, 0.0404 to 0.0850	pass

The property study preserves every ordinary survival instrument. These include horizon-specific double robustness, targeting, root-n, efficiency, calibration, null, power, and survivor-only recursion controls.

The overfitting pair uses a fully grown outcome tree at horizon two. Both arms use identical nonlinear survival panels and known treatment and censoring mechanisms. The joint verdict requires held-out fitting to restore SE scale and improve coverage over the in-sample control.

Under the pooled update the cross-fitted ratio is 0.983738, with a 99% interval from 0.963806 to 1.003666. The fold-fluctuated construction it replaced gave 1.102157 on the same seeds. RM18 at commit dea3297e records both values, in “What the pooled update found”.

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	paired replications
n	2000	observations per paired replication
independent_tests_total	16	implementation-estimand truth tests
independent_tests_passed	16	truth tests passing
paired_tests_total	8	paired estimand comparisons
paired_tests_passed	8	paired comparisons passing
property_cells_total	52	independent property cells
property_cells_passed	52	property cells passing
max_standardized_bias	0.0479	largest primary standardized bias
min_coverage	0.9437	lowest primary coverage
min_coverage_ci_lower	0.9272	lowest primary coverage lower endpoint
min_se_ratio_ci_lower	0.9395	lowest primary SE-ratio endpoint
max_se_ratio_ci_upper	1.0606	highest primary SE-ratio endpoint
properties[crossfit_overfitting/cross_fitted_survival_ltmle]:coverage	0.9430	cross-fitted tree coverage
properties[crossfit_overfitting/in_sample_control]:coverage	0.5693	in-sample tree coverage
properties[crossfit_overfitting/cross_fitted_survival_ltmle]:coverage_gain_ci_lower	0.3599	lower bound for the paired coverage gain
properties[crossfit_overfitting/cross_fitted_survival_ltmle]:replicates	8000	paired overfitting replications
properties[survival_recursion_necessity/always_t2__survival]:recursion_displacement	3.4932	survivor-only control 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 in pooled SDs
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 the fluctuation must move the estimate
margin:recursion_displacement	0.2500	least the survivor-only control must move the estimate
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, not numerical	The paired claim is similarity of means and non-inferiority. Per-replication estimates differ at statistical scale, because only the mechanism is shared. The sequential regressions are fitted differently, and lmtp 1.5.4 targets on each fold’s training rows where 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
Horizon one uses the binary-mean path in R	lmtp requires two event nodes for its survival path. The one-node binary mean is the same first-horizon cumulative-risk parameter
Inference is pointwise	The row does not validate a simultaneous curve band or enforce monotone reported estimates. The default-band study measures the default band of this study’s subject fit.
The event process has two horizons and one cause	Longer follow-up and competing-risk cumulative incidence need separate evidence
Flexible learning is an independent property instrument	The paired comparison uses one GLM learner on each side. The tree pair does not establish parity for learner-library selection
The primary mechanism bounds are nonbinding	No primary cell validates active bounds, weights, clustering, or severe practical-positivity violations

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

Reproduction

The fixture README gives the regeneration commands. The manifest records the seeds, the configuration, the pinned lmtp version and source commit, the digest of every study module and reference source, and the artifact hashes.