Point survival curve crossfit

This study validates longitudinal TMLE with survival_model="hazard" and five outer folds 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 fold fits the hazards, the treatment mechanism and the censoring mechanism on its training rows. One pooled targeting step then reads the stitched out-of-fold predictions. The section hazard-based survival targeting states the estimator.

The primary fit uses targeting="one_step". One walk moves one set of discrete hazards toward the score equation of every horizon and regimen at once. One calibration cell uses targeting="iterative", which targets each horizon on its own. 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.

No canonical implementation is compared. No maintained package ships hazard targeting with cross-fitted nuisances for a held baseline treatment. equivalence.csv has no rows, and this study is not pending. The theory and comparators rule lets the row stand on independent evidence. That evidence is the exact truths, the exact efficiency bounds, and the controls of the calibration, double-robustness and coverage cells.

What was compared

setting	cleverly
datasets	1,600 samples of 2,000 rows of the survival scenario
scenario	survival: five visits, the risks of both arms and their difference at visits 1, 3 and 5
property laws	survival and competing: four visits and two causes, the death incidence difference at visit 4
nuisances	the hazard learner is an unpenalized additive logistic regression on survival and the saturated cell fit on competing. The treatment and censoring learners are saturated cell fits
targeting	targeting="one_step" with step_size=1e-3 and tol=1e-10. One calibration cell uses targeting="iterative" with max_iter=100
cross-fitting	five outer folds, one pooled targeting step
intervals	pointwise 95% Wald from the stitched influence curve

Accuracy against known truth

law	estimand	what was tested	implementation	bias (99% interval)	coverage	SE ratio	result
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 cross-fitted point-treatment survival with hazard targeting	-0.000808 to 0.0011	0.9494	0.9955	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 cross-fitted point-treatment survival with hazard targeting	-0.0012 to 0.0017	0.9494	0.9915	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 cross-fitted point-treatment survival with hazard targeting	-0.000614 to 0.0025	0.9525	1.0122	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 cross-fitted point-treatment survival with hazard targeting	-0.000752 to 0.000721	0.9375	0.9791	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 cross-fitted point-treatment survival with hazard targeting	-0.0015 to 0.000586	0.9506	0.9936	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 cross-fitted point-treatment survival with hazard targeting	-0.0018 to 0.000324	0.9594	1.0478	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 cross-fitted point-treatment survival with hazard targeting	-0.000481 to 0.000714	0.9437	0.9973	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 cross-fitted point-treatment survival with hazard targeting	-0.0012 to 0.000803	0.9450	0.9767	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 cross-fitted point-treatment survival with hazard targeting	-0.000936 to 0.0014	0.9481	0.9924	pass

All nine implementation-estimand tests pass. No replication raised an error in the primary study or in any property cell (failed_replicates is zero in all 15 rows of properties.csv).

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 -0.0028 to 0.000648, margin 0.0059, SE ratio 1.0554	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 0.0322 to 0.0358, margin 0.0062, SE ratio 0.9799	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 -0.000268 to 0.0034, margin 0.0061, SE ratio 1.0223	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 -0.0011 to 0.0025, margin 0.0061, SE ratio 0.9805	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 0.9436 to 0.9597, SE ratio 0.9737 to 1.0259, empirical efficiency ratio 0.9912 to 1.0442, reported efficiency ratio 1.0158 to 1.0177	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 0.9412 to 0.9531, SE ratio 0.9890 to 1.0269, empirical efficiency ratio 0.9901 to 1.0280, reported efficiency ratio 1.0164 to 1.0171	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 0.8349 to 0.8541, SE ratio 0.7057 to 0.7331, empirical efficiency ratio 1.3870 to 1.4408, reported efficiency ratio 1.0164 to 1.0171	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 0.6932 to 0.7188, empirical efficiency ratio 0.9901 to 1.0266, reported efficiency ratio 0.7115 to 0.7119	pass
interval_calibration	survival_t5_per_horizon__correctly_specified	positive	difference of arm 1 and arm 0 at visit 5, five-visit held law, targeted one horizon at a time: 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 0.9604, SE ratio 1.0034 to 1.0593, empirical efficiency ratio 0.9597 to 1.0131, reported efficiency ratio 1.0161 to 1.0170	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 0.6568 to 0.6816	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 0.9393 to 0.9513	pass
simultaneous_coverage	curve_arm0__pointwise_joint_control	control	the arm-0 risk curve alone, at the five visits: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8334 to 0.8527	pass
simultaneous_coverage	curve_arm0__simultaneous_band	positive	the arm-0 risk curve alone, at the five visits: 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 0.9414 to 0.9532	pass
simultaneous_coverage	curve_arm1__pointwise_joint_control	control	the arm-1 risk curve alone, at the five visits: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8345 to 0.8537	pass
simultaneous_coverage	curve_arm1__simultaneous_band	positive	the arm-1 risk curve alone, at the five visits: 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 0.9405 to 0.9524	pass

All 15 property cells pass. Each positive calibration or coverage 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 (one step), the same difference targeted per horizon, 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, on the one-step survival cell only
double_robustness	the hazard correct, the mechanism correct, or both	both wrong
simultaneous_coverage	the max-t band over each arm’s five-visit risk curve, and over the fifteen reported parameters	the pointwise intervals of the same fits, read jointly

The per-horizon calibration cell has no control of its own. Its pass rests on the efficiency bound and the two bands.

The study has no targeting-necessity, power or root-n cell. The sibling hazard study holds those cells for the in-sample per-horizon fit. No cross-fitted cell shows that targeting moves a misspecified hazard, so the study makes no claim there.

Measured values

quantity	value	source
replicates	1600	primary replications per scenario
n	2000	observations per primary replication
independent_tests_total	9	implementation-estimand tests against the truth
independent_tests_passed	9	of those, passing
property_cells_total	15	repeated-sampling property cells
property_cells_passed	15	cells whose own and family verdicts pass
max_standardized_bias	0.0448	largest absolute primary bias in empirical standard deviations
min_coverage	0.9375	lowest measured primary-study coverage
min_se_ratio_ci_lower	0.9341	lowest bootstrap primary SE-ratio endpoint
max_se_ratio_ci_upper	1.1017	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
margin:calibration_coverage_upper	0.9800	calibration-cell coverage band, upper limit
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
margin:calibration_se_ratio_upper	1.0700	calibration-cell SE-ratio band, upper limit
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: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
no comparator	no maintained package fits this construction, so no row is paired. The independent evidence is the exact truths, the exact efficiency bounds and the controls
one scenario in the primary study	the nine truth tests read the five-visit survival law. The competing law enters one calibration cell only
learners that contain the truth	the evidence covers a correct additive logistic hazard on survival, a saturated hazard on competing, and saturated mechanisms. A flexible learner is outside it
one per-horizon cell	the per-horizon iteration appears only as one calibration cell. It has no double-robustness, coverage-band or control cell
one fold count	the study fits five fixed folds. Other fold counts and repeated splits are outside it
no targeting-necessity, power or root-n cell	the study does not show that targeting moves a misspecified cross-fitted hazard, or that its rate is root-n
no weights, clusters, policies or three arms	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 absent. Run python -m tests.canonical.point_survival_curve_crossfit.regenerate to regenerate the artifacts. The replications and the property results carry every published row.