# 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](../longitudinal-tmle.md#cross-fitting-the-recursion) of the technical
reference gives the construction.

The canonical comparison uses R [`lmtp`](https://github.com/nt-williams/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`](https://github.com/nt-williams/lmtp/commit/9996b04dcbb3ae0b1ef8862097c36d95e9f2fcf9)
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`](https://github.com/esbraun/cleverly-tmle/blob/main/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

<!-- generated: accuracy -->
| 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 |
<!-- /generated -->

## Agreement with the canonical implementation

<!-- generated: agreement -->
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 |
<!-- /generated -->

## Theory properties

<!-- generated: 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 |
<!-- /generated -->

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](default-simultaneous-bands.md) 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](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/lmtp_ltmle_survival/README.md)
gives the regeneration commands. The
[manifest](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/lmtp_ltmle_survival/manifest.json)
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.