# Cross-fitted weighted end-of-study longitudinal TMLE

This reporting study evaluates `cleverly`'s cross-fitted weighted LTMLE on a selected sample from
a known two-time-point law. The canonical comparison uses R `lmtp` 1.5.4. Each replication
contains exactly 2,000 selected rows, and both implementations use the identical rowwise
five-fold assignment.

The row is reporting evidence rather than a gated claim that every predeclared Monte Carlo cell
passed. The complete tables publish the independent validity checks beside the distributional R
comparison.

Each fold runs an untargeted weighted backward regression sequence on its training rows. One pooled
fluctuation per node then targets the out-of-fold predictions over every follower. Its loss weight
is the observation weight times the inverse of the out-of-fold cumulative mechanism. The
[cross-fitting section](../longitudinal-tmle.md#cross-fitting-the-recursion) 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`](https://github.com/nt-williams/lmtp/commit/9996b04dcbb3ae0b1ef8862097c36d95e9f2fcf9)
classifies that update as a bug. Each paired margin stays as registered.

## What was compared

| setting | `cleverly` | R `lmtp` |
| --- | --- | --- |
| samples | exact-size rejection samples selected by baseline `W1` | the identical selected rows |
| plans | never, always, and the dynamic rule | the same plans |
| outcome regressions | fold-specific untargeted weighted quasibinomial GLMs | a shared weighted GLM adapter |
| targeting | one pooled weighted fluctuation per node over every follower | a fluctuation on each fold's training rows, carried into that fold's next regression |
| mechanisms | generating treatment and censoring probabilities | the same density ratios |
| observation weights | fixed inverse-selection probabilities | `weights=` on every task |
| folds | one exact five-fold assignment | the identical assignment |
| intervals | pointwise 95% identity-scale Wald intervals | native Horvitz-Thompson influence-curve intervals |

The R learner adapter reads an auxiliary observation-weight column and removes it from the
predictor design. `lmtp` keeps the task weights in targeting, averaging, and covariance. The
diagnostic artifact records the native standard error beside direct Horvitz-Thompson and Hájek
calculations. It confirms that the native result uses the uncentered Horvitz-Thompson form.

The target-weight control uses regimen means because baseline selection shifts both means in the
same direction. That common shift can cancel in a contrast. The double-robustness and targeting
controls use contrasts because their deliberate mutations move those contrasts. The learner-weight
control uses a separate history-dependent selection law that moves every sequential nuisance.

## Accuracy against known truth

<!-- generated: accuracy -->
| law | estimand | what was tested | implementation | bias (99% interval) | coverage | SE ratio | result |
| --- | --- | --- | --- | --- | --- | --- | --- |
| selected two-time-point law with monotone censoring and fixed observation weights | `ate_regimen[always vs never]` | difference in mean outcome between the plans "treat at both times" against "treat at neither time" | `cleverly` cross-fitted weighted LTMLE | -0.0018 to 0.0050 | 0.9337 | 0.9698 | pass |
| selected two-time-point law with monotone censoring and fixed observation weights | `ate_regimen[always vs never]` | difference in mean outcome between the plans "treat at both times" against "treat at neither time" | R `lmtp` with observation weights | -0.0018 to 0.0049 | 0.9375 | 0.9810 | pass |
| selected two-time-point law with monotone censoring and fixed observation weights | `ate_regimen[treat then continue if l2 positive vs never]` | difference in mean outcome between the plans "treat, then continue only if L2 is positive" against "treat at neither time" | `cleverly` cross-fitted weighted LTMLE | -0.0037 to 0.0032 | 0.9450 | 0.9757 | pass |
| selected two-time-point law with monotone censoring and fixed observation weights | `ate_regimen[treat then continue if l2 positive vs never]` | difference in mean outcome between the plans "treat, then continue only if L2 is positive" against "treat at neither time" | R `lmtp` with observation weights | -0.0039 to 0.0030 | 0.9475 | 0.9888 | pass |
| selected two-time-point law with monotone censoring and fixed observation weights | `ey_regimen[always]` | mean outcome under the plan treat at both times | `cleverly` cross-fitted weighted LTMLE | -0.0011 to 0.0027 | 0.9300 | 0.9174 | pass |
| selected two-time-point law with monotone censoring and fixed observation weights | `ey_regimen[always]` | mean outcome under the plan treat at both times | R `lmtp` with observation weights | -0.0012 to 0.0026 | 0.9625 | 1.0897 | pass |
| selected two-time-point law with monotone censoring and fixed observation weights | `ey_regimen[never]` | mean outcome under the plan treat at neither time | `cleverly` cross-fitted weighted LTMLE | -0.0037 to 0.0020 | 0.9313 | 0.9881 | pass |
| selected two-time-point law with monotone censoring and fixed observation weights | `ey_regimen[never]` | mean outcome under the plan treat at neither time | R `lmtp` with observation weights | -0.0036 to 0.0020 | 0.9487 | 1.0316 | pass |
| selected two-time-point law with monotone censoring and fixed observation weights | `ey_regimen[treat then continue if l2 positive]` | mean outcome under the plan treat, then continue only if L2 is positive | `cleverly` cross-fitted weighted LTMLE | -0.0031 to 0.000887 | 0.9425 | 0.9628 | pass |
| selected two-time-point law with monotone censoring and fixed observation weights | `ey_regimen[treat then continue if l2 positive]` | mean outcome under the plan treat, then continue only if L2 is positive | R `lmtp` with observation weights | -0.0032 to 0.000733 | 0.9712 | 1.1109 | pass |
<!-- /generated -->

## Agreement with the canonical implementation

<!-- generated: agreement -->
Comparator-backed: a paired comparison with `lmtp-weighted` 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 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| selected two-time-point law with monotone censoring and fixed observation weights | `ate_regimen[always vs never]` | difference in mean outcome between the plans "treat at both times" against "treat at neither time" | 0.000070 | 0.0125 | 1.0186 | -0.0037 | different estimator | 0.0080 vs 0.0500 | equivalent |
| selected two-time-point law with monotone censoring and fixed observation weights | `ate_regimen[treat then continue if l2 positive vs never]` | difference in mean outcome between the plans "treat, then continue only if L2 is positive" against "treat at neither time" | 0.000184 | 0.0326 | 1.0240 | -0.0025 | different estimator | 0.0091 vs 0.0500 | equivalent |
| selected two-time-point law with monotone censoring and fixed observation weights | `ey_regimen[always]` | mean outcome under the plan treat at both times | 0.000026 | 0.0084 | 1.0162 | -0.0325 | different estimator | 0.1121 vs 0.0500 **>** | *underpowered* |
| selected two-time-point law with monotone censoring and fixed observation weights | `ey_regimen[never]` | mean outcome under the plan treat at neither time | -0.000043 | 0.0093 | 1.0245 | -0.0175 | different estimator | 0.0662 vs 0.0500 **>** | *underpowered* |
| selected two-time-point law with monotone censoring and fixed observation weights | `ey_regimen[treat then continue if l2 positive]` | mean outcome under the plan treat, then continue only if L2 is positive | 0.000141 | 0.0436 | 1.0175 | -0.0287 | different estimator | 0.1119 vs 0.0500 **>** | *underpowered* |
<!-- /generated -->

## Theory properties

<!-- generated: properties -->
| property | cell | role | what was tested | what must hold | measured | result |
| --- | --- | --- | --- | --- | --- | --- |
| `double_robustness` | `dynamic__both_correct` | positive | dynamic plan: 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 -0.0023 to 0.0021, margin 0.0074, SE ratio 0.9868 | pass |
| `double_robustness` | `dynamic__both_wrong` | control | dynamic plan: 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 0.0160 to 0.0210, margin 0.0085, SE ratio 1.0370 | pass |
| `double_robustness` | `dynamic__mechanism_correct` | positive | dynamic plan: 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 -0.0025 to 0.0024, margin 0.0082, SE ratio 0.9647 | pass |
| `double_robustness` | `dynamic__outcome_correct` | positive | dynamic plan: 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 -0.0017 to 0.0026, margin 0.0073, SE ratio 1.1400 | pass |
| `double_robustness` | `static__both_correct` | positive | static plan: 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 -0.000776 to 0.0101, margin 0.0183, SE ratio 0.9570 | pass |
| `double_robustness` | `static__both_wrong` | control | static plan: 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 -0.0251 to -0.0151, margin 0.0167, SE ratio 0.6640 | **fail** |
| `double_robustness` | `static__mechanism_correct` | positive | static plan: 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 0.0077, margin 0.0178, SE ratio 0.9928 | pass |
| `double_robustness` | `static__outcome_correct` | positive | static plan: 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 -0.0067 to 0.0040, margin 0.0180, SE ratio 0.6008 | pass |
| `interval_calibration` | `dynamic__correctly_specified` | positive | dynamic plan: 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 0.9273 to 0.9526, SE ratio 0.9486 to 1.0228, empirical efficiency ratio 0.9884 to 1.0657, reported efficiency ratio 1.0084 to 1.0142 | pass |
| `interval_calibration` | `dynamic__noise_control` | control | dynamic plan: one efficiency-bound unit of independent noise is added to each estimate | the empirical efficiency ratio must rise above the band | coverage 0.8098 to 0.8497, SE ratio 0.6803 to 0.7359, empirical efficiency ratio 1.3748 to 1.4858, reported efficiency ratio 1.0083 to 1.0141 | pass |
| `interval_calibration` | `dynamic__shrunken_se_control` | control | dynamic plan: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8020 to 0.8425, SE ratio 0.6637 to 0.7166, empirical efficiency ratio 0.9884 to 1.0654, reported efficiency ratio 0.7059 to 0.7099 | pass |
| `interval_calibration` | `static__correctly_specified` | positive | static plan: 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 0.9232 to 0.9492, SE ratio 0.9430 to 1.0203, empirical efficiency ratio 1.0195 to 1.1006, reported efficiency ratio 1.0333 to 1.0442 | **fail** |
| `interval_calibration` | `static__noise_control` | control | static plan: one efficiency-bound unit of independent noise is added to each estimate | the empirical efficiency ratio must rise above the band | coverage 0.7955 to 0.8366, SE ratio 0.6816 to 0.7347, empirical efficiency ratio 1.4147 to 1.5222, reported efficiency ratio 1.0333 to 1.0443 | pass |
| `interval_calibration` | `static__shrunken_se_control` | control | static plan: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.7873 to 0.8290, SE ratio 0.6600 to 0.7119, empirical efficiency ratio 1.0219 to 1.1001, reported efficiency ratio 0.7232 to 0.7309 | pass |
| `learner_weight_necessity` | `static__discarded_learner_weight_control` | control | static plan: nuisance learners discard sampling weights while later estimator stages retain them | population-target bias outside its margin, learner-selected-target bias inside its margin, and paired displacement above its threshold | bias 0.0378 to 0.0480, margin 0.0171, selected-target bias -0.000246 to 0.0100, margin 0.0171 | pass |
| `learner_weight_necessity` | `static__weighted_learners` | positive | static plan: sampling weights enter nuisance learning, targeting, averaging, and covariance | population-target bias interval inside the equivalence margin | bias -0.0067 to 0.0033, margin 0.0167 | pass |
| `power` | `static__alternative` | positive | static plan: the same test applied to a law with a real effect | rejection lower bound clears the minimum power | rejection 0.8788, 0.8461 to 0.9068 | pass |
| `root_n_and_efficiency` | `dynamic__n_2000` | positive | dynamic plan: bias, coverage and SE calibration at n = 2,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.000013, coverage 0.9311 to 0.9708, SE ratio 1.0042 | pass |
| `root_n_and_efficiency` | `dynamic__n_500` | control | dynamic plan: bias, coverage and SE calibration at n = 500 | coverage interval lies below nominal or clears the declared floor | bias -0.0023, coverage 0.9223 to 0.9647, SE ratio 1.0093 | pass |
| `root_n_and_efficiency` | `dynamic__n_8000` | positive | dynamic plan: bias, coverage and SE calibration at n = 8,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.000007, coverage 0.9386 to 0.9757, SE ratio 1.0101 | pass |
| `root_n_and_efficiency` | `static__n_2000` | positive | static plan: bias, coverage and SE calibration at n = 2,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.0014, coverage 0.9150 to 0.9596, SE ratio 0.9879 | pass |
| `root_n_and_efficiency` | `static__n_500` | control | static plan: bias, coverage and SE calibration at n = 500 | coverage interval lies below nominal or clears the declared floor | bias 0.000101, coverage 0.8420 to 0.9034, SE ratio 0.9386 | pass |
| `root_n_and_efficiency` | `static__n_8000` | positive | static plan: bias, coverage and SE calibration at n = 8,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias 0.000575, coverage 0.9386 to 0.9757, SE ratio 1.0589 | pass |
| `root_n_rate` | `dynamic__empirical_sd` | positive | dynamic plan: 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 -0.5505 to -0.4843 | pass |
| `root_n_rate` | `dynamic__reported_se` | positive | dynamic plan: the same regression applied to the mean reported standard error | slope interval inside the root-n band and excluding -1/4 | slope -0.5210 to -0.5129 | pass |
| `root_n_rate` | `static__empirical_sd` | positive | static plan: 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 -0.6113 to -0.5452 | pass |
| `root_n_rate` | `static__reported_se` | positive | static plan: the same regression applied to the mean reported standard error | slope interval inside the root-n band and excluding -1/4 | slope -0.5433 to -0.5253 | pass |
| `targeting_necessity` | `dynamic__targeted` | positive | dynamic plan: the estimator fluctuates a misspecified outcome model, so targeting does all the adjusting | bias interval inside the equivalence margin | bias -0.0033 to 0.0014, margin 0.0080 | pass |
| `targeting_necessity` | `dynamic__untargeted` | control | dynamic plan: the identical fit with every fluctuation step removed | bias interval must fall entirely outside the margin | bias 0.0220 to 0.0275, margin 0.0093 | pass |
| `targeting_necessity` | `static__targeted` | positive | static plan: the estimator fluctuates a misspecified outcome model, so targeting does all the adjusting | bias interval inside the equivalence margin | bias -0.0048 to 0.0054, margin 0.0171 | pass |
| `targeting_necessity` | `static__untargeted` | control | static plan: the identical fit with every fluctuation step removed | bias interval must fall entirely outside the margin | bias -0.0265 to -0.0171, margin 0.0157 | pass |
| `type_i_error` | `static__sharp_null` | positive | static plan: a confounded law whose true contrast is exactly zero | one-sided rejection bound stays under the declared type-I ceiling | rejection 0.0612, 0.0415 to 0.0864 | pass |
| `weight_necessity` | `dynamic__omitted_weight_control` | control | dynamic plan: the identical selected rows analyzed without any observation weights | population-target bias outside its margin, selected-target bias inside its margin, and paired displacement above its threshold | bias -0.0318 to -0.0276, margin 0.0071, selected-target bias -0.000595 to 0.0036, margin 0.0071 | pass |
| `weight_necessity` | `dynamic__weighted` | positive | dynamic plan: the selected sample analyzed with its fixed inverse-selection weights | population-target bias interval inside the equivalence margin | bias -0.0016 to 0.0037, margin 0.0090 | pass |
| `weight_necessity` | `static__omitted_weight_control` | control | static plan: the identical selected rows analyzed without any observation weights | population-target bias outside its margin, selected-target bias inside its margin, and paired displacement above its threshold | bias -0.0345 to -0.0272, margin 0.0124, selected-target bias -0.0033 to 0.0041, margin 0.0124 | pass |
| `weight_necessity` | `static__weighted` | positive | static plan: the selected sample analyzed with its fixed inverse-selection weights | population-target bias interval inside the equivalence margin | bias -0.0056 to 0.0038, margin 0.0158 | pass |
<!-- /generated -->

Agreement with `lmtp` is distributional. Its sequential regressions take a different solver path,
and its targeting step is the training-fold fluctuation. All ten implementation-estimand truth
tests pass. Two paired comparisons conclude equivalence, and both are contrasts.

The three regimen-mean comparisons conclude underpowered. Each misses the coverage
non-inferiority margin of -0.025. The comparison reads `lmtp`'s native Horvitz-Thompson standard
errors. The `reference-inference.csv.gz` artifact confirms that identity and records the centered
Hájek result separately.

| estimand | coverage difference | 99% lower endpoint | before the pooled update |
| --- | --- | --- | --- |
| `ey_regimen[always]` | -0.0325 | -0.0475 | underpowered, lower endpoint -0.0500 |
| `ey_regimen[treat then continue if l2 positive]` | -0.02875 | -0.042512 | underpowered, lower endpoint -0.0400 |
| `ey_regimen[never]` | -0.0175 | -0.030 | equivalent, lower endpoint -0.01875 |

The first two rows failed before the pooled update, and the inference-convention difference
accounts for them. The `ey_regimen[never]` row went red under the pooled update. Its paired mean
difference is -0.000043, with a 99% interval from -0.000350 to 0.000263 against a margin of
0.004659, so the two estimates agree. The failure is in coverage. `cleverly` covers 0.93125 of
draws, and `lmtp` covers 0.94875 with a native standard-error ratio of 1.0316. A declared
[code-by-runtime diagnostic](https://github.com/esbraun/cleverly-tmle/blob/985849c668a18cf800094714ddae3fea0675cb91/docs/roadmap.md#what-the-runtime-isolation-found) at commit `985849c6` attributes this
move to the pooled code, not to the Python and SciPy change.

One property cell also went red under the pooled update.
`interval_calibration/static__correctly_specified` fails its empirical efficiency-ratio band. The
ratio is 1.060724, and its 99% interval runs from 1.019495 to 1.100601 against the 1.10 upper edge.
Before the update, the ratio was 1.053468, with an upper endpoint of 1.092339. The cell's coverage
and SE-ratio intervals stay inside their bands.

The same diagnostic attributes this move to the pooled code too. It does not identify a defect in
pooled targeting. On this study's iid baseline-selection law, the fixed known weights define a
tilted empirical law; normalized weighted targeting, the Hájek plug-in and the whole-curve weight
multiplier implement that law's estimating equation. The two near-boundary failures therefore stay
as finite-sample reporting evidence rather than an argument for the unsupported fold-local update.

RM18 re-read these cells on fresh draws, under designs declared before their runs. No reading
moves a verdict of this study, and none names a defect in `cleverly`.

| cell | design and fresh draws | reading |
| --- | --- | --- |
| `interval_calibration/static__correctly_specified` | FW-A, 8,300 for each arm at n = 2,000, 8,000 and 32,000 | `finite-sample, contracting`. The empirical efficiency interval at 32,000 runs 0.9801 to 1.0200 |
| paired `ey_regimen[never]` | FW-B, 19,892 primary draws | `equivalent at the declared budget` |
| paired `ey_regimen[always]` and `ey_regimen[treat then continue if l2 positive]` | BD-P, the same 19,892 draws | `comparator SE convention`. Each row is `equivalent` with the Hájek standard error and fails the coverage leg with the native one |
| `double_robustness/static__both_wrong` | BD-3, 2,655 | `resolved: truth satisfies the gate`. The bias interval lies wholly outside its margin |

[What design FW found](https://github.com/esbraun/cleverly-tmle/blob/985849c668a18cf800094714ddae3fea0675cb91/docs/roadmap.md#what-design-fw-found) at commit `985849c6` and
[What design BD found](https://github.com/esbraun/cleverly-tmle/blob/985849c668a18cf800094714ddae3fea0675cb91/docs/roadmap.md#what-design-bd-found) at commit `985849c6` give each number and what each reading does
not show.
[`tests/diagnostics/rm18_fixed_weights/`](https://github.com/esbraun/cleverly-tmle/tree/main/tests/diagnostics/rm18_fixed_weights) and [`tests/diagnostics/rm18_boundary/`](https://github.com/esbraun/cleverly-tmle/tree/main/tests/diagnostics/rm18_boundary) hold the rows.

This reasoning does not transport automatically to complex surveys, calibrated or estimated
weights, clustering, or other longitudinal weight laws. The
`double_robustness/static__both_wrong` control was red before the update and stays red, because its
bias interval overlaps the discrimination boundary. The study therefore fails five verdicts. Two
are property cells, and three are the regimen-mean comparisons that conclude underpowered.
[RM18](https://github.com/esbraun/cleverly-tmle/blob/4ce96cda2bda93ba9233026977e3ff63ea3e0003/docs/roadmap.md#rm18-red-property-cells-after-the-fold-scale-and-law-changes) records each
one. The [red-cell ledger](red-cells.md) lists each red cell of this study with the roadmap ask that
owns it.

## Measured values

Names beginning `margin:` are thresholds declared before the run. Everything else is generated
from the committed artifacts and checked at the precision printed.

| quantity | value | source |
| --- | --- | --- |
| `replicates` | 800 | paired replications |
| `n` | 2000 | selected observations per paired replication |
| `independent_tests_total` | 10 | implementation-estimand truth tests |
| `independent_tests_passed` | 10 | truth tests passing |
| `paired_tests_total` | 5 | paired estimand comparisons |
| `paired_tests_passed` | 2 | paired comparisons passing |
| `property_cells_total` | 36 | independent property cells |
| `property_cells_passed` | 34 | property cells passing |
| `max_standardized_bias` | 0.0572 | largest primary standardized bias |
| `min_coverage` | 0.9300 | lowest primary coverage |
| `min_coverage_ci_lower` | 0.9035 | lowest primary coverage lower endpoint |
| `min_se_ratio_ci_lower` | 0.8591 | lowest primary SE-ratio endpoint |
| `max_se_ratio_ci_upper` | 1.1876 | highest primary SE-ratio endpoint |
| `max_margin_utilization` | 0.0436 | largest share of paired similarity margin used |
| `max_rmse_ratio_upper` | 1.0245 | largest paired RMSE-ratio bound |
| `min_coverage_difference_lower` | -0.0475 | smallest paired coverage-difference bound |
| `max_calibration_excess_upper` | 0.1050 | largest paired calibration-excess bound |
| `properties[weight_necessity/static__weighted]:weight_displacement` | 0.4736 | target-weight positive control displacement |
| `properties[learner_weight_necessity/static__weighted_learners]:learner_weight_displacement` | 0.6679 | learner-weight positive control displacement |
| `properties[double_robustness/static__both_wrong]:bias_ci_upper` | -0.0151 | both-wrong control endpoint |
| `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 lower screen |
| `margin:union_model_se_upper` | 10 | union-model SE-ratio upper screen |
| `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 targeting must move the estimate |
| `margin:weight_displacement` | 0.2500 | least target weighting must move the estimate |
| `margin:learner_weight_displacement` | 0.2500 | least learner weighting must move the estimate |

## Limitations

| limitation | what it means for use |
| --- | --- |
| The study is reporting evidence | Failed cells stay red. The static both-wrong control, the static calibration cell, and three regimen-mean paired gates fail. The row does not support a blanket claim that every predeclared finite-sample property passed |
| Agreement with `lmtp` is distributional | Different sequential regression implementations and different targeting steps can differ at statistical rather than solver scale |
| The observation weights are known and fixed | The study does not cover estimated weights, weight-model uncertainty, replicate weights, or calibration weights |
| One fixed five-fold assignment is studied | The row does not validate repeated folds or time-respecting splits |
| One selection law is studied | The selected sample uses one baseline-dependent probability with moderate weight variation, not severe practical positivity |
| The row covers one terminal binary mean per plan | Survival curves, competing risks, and longitudinal MSM projections have different parameters |
| The primary learner is a weighted GLM | The learner-weight property is a separate finite-support control, not parity for arbitrary learner libraries |
| Inference is pointwise | The row does not validate simultaneous bands or clustered covariance. The [default-band study](default-simultaneous-bands.md) measures the default band of this study's subject fit. |

The causal interpretation requires consistency, sequential exchangeability, longitudinal
positivity, conditionally independent censoring, and a selection model that identifies the
target population.

## Reproduction

The [fixture README](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/weighted_lmtp_ltmle/README.md)
gives the regeneration commands. The
[manifest](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/weighted_lmtp_ltmle/manifest.json)
records the seeds, configuration, pinned R source, adapter digests, study-module digests, and
artifact hashes.