Observational missing-data DR-TMLE#

This study tests the composite-indicator construction for an observational missing outcome and a missing treatment. The contract gives the construction and its conditions. For arm $a$ the fit targets $C_a = \Delta_A \Delta 1\{A = a\}$ with the mechanism $g_{c,a}(W) = P(\Delta_A = 1 \mid W)\,g(a \mid \Delta_A = 1, W)\,\pi(a, W)$.

The study has three scenarios. Each is a law of tests/studies/mar_arm_indexed_laws.py, with every table indexed by the three levels of $W$ and the arms.

scenario	arms	missing	smallest composite $g_{c,a}$
`binary_observational_mar`	2	the outcome	0.12
`binary_mar_outcome_and_treatment`	2	the outcome and the treatment	0.0825
`three_arm_mar_outcome_and_treatment`	3	the outcome and the treatment	0.07

The treatment is observational in each scenario. The fit estimates the treatment mechanism and receives no known probabilities. In the two missing-treatment scenarios the recording of the treatment depends on the treatment, so $P(A = a \mid W)$ is not identified.

The comparator is R drtmle 1.1.2 at pinned commit 538a3a2. It implements the same construction. An NA treatment gives DeltaA = 0, and its fluctuation indicator is A == a & DeltaA == 1 & DeltaY == 1. The runner passes the oracle outcome regressions and the oracle composite mechanism, so drtmle skips estimateG. out$drtmle pairs with the composite DR-TMLE. out$tmle is one logistic fluctuation along $C_a / g_{c,a}$, which on a binary outcome is the fit the composite TMLE reaches. It pairs with the composite TMLE under tmle_ate and tmle_ate_mid.

Accuracy against known truth#

law	estimand	what was tested	implementation	bias (99% interval)	coverage	SE ratio	result
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ate`	average treatment effect	`cleverly` composite-indicator missing-data DR-TMLE	-0.0039 to 0.0036	0.9400	0.9831	pass
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ate`	average treatment effect	R `drtmle` with an NA treatment and a missing outcome	-0.0039 to 0.0036	0.9387	0.9827	pass
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey0`	counterfactual mean under no treatment	`cleverly` composite-indicator missing-data DR-TMLE	-0.0027 to 0.0029	0.9325	0.9829	pass
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey0`	counterfactual mean under no treatment	R `drtmle` with an NA treatment and a missing outcome	-0.0027 to 0.0029	0.9363	0.9829	pass
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey1`	counterfactual mean under treatment	`cleverly` composite-indicator missing-data DR-TMLE	-0.0025 to 0.0023	0.9513	1.0149	pass
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey1`	counterfactual mean under treatment	R `drtmle` with an NA treatment and a missing outcome	-0.0025 to 0.0023	0.9513	1.0145	pass
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`or`	marginal odds ratio, reported on the log scale	`cleverly` composite-indicator missing-data DR-TMLE	-0.0134 to 0.0183	0.9387	0.9823	pass
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`or`	marginal odds ratio, reported on the log scale	R `drtmle` with an NA treatment and a missing outcome	-0.0134 to 0.0183	0.9387	0.9819	pass
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`rr`	marginal risk ratio, reported on the log scale	`cleverly` composite-indicator missing-data DR-TMLE	-0.0067 to 0.0105	0.9413	0.9806	pass
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`rr`	marginal risk ratio, reported on the log scale	R `drtmle` with an NA treatment and a missing outcome	-0.0066 to 0.0106	0.9413	0.9803	pass
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`tmle_ate`	average treatment effect of the composite TMLE, paired with R `drtmle`’s out$tmle	`cleverly` composite-indicator missing-data DR-TMLE	-0.0039 to 0.0036	0.9375	0.9775	pass
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`tmle_ate`	average treatment effect of the composite TMLE, paired with R `drtmle`’s out$tmle	R `drtmle` with an NA treatment and a missing outcome	-0.0039 to 0.0036	0.9375	0.9775	pass
L1: two-arm binary-outcome observational law with MAR outcomes	`ate`	average treatment effect	`cleverly` composite-indicator missing-data DR-TMLE	-0.0046 to 0.0015	0.9487	1.0050	pass
L1: two-arm binary-outcome observational law with MAR outcomes	`ate`	average treatment effect	R `drtmle` with an NA treatment and a missing outcome	-0.0046 to 0.0015	0.9487	1.0048	pass
L1: two-arm binary-outcome observational law with MAR outcomes	`ey0`	counterfactual mean under no treatment	`cleverly` composite-indicator missing-data DR-TMLE	-0.0017 to 0.0027	0.9475	1.0005	pass
L1: two-arm binary-outcome observational law with MAR outcomes	`ey0`	counterfactual mean under no treatment	R `drtmle` with an NA treatment and a missing outcome	-0.0017 to 0.0027	0.9487	1.0006	pass
L1: two-arm binary-outcome observational law with MAR outcomes	`ey1`	counterfactual mean under treatment	`cleverly` composite-indicator missing-data DR-TMLE	-0.0032 to 0.0011	0.9500	0.9952	pass
L1: two-arm binary-outcome observational law with MAR outcomes	`ey1`	counterfactual mean under treatment	R `drtmle` with an NA treatment and a missing outcome	-0.0032 to 0.0011	0.9500	0.9946	pass
L1: two-arm binary-outcome observational law with MAR outcomes	`or`	marginal odds ratio, reported on the log scale	`cleverly` composite-indicator missing-data DR-TMLE	-0.0171 to 0.0084	0.9450	1.0047	pass
L1: two-arm binary-outcome observational law with MAR outcomes	`or`	marginal odds ratio, reported on the log scale	R `drtmle` with an NA treatment and a missing outcome	-0.0172 to 0.0084	0.9450	1.0045	pass
L1: two-arm binary-outcome observational law with MAR outcomes	`rr`	marginal risk ratio, reported on the log scale	`cleverly` composite-indicator missing-data DR-TMLE	-0.0087 to 0.0049	0.9525	1.0064	pass
L1: two-arm binary-outcome observational law with MAR outcomes	`rr`	marginal risk ratio, reported on the log scale	R `drtmle` with an NA treatment and a missing outcome	-0.0087 to 0.0048	0.9525	1.0063	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ate[low vs high]`	difference in counterfactual means, low versus high	`cleverly` composite-indicator missing-data DR-TMLE	-0.0030 to 0.0060	0.9437	0.9702	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ate[low vs high]`	difference in counterfactual means, low versus high	R `drtmle` with an NA treatment and a missing outcome	-0.0030 to 0.0060	0.9437	0.9712	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ate[mid vs high]`	difference in counterfactual means, mid versus high	`cleverly` composite-indicator missing-data DR-TMLE	-0.0020 to 0.0064	0.9475	0.9844	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ate[mid vs high]`	difference in counterfactual means, mid versus high	R `drtmle` with an NA treatment and a missing outcome	-0.0020 to 0.0064	0.9475	0.9849	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey[high]`	counterfactual mean under treatment arm ‘high’	`cleverly` composite-indicator missing-data DR-TMLE	-0.0054 to 0.0013	0.9225	0.9342	fail
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey[high]`	counterfactual mean under treatment arm ‘high’	R `drtmle` with an NA treatment and a missing outcome	-0.0054 to 0.0013	0.9237	0.9349	fail
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey[low]`	counterfactual mean under treatment arm ‘low’	`cleverly` composite-indicator missing-data DR-TMLE	-0.0036 to 0.0025	0.9450	0.9988	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey[low]`	counterfactual mean under treatment arm ‘low’	R `drtmle` with an NA treatment and a missing outcome	-0.0036 to 0.0025	0.9450	0.9994	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey[mid]`	counterfactual mean under treatment arm ‘mid’	`cleverly` composite-indicator missing-data DR-TMLE	-0.0025 to 0.0028	0.9437	0.9859	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey[mid]`	counterfactual mean under treatment arm ‘mid’	R `drtmle` with an NA treatment and a missing outcome	-0.0025 to 0.0028	0.9437	0.9859	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`or[low vs high]`	marginal odds ratio, low versus high, reported on the log scale	`cleverly` composite-indicator missing-data DR-TMLE	-0.0208 to 0.0195	0.9437	0.9692	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`or[low vs high]`	marginal odds ratio, low versus high, reported on the log scale	R `drtmle` with an NA treatment and a missing outcome	-0.0207 to 0.0195	0.9450	0.9700	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`or[mid vs high]`	marginal odds ratio, mid versus high, reported on the log scale	`cleverly` composite-indicator missing-data DR-TMLE	-0.0130 to 0.0240	0.9437	0.9822	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`or[mid vs high]`	marginal odds ratio, mid versus high, reported on the log scale	R `drtmle` with an NA treatment and a missing outcome	-0.0130 to 0.0240	0.9437	0.9827	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`rr[low vs high]`	marginal risk ratio, low versus high, reported on the log scale	`cleverly` composite-indicator missing-data DR-TMLE	-0.0104 to 0.0085	0.9450	0.9840	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`rr[low vs high]`	marginal risk ratio, low versus high, reported on the log scale	R `drtmle` with an NA treatment and a missing outcome	-0.0104 to 0.0085	0.9450	0.9849	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`rr[mid vs high]`	marginal risk ratio, mid versus high, reported on the log scale	`cleverly` composite-indicator missing-data DR-TMLE	-0.0036 to 0.0101	0.9537	0.9885	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`rr[mid vs high]`	marginal risk ratio, mid versus high, reported on the log scale	R `drtmle` with an NA treatment and a missing outcome	-0.0036 to 0.0101	0.9537	0.9890	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`tmle_ate_mid`	difference in counterfactual means, mid versus high, of the composite TMLE, paired with R `drtmle`’s out$tmle	`cleverly` composite-indicator missing-data DR-TMLE	-0.0019 to 0.0064	0.9475	0.9839	pass
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`tmle_ate_mid`	difference in counterfactual means, mid versus high, of the composite TMLE, paired with R `drtmle`’s out$tmle	R `drtmle` with an NA treatment and a missing outcome	-0.0019 to 0.0064	0.9475	0.9839	pass

One arm mean is red in both implementations: ey[high] of the three-arm scenario. Its coverage is 0.9225 in the package and 0.9237 in R drtmle, and each 99% interval ends below the 0.90 floor. The two implementations differ by 4e-6 on average. high has the smallest composite mechanism of the law, 0.070 where W = 0. The mean standard error, 0.0342, is on the efficiency bound, 0.0344. The capped fits cover at 0.957.

The roadmap owner composite-high-arm records the reading. The row stays red under the reporting policy.

Agreement with the canonical implementation#

Comparator-backed: a paired comparison with drtmle-r-composite 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
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ate`	average treatment effect	-0.000015	0.0024	1.0007	0.0012	matching implementation	0.0013 vs 0.0500	equivalent
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey0`	counterfactual mean under no treatment	0.000003	0.000578	1.0019	-0.0037	matching implementation	0.0010 vs 0.0500	equivalent
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey1`	counterfactual mean under treatment	-0.000012	0.0031	1.0002	0	matching implementation	0.000654 vs 0.0500	equivalent
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`or`	marginal odds ratio, reported on the log scale	-0.000134	0.0021	1.0008	0	matching implementation	0.0013 vs 0.0500	equivalent
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`rr`	marginal risk ratio, reported on the log scale	-0.000030	0.0013	1.0011	0	matching implementation	0.0012 vs 0.0500	equivalent
L1: two-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`tmle_ate`	average treatment effect of the composite TMLE, paired with R `drtmle`’s out$tmle	1.668e-09	2.704e-07	1.0000	0	matching implementation	5.707e-09 vs 0.0500	equivalent
L1: two-arm binary-outcome observational law with MAR outcomes	`ate`	average treatment effect	0.000009	0.0017	1.0002	0	matching implementation	0.000534 vs 0.0500	equivalent
L1: two-arm binary-outcome observational law with MAR outcomes	`ey0`	counterfactual mean under no treatment	-0.000003	0.000798	1.0004	-0.0012	matching implementation	0.000595 vs 0.0500	equivalent
L1: two-arm binary-outcome observational law with MAR outcomes	`ey1`	counterfactual mean under treatment	0.000006	0.0016	0.9999	0	matching implementation	0.0017 vs 0.0500	equivalent
L1: two-arm binary-outcome observational law with MAR outcomes	`or`	marginal odds ratio, reported on the log scale	0.000070	0.0014	1.0003	0	matching implementation	0.000530 vs 0.0500	equivalent
L1: two-arm binary-outcome observational law with MAR outcomes	`rr`	marginal risk ratio, reported on the log scale	0.000027	0.0016	1.0004	0	matching implementation	0.000460 vs 0.0500	equivalent
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ate[low vs high]`	difference in counterfactual means, low versus high	-0.000007	0.000913	1.0015	0	matching implementation	0.000717 vs 0.0500	equivalent
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ate[mid vs high]`	difference in counterfactual means, mid versus high	-0.000001	0.000205	1.0013	0	matching implementation	0.000935 vs 0.0500	equivalent
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey[high]`	counterfactual mean under treatment arm ‘high’	0.000004	0.000791	1.0014	-0.0012	matching implementation	0.000952 vs 0.0500	equivalent
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey[low]`	counterfactual mean under treatment arm ‘low’	-0.000002	0.000479	1.0014	0	matching implementation	0.000684 vs 0.0500	equivalent
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`ey[mid]`	counterfactual mean under treatment arm ‘mid’	0.000003	0.000665	1.0008	0	matching implementation	0.000972 vs 0.0500	equivalent
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`or[low vs high]`	marginal odds ratio, low versus high, reported on the log scale	-6.250e-08	0.000006	1.0017	-0.0012	matching implementation	0.000738 vs 0.0500	equivalent
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`or[mid vs high]`	marginal odds ratio, mid versus high, reported on the log scale	0.000002	0.000088	1.0014	0	matching implementation	0.000914 vs 0.0500	equivalent
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`rr[low vs high]`	marginal risk ratio, low versus high, reported on the log scale	-0.000004	0.000479	1.0015	0	matching implementation	0.000658 vs 0.0500	equivalent
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`rr[mid vs high]`	marginal risk ratio, mid versus high, reported on the log scale	0.000002	0.000208	1.0012	0	matching implementation	0.000917 vs 0.0500	equivalent
L3: three-arm binary-outcome observational law with a MAR outcome and a MAR treatment whose recording depends on the treatment	`tmle_ate_mid`	difference in counterfactual means, mid versus high, of the composite TMLE, paired with R `drtmle`’s out$tmle	-2.193e-10	3.188e-08	1.0000	0	matching implementation	4.432e-09 vs 0.0500	equivalent

Repeated-sampling properties#

property	cell	role	what was tested	what must hold	measured	result
`corrected_mar_inference`	`composite_binary_ate__both_correct`	positive	the ATE of the two-arm law with a MAR outcome and treatment: the outcome regression and the composite mechanism are correct	bias interval inside the margin, coverage clears the floor, SE ratio inside the band, SE ratio must remain between 0.1 and 10.0	bias -0.0041 to 0.0036, coverage 0.9208 to 0.9637, SE ratio 0.9675	pass
`corrected_mar_inference`	`composite_binary_ate__both_wrong`	control	the ATE of the two-arm law with a MAR outcome and treatment: the outcome regression and the composite mechanism are both misspecified	bias interval must fall entirely outside the margin, and its distance from zero must clear the declared floor, SE ratio must remain between 0.1 and 10.0	bias -0.0530 to -0.0451, coverage 0.7308 to 0.8084, SE ratio 0.9468	pass
`corrected_mar_inference`	`composite_binary_ate__mechanism_drift`	positive	the ATE of the two-arm law with a MAR outcome and treatment: the outcome regression is correct and the treatment factor and treatment observation factor of the composite mechanism are misspecified	bias interval inside the margin, coverage clears the floor, SE ratio inside the band, SE ratio must remain between 0.1 and 10.0	bias -0.0063 to 0.000835, coverage 0.9416 to 0.9776, SE ratio 1.1390	pass
`corrected_mar_inference`	`composite_binary_ate__outcome_drift`	positive	the ATE of the two-arm law with a MAR outcome and treatment: the outcome regression is misspecified and the composite mechanism is correct	bias interval inside the margin, coverage clears the floor, SE ratio inside the band, SE ratio must remain between 0.1 and 10.0	bias -0.0016 to 0.0060, coverage 0.9267 to 0.9677, SE ratio 1.0077	pass
`corrected_mar_inference`	`composite_observational_ate__both_correct`	positive	the ATE of the two-arm law with an observational MAR outcome: the outcome regression and the composite mechanism are correct	bias interval inside the margin, coverage clears the floor, SE ratio inside the band, SE ratio must remain between 0.1 and 10.0	bias -0.0044 to 0.0018, coverage 0.9208 to 0.9637, SE ratio 0.9767	pass
`corrected_mar_inference`	`composite_observational_ate__both_wrong`	control	the ATE of the two-arm law with an observational MAR outcome: the outcome regression and the composite mechanism are both misspecified	bias interval must fall entirely outside the margin, and its distance from zero must clear the declared floor, SE ratio must remain between 0.1 and 10.0	bias -0.0941 to -0.0871, coverage 0.2068 to 0.2863, SE ratio 0.8904	pass
`corrected_mar_inference`	`composite_observational_ate__mechanism_drift`	positive	the ATE of the two-arm law with an observational MAR outcome: the outcome regression is correct and the treatment factor and treatment observation factor of the composite mechanism are misspecified	bias interval inside the margin, coverage clears the floor, SE ratio inside the band, SE ratio must remain between 0.1 and 10.0	bias -0.0022 to 0.0038, coverage 0.9297 to 0.9698, SE ratio 1.0626	pass
`corrected_mar_inference`	`composite_observational_ate__outcome_drift`	positive	the ATE of the two-arm law with an observational MAR outcome: the outcome regression is misspecified and the composite mechanism is correct	bias interval inside the margin, coverage clears the floor, SE ratio inside the band, SE ratio must remain between 0.1 and 10.0	bias -0.0029 to 0.0034, coverage 0.9282 to 0.9688, SE ratio 1.0063	pass
`corrected_mar_inference`	`composite_three_arm_ate_low__both_correct`	positive	the difference low versus high of the three-arm law with a MAR outcome and treatment: the outcome regression and the composite mechanism are correct	bias interval inside the margin, coverage clears the floor, SE ratio inside the band, SE ratio must remain between 0.1 and 10.0	bias -0.0065 to 0.0026, coverage 0.9238 to 0.9657, SE ratio 0.9564	pass
`corrected_mar_inference`	`composite_three_arm_ate_low__both_wrong`	control	the difference low versus high of the three-arm law with a MAR outcome and treatment: the outcome table’s arm columns rolled, a uniform treatment factor, and a wrong treatment observation factor: a drift of this contrast’s own	bias interval must fall entirely outside the margin, and its distance from zero must clear the declared floor, SE ratio must remain between 0.1 and 10.0	bias 0.0166 to 0.0255, coverage 0.9035 to 0.9512, SE ratio 1.0048	pass
`corrected_mar_inference`	`composite_three_arm_ate_low__mechanism_drift`	positive	the difference low versus high of the three-arm law with a MAR outcome and treatment: the outcome regression is correct and the treatment factor and treatment observation factor of the composite mechanism are misspecified	bias interval inside the margin, coverage clears the floor, SE ratio inside the band, SE ratio must remain between 0.1 and 10.0	bias -0.0014 to 0.0076, coverage 0.9208 to 0.9637, SE ratio 0.9703	pass
`corrected_mar_inference`	`composite_three_arm_ate_low__outcome_drift`	positive	the difference low versus high of the three-arm law with a MAR outcome and treatment: the outcome regression is misspecified and the composite mechanism is correct	bias interval inside the margin, coverage clears the floor, SE ratio inside the band, SE ratio must remain between 0.1 and 10.0	bias -0.0071 to 0.0020, coverage 0.9267 to 0.9677, SE ratio 0.9798	pass
`corrected_mar_inference`	`composite_three_arm_ate_mid__both_correct`	positive	the difference mid versus high of the three-arm law with a MAR outcome and treatment: the outcome regression and the composite mechanism are correct	bias interval inside the margin, coverage clears the floor, SE ratio inside the band, SE ratio must remain between 0.1 and 10.0	bias -0.0061 to 0.0023, coverage 0.9092 to 0.9554, SE ratio 0.9852	pass
`corrected_mar_inference`	`composite_three_arm_ate_mid__both_wrong`	control	the difference mid versus high of the three-arm law with a MAR outcome and treatment: the outcome regression and the composite mechanism are both misspecified	bias interval must fall entirely outside the margin, and its distance from zero must clear the declared floor, SE ratio must remain between 0.1 and 10.0	bias -0.0797 to -0.0711, coverage 0.5644 to 0.6543, SE ratio 1.0003	pass
`corrected_mar_inference`	`composite_three_arm_ate_mid__mechanism_drift`	positive	the difference mid versus high of the three-arm law with a MAR outcome and treatment: the outcome regression is correct and the treatment factor and treatment observation factor of the composite mechanism are misspecified	bias interval inside the margin, coverage clears the floor, SE ratio inside the band, SE ratio must remain between 0.1 and 10.0	bias 0.000142 to 0.0081, coverage 0.9356 to 0.9737, SE ratio 1.0469	pass
`corrected_mar_inference`	`composite_three_arm_ate_mid__outcome_drift`	positive	the difference mid versus high of the three-arm law with a MAR outcome and treatment: the outcome regression is misspecified and the composite mechanism is correct	bias interval inside the margin, coverage clears the floor, SE ratio inside the band, SE ratio must remain between 0.1 and 10.0	bias -0.0072 to 0.0013, coverage 0.9223 to 0.9647, SE ratio 0.9826	pass
`correction_necessity`	`composite_cycle__closed_score`	positive	composite-indicator correction cycle: the largest equation-(9) and equation-(10) scores over the arms after the cycle, under the outcome drift	the upper confidence endpoint is below the declared fraction of the initial-score lower endpoint	score 4.071e-11 to 4.475e-11	pass
`correction_necessity`	`composite_cycle__initial_score_control`	control	composite-indicator correction cycle: the largest equation-(10) score over the arms before the cycle is run	the lower confidence endpoint clears the declared unresolved-score floor	score 0.0024 to 0.0027	pass
`interval_calibration`	`ate__correctly_specified`	positive	average treatment effect: all four required nuisance functions 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 0.9255 to 0.9511, SE ratio 0.9305 to 1.0022, empirical efficiency ratio 0.9975 to 1.0741, reported efficiency ratio 0.9975 to 1.0018	pass
`interval_calibration`	`ate__noise_control`	control	average treatment effect: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8046 to 0.8449, SE ratio 0.6677 to 0.7185, empirical efficiency ratio 1.3914 to 1.4974, reported efficiency ratio 0.9976 to 1.0019	pass
`interval_calibration`	`ate__shrunken_se_control`	control	average treatment effect: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7894 to 0.8310, SE ratio 0.6524 to 0.7016, empirical efficiency ratio 0.9973 to 1.0724, reported efficiency ratio 0.6983 to 0.7013	pass
`ordinary_targeting`	`binary`	positive	the composite TMLE on the two-arm law with a MAR outcome and treatment	bias interval inside the margin, coverage lower bound at least 0.90, SE ratio inside (0.80, 1.20)	bias -0.0034 to 0.0042, coverage 0.9136 to 0.9585, SE ratio 0.9659	pass
`ordinary_targeting`	`binary_msm`	positive	the composite TMLE of the linear arm MSM slope on the two-arm law with a MAR outcome and treatment	bias interval inside the margin, coverage lower bound at least 0.90, SE ratio inside (0.80, 1.20)	bias -0.0021 to 0.0051, coverage 0.9252 to 0.9667, SE ratio 1.0247	pass
`ordinary_targeting`	`binary_regime`	positive	the composite TMLE of a known W-dependent regime mean on the two-arm law with a MAR outcome and treatment	bias interval inside the margin, coverage lower bound at least 0.90, SE ratio inside (0.80, 1.20)	bias -0.0027 to 0.0018, coverage 0.9121 to 0.9575, SE ratio 1.0148	pass
`ordinary_targeting`	`three_arm`	positive	the composite TMLE on the three-arm law, mid versus high	bias interval inside the margin, coverage lower bound at least 0.90, SE ratio inside (0.80, 1.20)	bias -0.0036 to 0.0043, coverage 0.9386 to 0.9757, SE ratio 1.0442	pass
`power`	`ate`	positive	the same test applied to the binary missing-treatment law’s ATE of 0.21, at n = 1,000	rejection lower bound clears the minimum power	rejection 0.9350, 0.9145 to 0.9520	pass
`root_n_and_efficiency`	`n_2000`	positive	bias, coverage and SE calibration at n = 2,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000450, coverage 0.9182 to 0.9549, SE ratio 0.9668	pass
`root_n_and_efficiency`	`n_500`	control	bias, coverage and SE calibration at n = 500	coverage interval lies below nominal or clears the declared floor	bias -0.000127, coverage 0.9258 to 0.9606, SE ratio 0.9742	pass
`root_n_and_efficiency`	`n_8000`	positive	bias, coverage and SE calibration at n = 8,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias -0.0014, coverage 0.9296 to 0.9634, SE ratio 0.9808	pass
`root_n_rate`	`empirical_sd`	positive	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 -0.5292 to -0.4748	pass
`root_n_rate`	`reported_se`	positive	the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5017 to -0.4969	pass
`simultaneous_coverage`	`composite_binary__pointwise_joint_control`	control	the two arm means, the difference, the risk ratio and the odds ratio of the two-arm law with a MAR outcome and treatment: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8474 to 0.8836	pass
`simultaneous_coverage`	`composite_binary__simultaneous_band`	positive	the two arm means, the difference, the risk ratio and the odds ratio of the two-arm law with a MAR outcome and treatment: 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 0.9250 to 0.9507	pass
`simultaneous_coverage`	`composite_observational__pointwise_joint_control`	control	the two arm means, the difference, the risk ratio and the odds ratio of the two-arm law with an observational MAR outcome: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8659 to 0.9000	pass
`simultaneous_coverage`	`composite_observational__simultaneous_band`	positive	the two arm means, the difference, the risk ratio and the odds ratio of the two-arm law with an observational MAR outcome: 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 0.9337 to 0.9578	pass
`simultaneous_coverage`	`composite_three_arm__pointwise_joint_control`	control	the three arm means, two differences, two risk ratios and two odds ratios of the three-arm law with a MAR outcome and treatment: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.7994 to 0.8402	pass
`simultaneous_coverage`	`composite_three_arm__simultaneous_band`	positive	the three arm means, two differences, two risk ratios and two odds ratios of the three-arm law with a MAR outcome and treatment: 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 0.9383 to 0.9615	pass
`treatment_complete_case`	`drop_unrecorded__control`	control	the rows with an unrecorded treatment dropped, and the rest fitted with delta= alone	bias interval must fall entirely outside the margin	bias -0.0487 to -0.0422, margin 0.0089	pass
`type_i_error`	`sharp_null`	positive	a confounded law whose true contrast is exactly zero	one-sided rejection bound stays under the declared type-I ceiling	rejection 0.0533, 0.0380 to 0.0723	pass

The study declared every budget, seed, law, learner, size, drift and floor before any verdict. The policy is reporting: a red cell stays red at its budget and margin, and the red-cell ledger records it.

family	what it tests
`corrected_mar_inference`	each contrast with both nuisances correct, the outcome regression wrong, the composite mechanism wrong, and both wrong. The outcome drift is the constant regression $\bar Q = 0.5$. The mechanism drift replaces $g(a \mid \Delta_A = 1, W)$ and, where the treatment can be missing, $P(\Delta_A = 1 \mid W)$. The both-wrong control must clear a declared floor of half its large-sample bias. Under the shared drifts the three-arm `low` contrast moves by at most 0.010, inside the margin. Its control therefore runs under its own drift: the outcome table’s arm columns rolled, a uniform treatment factor, and the wrong observation factor
`ordinary_targeting`	the composite TMLE, `guard=()`, on the two missing-treatment scenarios. Two further cells fit the binary missing-treatment scenario: the mean of a known `W`-dependent regime, and the slope of the linear arm MSM
`root_n_and_efficiency`, `root_n_rate`	the `ate` of the binary missing-treatment scenario at n = 500, 2,000 and 8,000, and the efficiency ratio against the exact EIF SD
`interval_calibration`	the same `ate` against the calibration bands, with a shrunken-SE and a noise control
`simultaneous_coverage`	the default band over every reported name of each scenario, and its pointwise joint control
`type_i_error`, `power`	the `ate` at a sharp null, and at n = 1,000
`correction_necessity`	the extra scores of every arm after and before the correction cycle, under the outcome drift
`treatment_complete_case`	a control that drops the rows with an unrecorded treatment. It must miss the truth

Each property row and each package primary row records how the fit’s DR-TMLE outer loop ended, in exit_reason and rounds. fit-exits.csv publishes the primary fits’ records. A composite TMLE fit has no outer loop and records none. A fit that reaches max_outer=100 rounds records cap. It counts as it is when its scores pass. The study does not raise max_outer after a result. Of the 2,400 primary DR-TMLE fits, 48 reached the cap and 9 stalled, 47 and 8 of them on the three-arm scenario. tests/unit/test_composite_high_arm_reading.py recomputes these counts from fit-exits.csv.

The power cell runs at n = 1,000, not at the plan’s n = 500. At n = 500 the planned power of the two-sided test is 0.738, and at n = 1,000 it is 0.957. The design of the band cells is in tests/unit/test_simultaneous_cell_design.py: pointwise joint coverage 0.8832, 0.8835 and 0.8220, and control power 1.0 at 2,400 replications.

Measured values and declared margins#

quantity	value	source
`replicates`	800	paired replications
`n`	2000	observations per primary replication
`independent_tests_passed`	40	truth tests passing
`independent_tests_total`	42	truth tests reported
`paired_tests_passed`	21	paired comparisons passing
`paired_tests_total`	21	paired comparisons reported
`property_cells_passed`	39	property cells passing
`property_cells_total`	39	property cells reported
`max_standardized_bias`	0.0565	largest primary standardized bias
`min_coverage`	0.9225	lowest primary coverage
`max_margin_utilization`	0.0031	largest paired similarity-margin share
`margin:confidence_level`	0.9900	Monte Carlo confidence level
`margin:alpha`	0.0500	nominal test size
`margin:nominal_coverage`	0.9500	nominal interval coverage
`margin:standardized_bias`	0.2500	standardized-bias margin
`margin:coverage_floor`	0.9000	primary coverage floor
`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_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:minimum_power`	0.8000	minimum power lower bound
`margin:bootstrap_replicates`	10000	resamples behind every bootstrap interval
`margin:paired_difference`	0.1500	paired similarity margin, in pooled empirical standard deviations
`margin:coverage_noninferiority`	-0.0250	smallest external-comparison coverage difference bound
`margin:rmse_noninferiority`	1.1000	largest external-comparison RMSE ratio bound
`margin:calibration_noninferiority`	0.0500	largest external-comparison calibration excess bound
`margin:over_coverage_ceiling`	0.9900	above this, coverage is conservative rather than invalid
`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:efficiency_ratio_lower`	0.9000	efficiency-ratio lower bound
`margin:efficiency_ratio_upper`	1.1000	efficiency-ratio upper bound
`margin:shrunken_se_factor`	0.7000	negative-control SE multiplier
`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:excluded_slope`	-0.2500	slower rate a root-n interval must exclude
`margin:correction_score_ratio`	0.0100	maximum closed-to-initial score-endpoint ratio
`margin:uncorrected_score_floor`	0.0010	unresolved initial-score floor
`margin:union_model_se_lower`	0.1000	union-model SE-ratio screen, lower limit. No cell of this study reads it
`margin:union_model_se_upper`	10	union-model SE-ratio screen, upper limit. No cell of this study reads it

Limits#

The study covers a binary outcome, one three-level baseline covariate, and finite-support oracle primaries. The reduced regressions are linear and logistic models fitted in sample.
Partial guards, the bivariate reduction, weights and clusters have no coverage cell of their own. The exact laws of tests/unit/test_composite_missing_data.py cover the guards, the reductions and a weight. The weighted and clustered studies cover the weight and cluster algebra, which the composite does not change.
The composite is tilted inside $[10^{-6}, 0.99]$ at g_bounds=(0.01, 0.99) and nuisance_bound=0.01 with both indicators, against $10^{-4}$ with a missing outcome alone. The default g_bounds="auto" floors the treatment factor at $5 / (\sqrt{n} \ln n)$ instead. No scenario reaches that floor.
No instrument here can detect a violation of the treatment condition, $Y(a)$ independent of $\Delta_A$ given $(A, W)$.
The drift cells give the consistent nuisance as its exact law table, so the conditioning terms of the theorem are zero by construction. The cells measure the targeting, not one-wrong inference with an estimated nuisance.

Reproduction#

The fixture README, manifest, replications, paired decisions, and property results carry the protocol, provenance, and every published row.