MTP boundaries

This study validates a longitudinal modified treatment policy on a continuous dose whose declared support depends on the history. The policies bind at that support, change their Jacobian with the dose, have two inverse branches, or send an interval of doses to a declared atom. LTMLE and SDR read each policy at one fold on the density route. The modified treatment policies at a node section states the estimator and its conditions.

Status of this page. The study is registered, and its Python phases have run. The evidence label is “Python property evidence, with comparator runs pending”. The study record sets pending_reference="lmtp", so no paired row is published. The publication policy is reporting. A red cell stays red on this page and in the red-cell ledger, with the owner row that names it.

part	what it is	status
Python property evidence	exact laws, interval calibration with two controls, and four necessity pairs	the tables below give the verdicts. It decides whether the method ships
lmtp comparator runs	the pinned lmtp 1.5.4 fits the same samples, and the study pairs the results	pending. The runs register in a later change, and a finding in them does not block the method

What was compared

The primary phase draws 1,000 samples of 5,000 rows for each of four scenarios.

scenario	law and plans	pairing
boundaries_ltmle	law B, LTMLE, plans natural and p1 to p4. Each node reads the oracle binned density, and the per-node ratio and the shifted values go beside the sample	exact under a gap of \(10^{-6}\)
boundaries_sdr	the same draw as boundaries_ltmle, SDR	exact under a gap of \(10^{-6}\)
atom_ltmle	law B’, LTMLE, plans natural and p5. Node 2 reads the oracle mixed density: the exact atom probability, and the oracle hazard of the rows off the atom	margin-read. The outcome design of the package holds the atom indicator, which the shifted frame of lmtp cannot carry
atom_sdr	the same draw as atom_ltmle, SDR	margin-read, as above

Law B has two nodes. Each dose lies on the support \([0, u]\) with \(u = 6 + 2 W_2\), so the support depends on a baseline covariate. A truncated normal draws each dose given its history. A Bernoulli law draws the outcome. Law B’ adds an atom at node 2: the dose equals the list price 3 with a probability that depends on the history, and otherwise follows law B.

plan	map	what it tests
natural	no change	the reference value
p1	scale by 0.9	a map that never binds at the support
p2	add 1 below \(u - 1\), hold above	the upper boundary binds
p3	\(u - D(u - a)\), with \(D\) a smooth warp	one piece whose inverse slope runs from 0.63 to 2.5, so the Jacobian is not 1
p4	add 1 below 3, subtract 1.5 above	two inverse branches
p5	\(\max(3, 0.65 a)\) at node 2 on law B’	the interval below \(3 / 0.65\) goes to the declared atom 3

setting	cleverly	R lmtp
datasets	1,000 samples of 5,000 rows per scenario	the identical rows
density ratio	an oracle binned density with ceil(320 (n / 2000)^(2/3)) bins (320 at n = 2,000), and the exact atom probability on law B’	the same ratio array, read from the replicate data
node regressions	a quasibinomial GLM at the last node and least squares at the first	SL.glm on the same columns
intervals	pointwise 95% Wald from the influence curve	the same, from lmtp’s influence curve

The property rows read a correctly specified final model and a rich first-node basis. The SDR property cells read a first-node learner that projects onto [0, 1]. The comparator adapters are tests/canonical/lmtp_mtp_adapter.R and tests/canonical/lmtp_sdr_adapter.R. Both sides read the columns shift__<plan>__<node>__1 and ratio__<plan>__<node>, so neither side estimates a ratio that the other does not see.

The first reading of the primary phase used n = 2,000. The two boundaries_ltmle rows of plan p4 read coverage 0.916 and 0.922 and an SE ratio of 0.925, with a bias under 0.03 standard deviations. The p4 calibration cell showed the same shortfall of the influence-curve variance at n = 2,000 and passed at n = 4,000. The primary therefore moved to n = 5,000, and the property cells kept their declared sizes. At n = 5,000 the two p4 rows read coverage 0.929 to 0.937 and an SE ratio of 0.911 to 0.917, and they pass their declared rule. All 24 truth rows pass. tests/studies/canonical_mtp_boundaries.py records the declaration.

Accuracy against known truth

law	estimand	what was tested	implementation	bias (99% interval)	coverage	SE ratio	result
the same law with a declared atom at the second dose, LTMLE	ate_regimen[p5 vs natural]	difference in mean outcome between the plans “set the second dose to the larger of 3 and 0.65 times the dose” against “leave the observed dose unchanged at both times”	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.0018 to 0.000616	0.9620	1.0280	pass
the same law with a declared atom at the second dose, LTMLE	ey_regimen[natural]	mean outcome under the plan leave the observed dose unchanged at both times	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000166 to 0.000977	0.9530	0.9818	pass
the same law with a declared atom at the second dose, LTMLE	ey_regimen[p5]	mean outcome under the plan set the second dose to the larger of 3 and 0.65 times the dose	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.0015 to 0.0011	0.9590	1.0420	pass
the same law with a declared atom at the second dose, SDR	ate_regimen[p5 vs natural]	difference in mean outcome between the plans “set the second dose to the larger of 3 and 0.65 times the dose” against “leave the observed dose unchanged at both times”	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.0018 to 0.000642	0.9620	1.0275	pass
the same law with a declared atom at the second dose, SDR	ey_regimen[natural]	mean outcome under the plan leave the observed dose unchanged at both times	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000166 to 0.000977	0.9530	0.9818	pass
the same law with a declared atom at the second dose, SDR	ey_regimen[p5]	mean outcome under the plan set the second dose to the larger of 3 and 0.65 times the dose	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.0015 to 0.0012	0.9620	1.0413	pass
two-node law with a truncated-normal dose on a history-dependent support, LTMLE	ate_regimen[p1 vs natural]	difference in mean outcome between the plans “multiply the dose by 0.9 at both times” against “leave the observed dose unchanged at both times”	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000417 to 0.000457	0.9490	1.0032	pass
two-node law with a truncated-normal dose on a history-dependent support, LTMLE	ate_regimen[p2 vs natural]	difference in mean outcome between the plans “add 1 to the dose at both times, holding doses within 1 of the support’s upper end” against “leave the observed dose unchanged at both times”	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000804 to 0.000653	0.9480	1.0141	pass
two-node law with a truncated-normal dose on a history-dependent support, LTMLE	ate_regimen[p3 vs natural]	difference in mean outcome between the plans “map the dose a to u - D(u - a) at both times, D a smooth warp whose slope runs from 0.4 to 1.6, u the support’s upper end” against “leave the observed dose unchanged at both times”	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000509 to 0.000634	0.9520	1.0078	pass
two-node law with a truncated-normal dose on a history-dependent support, LTMLE	ate_regimen[p4 vs natural]	difference in mean outcome between the plans “add 1 to a dose below 3 and subtract 1.5 from a dose at or above 3, at both times” against “leave the observed dose unchanged at both times”	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.0013 to 0.0027	0.9290	0.9169	pass
two-node law with a truncated-normal dose on a history-dependent support, LTMLE	ey_regimen[natural]	mean outcome under the plan leave the observed dose unchanged at both times	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000544 to 0.000552	0.9510	1.0169	pass
two-node law with a truncated-normal dose on a history-dependent support, LTMLE	ey_regimen[p1]	mean outcome under the plan multiply the dose by 0.9 at both times	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000706 to 0.000754	0.9530	0.9930	pass
two-node law with a truncated-normal dose on a history-dependent support, LTMLE	ey_regimen[p2]	mean outcome under the plan add 1 to the dose at both times, holding doses within 1 of the support’s upper end	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000962 to 0.000819	0.9580	1.0167	pass
two-node law with a truncated-normal dose on a history-dependent support, LTMLE	ey_regimen[p3]	mean outcome under the plan map the dose a to u - D(u - a) at both times, D a smooth warp whose slope runs from 0.4 to 1.6, u the support’s upper end	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000726 to 0.000858	0.9540	1.0240	pass
two-node law with a truncated-normal dose on a history-dependent support, LTMLE	ey_regimen[p4]	mean outcome under the plan add 1 to a dose below 3 and subtract 1.5 from a dose at or above 3, at both times	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.0014 to 0.0028	0.9320	0.9111	pass
two-node law with a truncated-normal dose on a history-dependent support, SDR	ate_regimen[p1 vs natural]	difference in mean outcome between the plans “multiply the dose by 0.9 at both times” against “leave the observed dose unchanged at both times”	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000411 to 0.000463	0.9500	1.0031	pass
two-node law with a truncated-normal dose on a history-dependent support, SDR	ate_regimen[p2 vs natural]	difference in mean outcome between the plans “add 1 to the dose at both times, holding doses within 1 of the support’s upper end” against “leave the observed dose unchanged at both times”	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000822 to 0.000641	0.9480	1.0110	pass
two-node law with a truncated-normal dose on a history-dependent support, SDR	ate_regimen[p3 vs natural]	difference in mean outcome between the plans “map the dose a to u - D(u - a) at both times, D a smooth warp whose slope runs from 0.4 to 1.6, u the support’s upper end” against “leave the observed dose unchanged at both times”	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000518 to 0.000626	0.9500	1.0079	pass
two-node law with a truncated-normal dose on a history-dependent support, SDR	ate_regimen[p4 vs natural]	difference in mean outcome between the plans “add 1 to a dose below 3 and subtract 1.5 from a dose at or above 3, at both times” against “leave the observed dose unchanged at both times”	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.0013 to 0.0027	0.9370	0.9162	pass
two-node law with a truncated-normal dose on a history-dependent support, SDR	ey_regimen[natural]	mean outcome under the plan leave the observed dose unchanged at both times	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000544 to 0.000552	0.9510	1.0169	pass
two-node law with a truncated-normal dose on a history-dependent support, SDR	ey_regimen[p1]	mean outcome under the plan multiply the dose by 0.9 at both times	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000700 to 0.000759	0.9520	0.9929	pass
two-node law with a truncated-normal dose on a history-dependent support, SDR	ey_regimen[p2]	mean outcome under the plan add 1 to the dose at both times, holding doses within 1 of the support’s upper end	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000980 to 0.000806	0.9570	1.0147	pass
two-node law with a truncated-normal dose on a history-dependent support, SDR	ey_regimen[p3]	mean outcome under the plan map the dose a to u - D(u - a) at both times, D a smooth warp whose slope runs from 0.4 to 1.6, u the support’s upper end	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.000734 to 0.000850	0.9550	1.0242	pass
two-node law with a truncated-normal dose on a history-dependent support, SDR	ey_regimen[p4]	mean outcome under the plan add 1 to a dose below 3 and subtract 1.5 from a dose at or above 3, at both times	cleverly LTMLE and SDR under modified treatment policies with declared supports and atoms	-0.0014 to 0.0029	0.9360	0.9105	pass

Agreement with the canonical implementation

Python property evidence, with comparator runs pending. The lmtp runs have not run, so this study publishes no paired row, and equivalence.csv is empty. The change that registers the runs adds the paired table here.

Theory properties

property	cell	role	what was tested	what must hold	measured	result
atom_necessity	p5__declared	positive	the two-node contrast of the map that sends an interval to the declared atom against the natural course: the ratio at the atom adds the mass of the interval sent to it, with the outcome misspecified	bias interval inside the equivalence margin	bias -0.0024 to 0.0014, margin 0.0059	pass
atom_necessity	p5__mass_dropped_control	control	the two-node contrast of the map that sends an interval to the declared atom against the natural course: the same fit drops that mass, so the ratio at the atom is one	bias interval must fall entirely outside the margin	bias 0.0087 to 0.0135, margin 0.0073	pass
branch_necessity	p4__declared	positive	the two-node contrast of the two-branch map against the natural course: the density ratio sums over both inverse branches, with the outcome misspecified	bias interval inside the equivalence margin	bias -0.0034 to 0.0026, margin 0.0093	pass
branch_necessity	p4__one_branch_control	control	the two-node contrast of the two-branch map against the natural course: the same fit sums over the first branch only	bias interval must fall entirely outside the margin	bias -0.0311 to -0.0249, margin 0.0095	pass
interval_calibration	p1__correctly_specified	positive	the two-node contrast of the nonbinding 0.9 scale against the natural course: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9470 to 0.9539, SE ratio 0.9897 to 1.0128	pass
interval_calibration	p1__noise_control	control	the two-node contrast of the nonbinding 0.9 scale against the natural course: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8317 to 0.8434, SE ratio 0.7029 to 0.7191	pass
interval_calibration	p1__shrunken_se_control	control	the two-node contrast of the nonbinding 0.9 scale against the natural course: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8254 to 0.8373, SE ratio 0.6926 to 0.7087	pass
interval_calibration	p2__correctly_specified	positive	the two-node contrast of the shift held at the history-dependent support boundary against the natural course: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9439 to 0.9510, SE ratio 0.9712 to 1.0003	pass
interval_calibration	p2__noise_control	control	the two-node contrast of the shift held at the history-dependent support boundary against the natural course: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8322 to 0.8439, SE ratio 0.7039 to 0.7212	pass
interval_calibration	p2__shrunken_se_control	control	the two-node contrast of the shift held at the history-dependent support boundary against the natural course: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8218 to 0.8338, SE ratio 0.6795 to 0.7002	pass
interval_calibration	p3__correctly_specified	positive	the two-node contrast of the warped map against the natural course: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9423 to 0.9495, SE ratio 0.9871 to 1.0098	pass
interval_calibration	p3__noise_control	control	the two-node contrast of the warped map against the natural course: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8242 to 0.8361, SE ratio 0.6965 to 0.7125	pass
interval_calibration	p3__shrunken_se_control	control	the two-node contrast of the warped map against the natural course: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8224 to 0.8344, SE ratio 0.6909 to 0.7068	pass
interval_calibration	p4__correctly_specified	positive	the two-node contrast of the two-branch map against the natural course: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9346 to 0.9423, SE ratio 0.9466 to 0.9683	pass
interval_calibration	p4__noise_control	control	the two-node contrast of the two-branch map against the natural course: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8068 to 0.8192, SE ratio 0.6799 to 0.6956	pass
interval_calibration	p4__shrunken_se_control	control	the two-node contrast of the two-branch map against the natural course: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8023 to 0.8148, SE ratio 0.6625 to 0.6773	pass
interval_calibration	p4_sdr__correctly_specified	positive	the two-branch contrast read by the sequentially doubly robust estimator: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9233 to 0.9467, SE ratio 0.9060 to 0.9775	fail
interval_calibration	p4_sdr__noise_control	control	the two-branch contrast read by the sequentially doubly robust estimator: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.7999 to 0.8364, SE ratio 0.6628 to 0.7100	pass
interval_calibration	p4_sdr__shrunken_se_control	control	the two-branch contrast read by the sequentially doubly robust estimator: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.7809 to 0.8188, SE ratio 0.6345 to 0.6836	pass
interval_calibration	p5__correctly_specified	positive	the two-node contrast of the map that sends an interval to the declared atom against the natural course: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9335 to 0.9412, SE ratio 0.9643 to 0.9863	pass
interval_calibration	p5__noise_control	control	the two-node contrast of the map that sends an interval to the declared atom against the natural course: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8067 to 0.8191, SE ratio 0.6779 to 0.6934	pass
interval_calibration	p5__shrunken_se_control	control	the two-node contrast of the map that sends an interval to the declared atom against the natural course: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8085 to 0.8209, SE ratio 0.6750 to 0.6902	pass
interval_calibration	p5_sdr__correctly_specified	positive	the declared-atom contrast read by the sequentially doubly robust estimator: both nuisances are correctly specified	SE ratio and coverage intervals both inside their calibration bands	coverage 0.9451 to 0.9521, SE ratio 0.9771 to 0.9988	pass
interval_calibration	p5_sdr__noise_control	control	the declared-atom contrast read by the sequentially doubly robust estimator: a declared scale of independent noise is added to each estimate	the SE-ratio interval must fall below the calibration band	coverage 0.8144 to 0.8266, SE ratio 0.6844 to 0.7000	pass
interval_calibration	p5_sdr__shrunken_se_control	control	the declared-atom contrast read by the sequentially doubly robust estimator: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8166 to 0.8287, SE ratio 0.6840 to 0.6990	pass
jacobian_necessity	p3__declared	positive	the two-node contrast of the warped map against the natural course: the density ratio reads each piece’s inverse slope, with an outcome model blind to the second dose	bias interval inside the equivalence margin	bias -0.0013 to 0.000545, margin 0.0028	pass
jacobian_necessity	p3__jacobian_dropped_control	control	the two-node contrast of the warped map against the natural course: the same fit replaces each inverse slope with one	bias interval must fall entirely outside the margin	bias 0.0075 to 0.0085, margin 0.0014	pass
ratio_necessity	p2__declared	positive	the two-node contrast of the shift held at the history-dependent support boundary against the natural course: the shifted-to-natural density ratio is used in the declared direction	bias interval inside the equivalence margin	bias -0.0017 to 0.000682, margin 0.0037	pass
ratio_necessity	p2__unit_ratio_control	control	the two-node contrast of the shift held at the history-dependent support boundary against the natural course: the same fit replaces the density ratio with one, with the outcome misspecified	bias interval must fall entirely outside the margin	bias 0.0105 to 0.0121, margin 0.0025	pass

The truths come from the exact laws and their closed forms (tests/studies/mtp_boundaries_common.py). Quadrature gives each truth, and the code checks it against a rule of twice the order at \(10^{-10}\).

family	cells	replications and size
interval_calibration	seven positives: LTMLE under p1 to p4 on law B and p5 on law B’, and SDR under p4 and p5. Each positive has a shrunken-SE control and a noise control	26,400 replications at n = 2,000, and at n = 4,000 for p4. The p4_sdr cell reports with 3,000 replications at n = 4,000
jacobian_necessity	p3, dose-blind outcome. The declared fit against the same draw with every inverse slope replaced by 1	1,000 pairs at n = 2,000
branch_necessity	p4, wrong outcome. The declared fit against the same draw with Equation (3) summed over the first branch only	1,000 pairs at n = 2,000
atom_necessity	p5, wrong outcome. The declared fit against the same draw with the atom’s ratio taken without the mass of the interval sent to it	1,000 pairs at n = 2,000
ratio_necessity	p2, wrong outcome. The declared ratio against a ratio of one	1,000 pairs at n = 2,000

Each necessity control removes one term that can vanish at the truth, so each needs a nonzero witness. With a wrong outcome regression the targeting step carries the whole correction, and each defect then moves the estimate. The Jacobian pair reads a dose-blind outcome model, because a factor that is monotone in the dose is absorbed by the targeting step under the wrong model. tests/unit/test_mtp_boundaries_design.py checks the sizes and the displacements before the run.

The p4 cell of LTMLE moved to n = 4,000 because its pilot at n = 2,000 read a right-skewed standard error from rare large weights. The p4_sdr cell stays outside the screen at both sizes, so the study declares it reporting before the run. Its owner is the SDR limit in the interval under heavy cumulative density ratios.

Measured values and declared margins

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	1000	paired replications
n	5000	observations per paired replication
independent_tests_passed	24	truth tests passing
independent_tests_total	24	truth tests reported
paired_tests_passed	0	paired comparisons passing
paired_tests_total	0	paired comparisons reported
property_cells_passed	28	property cells passing
property_cells_total	29	property cells reported
max_standardized_bias	0.0579	largest primary standardized bias
min_coverage	0.9290	lowest primary coverage
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	root-n slope lower bound
margin:root_n_slope_upper	-0.3750	root-n slope upper bound
margin:excluded_slope	-0.2500	slower rate the interval must exclude
margin:shrunken_se_factor	0.7000	negative-control SE multiplier
margin:necessity_displacement	0.1000	minimum necessity displacement of the four ratio and map pairs
margin:subject_failure_bound	0.0100	declared share of replications a cell may lose to a recordable fitting failure
margin:subject_failures_allowed	10	the same bound, in primary replications

Limits

limit	what it means for use
two laws with two nodes and a binary outcome	the evidence covers a Bernoulli outcome, and a continuous outcome needs q_bounds. The study has no size ladder, so it claims no rate
the density is an oracle	the density route reads the generating pooled-hazard probabilities. The default estimated density is not tested here
the declared support is the true support	a declared support that is wrong but consistent with the data is outside this evidence
the p4_sdr cell reports	the SDR interval runs short of nominal under heavy cumulative density ratios. The package treats the interval as experimental, with the measured numbers of the red-cell owner X40-sdr-heavy-ratios
the p4 standard error is short at n = 5,000	the two p4 rows of boundaries_ltmle read an SE ratio of 0.911 to 0.917 and coverage of 0.929 to 0.937. The rows pass the declared rule. Read an interval under this plan as slightly narrow
the primary rows use main-terms learners	the primary phase matches the comparator’s SL.glm. The property cells read the correct outcome model
the atom covers one node	plan p5 sends an interval to an atom at node 2 only. An atom with a near-zero mass is outside this evidence
the lmtp comparison is pending	the agreement table is empty until the reference runs register. The Python cells carry the claim until then