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Fix bootstrap CI scaling and selection.random standardization - #176
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Each bootstrap resample draws bootstrap.sample * n of the n subjects (an m-out-of-n bootstrap), so the spread of the bootstrap estimates reflects a sample of size m and the standard errors and confidence intervals were about 1 / sqrt(bootstrap.sample) times too wide - about 12% at the default of 0.8. The draws are now shrunk towards the full-data estimate by sqrt(bootstrap.sample) before the SE or percentile interval is taken, for the risks and their differences and ratios, hazard ratios, and end-of-follow-up estimates. Results with bootstrap.sample = 1 are unchanged.
selection.random keeps a proportion selection.prob of the trials starting on the first level of treat.level, but the risk curves and the hazard-ratio simulation standardized over the kept trials unweighted, under-representing that arm's covariate distribution: in SEQdata with selection.prob = 0.3 both ITT risks at follow-up 60 averaged about 0.011 too high over 20 seeds. Kept first-level trials now carry weight 1 / selection.prob in the standardization and in the hazard-ratio Cox fit, which removes the bias. The outcome and weight models are unchanged, as selection depends only on baseline treatment. Bootstrap CIs already include the selection variability (resampling subjects from the kept trials is equivalent to resampling then selecting; checked by simulation), so the documentation now says so instead of changing them.
ryan-odea
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Nov 8, 2026
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Sorry for the delay - took me a bit to wrap my head around the issue.
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The bootstrap sampling option has been niggling away at the back of my mind. I believe it needs this rescaling
sqrt(bootstrap.sample)so SEs and CIs refer to the full sample size; they were about 12% too wide at the default of 0.8. Ratios are rescaled on the log scale.And this also
selection.randomby1 / selection.probwhen standardizing risks and fitting the hazard-ratio Cox model, removing a bias in the risks.