From 863bee4b1aa0e8fc1137b865bb91314718e27263 Mon Sep 17 00:00:00 2001 From: Alessandro Noci <59877596+nociale@users.noreply.github.com> Date: Wed, 24 Jan 2024 11:25:21 +0100 Subject: [PATCH] Apply suggestions from code review Co-authored-by: Craig Gower-Page Signed-off-by: Alessandro Noci <59877596+nociale@users.noreply.github.com> --- vignettes/CondMean_Inference.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/vignettes/CondMean_Inference.Rmd b/vignettes/CondMean_Inference.Rmd index 3089762af..7e54d6a94 100644 --- a/vignettes/CondMean_Inference.Rmd +++ b/vignettes/CondMean_Inference.Rmd @@ -31,7 +31,7 @@ knitr::opts_chunk$set( As described in section 3.10.2 of the statistical specifications of the package (`vignette(topic = "stat_specs", package = "rbmi")`), two different types of variance estimators have been proposed for reference-based imputation methods in the statistical literature (@Bartlett2021). The first is the frequentist variance which describes the actual repeated sampling variability of the estimator and results in inference which is correct in the frequentist sense, i.e. hypothesis tests have accurate type I error control and confidence intervals have correct coverage probabilities under repeated sampling if the reference-based assumption is correctly specified (@Bartlett2021, @Wolbers2021). Reference-based missing data assumption are strong and borrow information from the control arm for imputation in the active arm. As a consequence, the size of frequentist standard errors for treatment effects may decrease with increasing amounts of missing data. The second is the so-called "information-anchored" variance which was originally proposed in the context of sensitivity analyses (@CroEtAl2019). This variance estimator is based on disentangling point estimation and variance estimation altogether. The resulting information-anchored variance is typically very similar to the variance under missing-at-random (MAR) imputation and increases with increasing amounts of missing data at approximately the same rate as MAR imputation. However, the information-anchored variance does not reflect the actual variability of the reference-based estimator and the resulting frequentist inference is highly conservative resulting in a substantial power loss. Reference-based conditional mean imputation combined with a resampling method such as the jackknife or the bootstrap was first introduced in @Wolbers2021. This approach naturally targets the frequentist variance. The information-anchored variance is typically estimated using Rubin's rules for Bayesian multiple imputation which are not applicable within the conditional mean imputation framework. However, an alternative information-anchored variance proposed by @Lu2021 can easily be obtained as we show below. The basic idea of @Lu2021 is to obtain the information-anchored variance via a MAR imputation combined with a delta-adjustment where delta is selected in a data-driven way to match the reference-based estimator. For conditional mean imputation, the proposal by @Lu2021 can be implemented by choosing the delta-adjustment as the difference between the conditional mean imputation under the chosen reference-based assumption and MAR on the original dataset. The variance can then be obtained via the jackknife or the bootstrap while keeping the delta-adjustment fixed. The resulting variance estimate is very similar to Rubin's variance. Moreover as shown in @CroEtAl2019, the variance of MAR-imputation combined with a delta-adjustment achieves even better information-anchoring properties than Rubin's variance for reference-based imputation. - +Reference-based missing data assumptions are strong and borrow information from the control arm for imputation in the active arm. This vignette demonstrates first how to obtain frequentist inference using reference-based conditional mean imputation using `rbmi`, and then shows that an information-anchored inference can also be easily implemented using the package. # Data and model specification