Abstract

The primary analysis of time‐to‐event data typically makes the censoring at random assumption, that is, that—conditional on covariates in the model—the distribution of event times is the same, whether they are observed or unobserved. In such cases, we need to explore the robustness of inference to more pragmatic assumptions about patients post‐censoring insensitivity analyses. Reference‐based multiple imputation, which avoids analysts explicitly specifying the parameters of the unobserved data distribution, has proved attractive to researchers. Building on results for longitudinal continuous data, we show that inference using a Tobit regression imputation model for reference‐based sensitivity analysis with right censored log normal data isinformation anchored, meaning the proportion of information lost due to missing data under the primary analysis is held constant across the sensitivity analyses. We illustrate our theoretical results using simulation and a clinical trial case study.

Highlights

  • Carefully clinical trials are designed and planned, some outcome data are often missing

  • Given the increasingly prominent role of sensitivity analysis in the analysis of clinical trials, exemplified by the ICH E9 addendum published in 2019 CHMP (2019), it is important to provide methods which are easy to implement and use, but which are clinically plausible and contextually relevant to the trial team and other stakeholders

  • This responds to the FDA mandated report by the U.S National Research Council in 2010, which highlighted the lack of such sensitivity analysis methods NRC (2010)

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Summary

INTRODUCTION

Carefully clinical trials are designed and planned, some outcome data are often missing. Recently Cro, Carpenter, and Kenward (2019) proved that, at least for continuous longitudinal data, RBMI is information anchored, meaning that the proportion of information lost due to missing data is held constant across the primary and sensitivity analysis. We are using “information” in a rather specific sense, defined to be the inverse of the derived estimator of the sampling variance In their recent paper Atkinson et al showed that, counterintuitively, the empirical variance decreases as the proportion of censored data increases (columns 7 and 8 of Table 1 of reference 2), whereas information anchoring was shown to hold for Rubin’s variance estimator (albeit with simulated data). That of Cro et al, in this article we provide theoretical results showing that information anchoring holds for a reference-based sensitivity analysis with a Tobit imputation model assuming truncated normal data. Notes: Comparison of variances under J2R: A, Theoretical calculation of information anchored variance (the gold standard); B, Theoretical calculation of Rubin’s MI variance; C, Empirical estimate of information anchored variance; D, Empirical estimate of MI variance under J2R

MOTIVATING DATA
INFORMATION ANCHORED SENSITIVITY ANALYSIS
Clinical trial setting with time-to-event data
Tobit imputation model
Information anchoring under Jump to Reference
SIMULATION STUDY
ILLUSTRATIVE EXAMPLE BASED ON THE RITA-2 TRIAL
Findings
DISCUSSION
Full Text
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