This package contains the functions for drawing inference in randomized clinical trials with death and intermittent missingness.
Consider a two-arm randomized study. Let \(Y_k\) denote outcome measured at time \(t_k\) and \(Z\) denote a functional endpoint that is a function of \(Y\). Let \(L\) denote the survival time. Let \(X\) denote the baseline covariates and \(T\) denote the treatment assignment.
If two subject were both alive at the end of the study, they are ranked based on functional outcome \(Z\). If at least one subject was dead at the end of the study, they are ranked based on survival time \(L\).
Treatment effect, \(\theta\) is defined as the probability that the outcome for a random individual randomized to treatment \(T=0\) is less than the outcome of a random individual randomized to treatment \(T=1\) minus the probability that the outcome for a random individual randomized to treatment \(T=0\) is greater than the outcome of a random individual randomized to treatment \(T=1\).
In order to estimate \(\theta\) in the presence of missing data, we need to impute \(Z\) for subjects alive at the end of the study with \(Y_k\) missing for some \(k\).
The benchmark assumption we consider for the imputation is the complete case missing value (CCMV) restrictions. We then consider exponential tilting models for introducing sensitivity parameters for evaluating the robustness of the findings with regards to different missing data mechanism assumptions. The models are as follows:
$$ f(Y^{(s)}_{mis} | Y^{(s)}_{obs}, Y_0, X, T,S=s) \propto \exp( \beta_T Z) f(Y^{(s)}_{mis} | Y^{(s)}_{obs}, Y_0, X, T,S=1) $$
where \(S\) denotes the missingness patterns, \(S=1\) denotes the completers and \(\beta_T\) denotes the sensitivity parameter for arm \(T\).
This package provides a web-based GUI. See imShiny for
details.
Wang C, Scharfstein DO, Colantuoni E, Girard T, Yan Y (2016). Inference in Randomized Trials with Death and Missingness. <DOI:10.1111/biom.12594>
Wang C, Colantuoni E, Leroux A, Scharfstein DO (2020). idem: An R Package for Inferences in Clinical Trials with Death and Missingness. <DOI:10.18637/jss.v093.i12>