Envelope method was recently proposed as a method to reduce the dimension of responses in multivariate regressions. However, when there exists missing data, the envelope method using the complete case observations may lead to biased and inefficient results. In this paper, we generalize the envelope estimation when the predictors and/or the responses are missing at random.
View Article and Find Full Text PDFWhen the primary outcome is difficult to collect, a surrogate endpoint is typically used as a substitute. It is possible that for every individual, the treatment has a positive effect on the surrogate, and the surrogate has a positive effect on the primary outcome, but for some individuals, the treatment has a negative effect on the primary outcome. For example, a treatment may be substantially effective in preventing the stroke for everyone, and lowering the risk of stroke is universally beneficial for life expectancy; however, the treatment may still cause death for some individuals.
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