Designing a logistic regression study using surrogate measures for exposure and outcome

Suppose that a binary or polytomous outcome variable is related to a possibly continuous exposure variable through a logistic regression model, and that prior to sample selection subjects can be characterized according to ‘surrogates’ for outcome and exposure. The surrogate variables are assumed to satisfy certain conditional independence properties commonly used in errors-in-variables models. This paper considers the problem of using the surrogate variables to select subjects for measurement of the true values with the goal of minimizing the variance of an estimate of the log odds ratio. We describe three possible sampling plans and show that the log odds ratio parameter can be estimated in each plan using ordinary logistic regression.