Sample size determinations using logistic regression with pilot data.

Abstract

Suppose the goal of a projected study is to estimate accurately the value of a 'prediction' proportion p that is specific to a given set of covariates. Available pilot data show that (1) the covariates are influential in determining the value of p and (2) their relationship to p can be modelled as a logistic regression. A sample size justification for the projected study can be based on the logistic model; the resulting sample sizes not only are more reasonable than the usual binomial sample size values from a scientific standpoint (since they are based on a model that is more realistic), but also give smaller prediction standard errors than the binomial approach with the same sample size. In appropriate situations, the logistic-based sample sizes could make the difference between a feasible proposal and an unfeasible, binomial-based proposal. An example using pilot study data of dental radiographs demonstrates the methods.