Sample size and power determination for a binary outcome and an ordinal exposure when logistic regression analysis is planned.

General methods of sample size determination for logistic regression analyses are now available, but these will often require substantial information for their application. The author presents methods useful in the special case of a binary outcome and a three-level quantitative exposure, which includes application to a three-level ordinal exposure for a specified scaling. The computationally simple methods were developed in planning an investigation of the prognostic value of multidrug resistance gene (mdr1) expression in sarcoma. Because logistic regression was planned for the analysis, calculations were based on the ability to detect a linear trend in the log odds of tumor response to chemotherapy associated with increases in the level of mdr1 expression from negative to low positive to high positive. Closed form expressions were used to assess sensitivity to the ordinal scaling and the distribution of the mdr1 levels, and to the assumption of a linear trend in the log odds versus a linear trend in the proportions.