Sample size evaluation for a multiply matched case–control study using the score test from a conditional logistic (discrete Cox PH) regression model

The conditional logistic regression model ( Biometrics 1982; 38 :661–672) provides a convenient method for the assessment of qualitative or quantitative covariate effects on risk in a study with matched sets, each containing a possibly different number of cases and controls. The conditional logistic likelihood is identical to the stratified Cox proportional hazards model likelihood, with an adjustment for ties ( J. R. Stat. Soc. B 1972; 34 :187–220). This likelihood also applies to a nested case–control study with multiply matched cases and controls, selected from those at risk at selected event times. Herein the distribution of the score test for the effect of a covariate in the model is used to derive simple equations to describe the power of the test to detect a coefficient θ (log odds ratio or log hazard ratio) or the number of cases (or matched sets) and controls required to provide a desired level of power. Additional expressions are derived for a quantitative covariate as a function of the difference in the assumed mean covariate valuesamong cases and controls and for a qualitative covariate in terms of the difference in the probabilities of exposure for cases and controls. Examples are presented for a nested case–control study and a multiply matched case–control study. Copyright © 2007 John Wiley & Sons, Ltd.