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

The following is an erratum to my 2008 paper.1 The paper describes the evaluation of sample size and power for the test of a quantitative or qualitative covariate effect on the odds of the outcome in a conditional logistic regression model as a function of the log odds ratio θ per unit change in the covariate. Section 3.2 derives an equation such that the value of θ can be obtained as a function of the covariate mean among cases (μ1) and controls (μ2) for a quantitative covariate, and Section 3.3 likewise as a function of the probabilities (π1 and π2) for a qualitative covariate. However, there is an error in this derivation. This satisfies the Vandermonde identity whereby , so that the ratio of each term is a probability. Note that this expression applies for any m and d since for any a>m under the convention for computing binomial coefficients. The subsequent expressions are unaffected, including the numerical example with d=2 and m=3 in Equation 30.