Sparse conditional logistic regression for analyzing large-scale matched data from epidemiological studies: a simple algorithm

This paper considers the problem of estimation and variable selection for large high-dimensional data (high number of predictors p and large sample size N, without excluding the possibility that N < p) resulting from an individually matched case-control study. We develop a simple algorithm for the adaptation of the Lasso and related methods to the conditional logistic regression model. Our proposal relies on the simplification of the calculations involved in the likelihood function. Then, the proposed algorithm iteratively solves reweighted Lasso problems using cyclical coordinate descent, computed along a regularization path. This method can handle large problems and deal with sparse features efficiently. We discuss benefits and drawbacks with respect to the existing available implementations. We also illustrate the interest and use of these techniques on a pharmacoepidemiological study of medication use and traffic safety.