Variable Selection for Latent Class Analysis with Application to Low Back Pain Diagnosis

The identification of most relevant clinical criteria related to low back pain disorders is a crucial task for a quick and correct diagnosis of the nature of pain and its treatment. Data concerning low back pain can be of categorical nature, in form of check-list in which each item denotes presence or absence of a clinical condition. Latent class analysis is a model-based clustering method for multivariate categorical responses which can be applied to such data for a preliminary diagnosis of the type of pain. In this work we propose a variable selection method for latent class analysis applied to the selection of the most useful variables in detecting the group structure in the data. The method is based on the comparison of two different models and allows the discarding of those variables with no group information and those variables carrying the same information as the already selected ones. We consider a swap-stepwise algorithm where at each step the models are compared through and approximation to their Bayes factor. The method is applied to the selection of the clinical criteria most useful for the clustering of patients in different classes of pain. It is shown to perform a parsimonious variable selection and to give a good clustering performance. The quality of the approach is also assessed on simulated data.