Pattern‐Mixture Zero‐Inflated Mixed Models for Longitudinal Unbalanced Count Data with Excessive Zeros

Abstract

Analysis of longitudinal data with excessive zeros has gained increasing attention in recent years; however, current approaches to the analysis of longitudinal data with excessive zeros have primarily focused on balanced data. Dropouts are common in longitudinal studies; therefore, the analysis of the resulting unbalanced data is complicated by the missing mechanism. Our study is motivated by the analysis of longitudinal skin cancer count data presented by Greenberg, Baron, Stukel, Stevens, Mandel, Spencer, Elias, Lowe, Nierenberg, Bayrd, Vance, Freeman, Clendenning, Kwan, and the Skin Cancer Prevention Study Group[New England Journal of Medicine 323, 789-795]. The data consist of a large number of zero responses (83% of the observations) as well as a substantial amount of dropout (about 52% of the observations). To account for both excessive zeros and dropout patterns, we propose a pattern-mixture zero-inflated model with compound Poisson random effects for the unbalanced longitudinal skin cancer data. We also incorporate an autoregressive of order 1 correlation structure in the model to capture longitudinal correlation of the count responses. A quasi-likelihood approach has been developed in the estimation of our model. We illustrated the method with analysis of the longitudinal skin cancer data.