Count data are increasingly ubiquitous in genetic association studies, where it is possible to observe excess zero counts as compared to what is expected based on standard assumptions. For instance, in rheumatology, data are usually collected in multiple joints within a person or multiple sub-regions of a joint, and it is not uncommon that the phenotypes contain enormous number of zeroes due to the presence of excessive zero counts in majority of patients. Most existing statistical methods assume that the count phenotypes follow one of these four distributions with appropriate dispersion-handling mechanisms: Poisson, Zero-inflated Poisson (ZIP), Negative Binomial, and Zero-inflated Negative Binomial (ZINB). However, little is known about their implications in genetic association studies. Also, there is a relative paucity of literature on their usefulness with respect to model misspecification and variable selection. In this article, we have investigated the performance of several state-of-the-art approaches for handling zero-inflated count data along with a novel penalized regression approach with an adaptive LASSO penalty, by simulating data under a variety of disease models and linkage disequilibrium patterns. By taking into account data-adaptive weights in the estimation procedure, the proposed method provides greater flexibility in multi-SNP modeling of zero-inflated count phenotypes. A fast coordinate descent algorithm nested within an EM (expectation-maximization) algorithm is implemented for estimating the model parameters and conducting variable selection simultaneously. Results show that the proposed method has optimal performance in the presence of multicollinearity, as measured by both prediction accuracy and empirical power, which is especially apparent as the sample size increases. Moreover, the Type I error rates become more or less uncontrollable for the competing methods when a model is misspecified, a phenomenon routinely encountered in practice.