The relationship between genetic variability and individual phenotypes is usually investigated by testing for association relying on called genotypes. Allele counts obtained from next-generation sequence data could be used for this purpose too. Genetic association can be examined by treating alternative allele counts (AACs) as the response variable in negative binomial regression. AACs from sequence data often contain an excess of zeros, thus motivating the use of Hurdle and zero-inflated models. Here we examine rough type I error rates and the ability to pick out variants with small probability values for 7 different testing approaches that incorporate AACs as an explanatory or as a response variable. Model comparisons relied on chromosome 3 DNA sequence data from 407 Hispanic participants in the Type 2 Diabetes Genetic Exploration by Next-generation sequencing in Ethnic Samples (T2D-GENES) project 1 with complete information on diastolic blood pressure and related medication. Our results suggest that in the investigation of the relationship between AAC as response variable and individual phenotypes as explanatory variable, Hurdle-negative binomial regression has some advantages. This model showed a good ability to discriminate strongly associated variants and controlled overall type I error rates. However, probability values from Hurdle-negative binomial regression were not obtained for approximately 25 % of the investigated variants because of convergence problems, and the mass of the probability value distribution was concentrated around 1.