High-throughput sequencing is now commonplace for measuring RNA and DNA in samples. Sequencing technology results in count-based data, and several established pipelines exist for statistical analysis, but are typically limited to simple comparisons and fixed effects. As more sequencing study designs are resulting in repeated, correlated or clustered data, there is need for analysis methods that can account for more complicated study designs. As an example, we focus on the calculation of the heritability of traits derived from sequencing studies in animal models, by comparing repeated measurements within strains and across strains. We propose a measure of heritability, hypothesis test and interval estimation, based on generalized linear mixed effects models using the negative binomial or compound Poisson distributions. Applications to simulated and example data sets provide recommendations for different methods that are implemented in the HeritSeq R package available in CRAN. Although heritability provides a motivating case study, we have also explored a more general framework for a variety of study designs based on a Bayesian hierarchical model that allows for random effects.