Statistical model¤

jaxQTL models a molecular phenotype y_i for individual i with covariates x_i, genotype g_i, and an optional fixed offset o_i:

\[ g(\mu_i) = x_i^\mathsf{T}\beta + g_i\beta_g + o_i, \qquad \mu_i = E(y_i \mid x_i, g_i). \]

The link function g and response variance are determined by the selected family.

The CLI supports gaussian for continuous phenotypes, poisson for counts with variance equal to the mean, and nb for overdispersed counts.

Count models¤

For Poisson and Negative Binomial expression models, jaxQTL uses a log link. With library-size exposure, the model is

\[ \log(\mu_i) = x_i^\mathsf{T}\beta + g_i\beta_g + \log(l_i). \]

The Negative Binomial model uses the NB2 variance

\[ \operatorname{Var}(y_i \mid x_i, g_i) = \mu_i + \alpha\mu_i^2, \]

where alpha is the fitted overdispersion. Setting alpha = 0 gives the Poisson variance.

Effect interpretation¤

Under the log link, exp(beta_g) is the multiplicative change in the expected count for a one-unit increase in the counted a1 allele, holding covariates and exposure fixed.

Check the model and counted allele before interpreting effects

Do not apply the count-model rate-ratio interpretation to Gaussian models or to an allele other than the output a1. Always read the effect together with the selected family, link, and allele metadata.

See Troubleshooting for NB2 estimation and solver controls, Tests and gene-level calibration for inference choices, and Models and distributions for the Python API.