Natural interpretations in Tobit regression models using marginal estimation methods

The Tobit model, also known as a censored regression model to account for left- and/or right-censoring in the dependent variable, has been used in many areas of applications, including dental health, medical research and economics. The reported Tobit model coefficient allows estimation and inference of an exposure effect on the latent dependent variable. However, this model does not directly provide overall exposure effects estimation on the original outcome scale. We propose a direct-marginalization approach using a reparameterized link function to model exposure and covariate effects directly on the truncated dependent variable mean. We also discuss an alternative average-predicted-value, post-estimation approach which uses model-predicted values for each person in a designated reference group under different exposure statuses to estimate covariate-adjusted overall exposure effects. Simulation studies were conducted to show the unbiasedness and robustness properties for both approaches under various scenarios. Robustness appears to diminish when covariates with substantial effects are imbalanced between exposure groups; we outline an approach for model choice based on information criterion fit statistics. The methods are applied to the Genetic Epidemiology Network of Arteriopathy (GENOA) cohort study to assess associations between obesity and cognitive function in the non-Hispanic white participants.