Tobit Regression Comparison between R and SAS

A recent CAMIS contribution explored the standard Tobit model for a virology endpoint (viral load) with a lower detection limit.

Tobit regression, a censored regression model, estimates linear relationships between independent variables and a dependent variable that is either left- or right-censored at a specific known value.

The implementations of Tobit regression in R and SAS were compared (link to full comparison on CAMIS website: R vs SAS Tobit Regression). In SAS, the LIFEREG procedure was used, which requires a specific structure in the MODEL statement, namely “(lower, upper)”. Here, if the lower value is missing, then the upper value is used as a left-censored value.

In R, the censReg, survival, and VGAM packages were explored. The censReg() and survreg() (from the survival package) functions provided matching results with SAS LIFEREG. In both cases estimation is being done by the maximum likelihood approach. The vglm() function in VGAM showed slight numerical differences due to a different estimation technique. The VGAM package uses vector generalized linear and additive models which are estimated using an iteratively reweighted least squares (IRLS) algorithm.

Typically, the Tobit model assumes normally distributed data, and the standard Tobit regression results matched between R and SAS when a normally distributed endpoint was assumed. Additionally, this comparison also highlighted the flexibility of Tobit regression implementations across different software (as well as the importance of being aware of different default and available options), with SAS LIFEREG and R’s survival package offering multiple different distributional assumptions.

CAMIS is a PHUSE working group in collaboration with PSI AIMS SIG. For more on CAMIS’s goals and repository, as well as how to contribute, visit the CAMIS website: https://psiaims.github.io/CAMIS/.