Accelerated failure time model with time-varying covariates

[Timothy Yeung]

Hi all,

I have questions related to survival analysis (streg , time).

First, I would like to know if it is possible to employ control function approach with AFT survival analysis. I think it is alright as AFT model is indeed a linear regression and restriction on the distribution of the error terms should not affect the usage of control function.

Second, if the answer to the first question is positive. How do I know what exactly the regression equation is of a AFT model with time-varying covariates? Once I know what exactly the Stata is regressing, I can regress separately the endogenous variables on all the covariates in the AFT model plus extra exogenous variables in the first stage to obtain the predicted residuals. Together with the explicit covariates input, I think ln(time of the obs) is included in the regression. But I don't know what Stata does with the issue of multiple-record-per-subject. In other words, how does Stata run the regression when the dataset is now claimed to have multiple-record-per-subject?

Your help is very much appreciated! Thanks!

[Steve Samuels]

The Manual entry for streg (page 271) shows the log-likelihood for shared frailty data on page. This formula also applies to multiple record data, including data for time-varying covariates. For multiple record data, the variable \(i\) in the formula indexes individuals, and \(i j\) indexes the multiple records. Note that the equation is a function of the hazard function \(h\) and the survival function \(S\). In other words, you can't write an ordinary "linear regression" equation with time-varying covariates. You must use the proportional hazards paradigm (p. 245).