Survival analysis for right-truncated data

[Germain Jean Gauthier]

Hello Stata enthusiasts,

I would like to fit a parametric (Weibull) or semi-parametric (Cox) duration model with time-dependent covariates using Stata.

My data has one specificity: it is right-truncated (and there is not much I can do about it).

I believe the biomedical and the marketing literatures have come up with solutions:
- "Using Advance Purchase Orders to Forecast New Product Sales", Wendy W. Moe and Peter S. Fader, Marketing Science, Vol. 21, No. 3 (Summer, 2002), pp. 347-364
- "Tricked by Truncation: Spurious Duration Dependence and Social Contagion in Hazard Models", Christophe Van den Bulte & Raghuram Iyengar, Marketing Science (2011)
- "Cox regression model with doubly truncated data.", Rennert L and Xie SX, Biometrics, 74(2):725-733.(2017)
- "Cox Regression Model under Dependent Truncation", Lior Rennert and Sharon X. Xie (2018)
- “Inverse Probability Weighting Methods for Cox Regression with Right-Truncated Data.”, Vakulenko-Lagun, B., M. Mandel, and R. A. Betensky. (2019)

I took a look at stata's survival analysis reference manual. It appears that Stata only handles left-truncation.

Therefore I have two questions:

1. Am I right in believing so?
2. Has someone already dealt with a similar issue and found a work-around?

Thanks for taking the time to read this post.

Best regards,
Germain

PS: I think the two first papers from Marketing Science are closer to my empirical application than the additional references I provided.

[Carlo Lazzaro]

Germain:
welcome to this forum.
Tricky issue indeed.
In https://www.stata.com/bookstore/survival-analysis-stata-introduction/ (page 36) Authors recommend the approach followed in https://doi.org/10.1093/biomet/75.3.515.

I've never challenged myself with that stuff, though.

[Germain Jean Gauthier]

Thank you for your response. I found this paper (attached) to estimate a semi-parametric regression model, but I find it hard to link this to any practical implementation in stata for now.

PS: just thought I would share if anyone encounters the same difficulties.

[Stephen Jenkins]

Is the paper you attached not subject to copyright restrictions on distribution?

The bottom line from the paper appears at first glance to be that if you work using the data converted to the "reverse time hazard" metric, then you can apply methods conventionally applied to left-truncated data. I didn't look much at the partial likelihood models, but the likelihoods for discrete time regression modelling, especially cloglog, look very similar in structure to those for left-truncated data. The latter are very easy to fit using Stata (see the relevant sections of Survival Analysis Using Stata). So, look first at transforming to reverse time hazard ?

[Germain Jean Gauthier]

Thank you for your answer Stephen.

I downloaded the paper via Google Scholar, so I don't think so. In any case, if the moderators prefer to delete it this is fine by me. The reference is:

Kalbfleisch, J. D., & Lawless, J. F. (1991). Regression models for right truncated data with applications to AIDS incubation times and reporting lags. Statistica Sinica, 19-32.

I will dig reverse time hazard and come back to you with a reproducible example if I find an easy-to-implement solution (no guarantee on that!).