Abstract
Causal inference in survival analysis has been centered on treatment effect assessment with adjustment of covariates. The direct adjustment method is usually employed to find the survival function of a treatment. A Cox model that stratifies the cumulative hazard by treatment is an ideal choice for performing direct adjustment because the treatment effects are allowed to vary over time. A SAS macro was developed to implement comparison of direct adjusted survivals between treatments at a selected time point. The restricted mean survival time can be derived from a direct adjusted survival function. This statistic summarizes the survival outcome of a treatment. Comparison of restricted means provides assessment of treatment effect over a time interval. The first aim of this article was to provide an overview of the restricted mean survival time. The second aim was to introduce a SAS macro that computes the restricted mean survival times from direct adjusted survivals based on a stratified Cox model. Data preparation and macro invocation are illustrated in an analysis of survival data involving three types of stem cell transplants.
The author thanks Ms. Mary Manuel for reading the manuscript. Her valuable comments helped the author to improve the manuscript.
References
1. Cox DR. Regression models and life-tables (with discussion). J R Stat Soc B 1972;34:187–220.Search in Google Scholar
2. Chang IM, Gelman R, Pagano M. Corrected group prognostic curves and summary statistics. J Chron Dis 1982;35: 669–74.10.1016/0021-9681(82)90019-4Search in Google Scholar
3. Makuch RW. Adjusted survival curve estimation using covariates. J Chron Dis 1982;35:437–43.10.1016/0021-9681(82)90058-3Search in Google Scholar
4. Gail MH, Byar DP. Variance calculations for direct adjusted survival curves, with applications to testing for no treatment effect. Biom J 1986;28:587–99.10.1002/bimj.4710280508Search in Google Scholar
5. Zhang X, Loberizab FR, Klein JP, Zhang MJ. A SAS macro for estimation of direct adjusted survival curves based on a stratified Cox regression model. Comput Methods Programs Biomed 2007;88: 95–101.10.1016/j.cmpb.2007.07.010Search in Google Scholar PubMed
6. Zucker DM. Restricted mean life with covariates: modification and extension of a useful survival analysis method. J Am Stat Assoc 1998;93:702–9.10.1080/01621459.1998.10473722Search in Google Scholar
7. Chen PY, Tsiatis AA. Causal inference on the difference of the restricted mean lifetime between two groups. Biometrics 2001;57:1030–8.10.1111/j.0006-341X.2001.01030.xSearch in Google Scholar
8. Andersen PK, Borgan O, Gill RD, Keiding N. Statistical models based on counting processes. New York: Springer-Verlag, 1993.10.1007/978-1-4612-4348-9Search in Google Scholar
9. Klein JP, Moeschberger ML. Survival analysis: techniques for censored and truncated data, 2nd ed. New York: Springer-Verlag, 2003.Search in Google Scholar
10. Besien KV, Loberiza FR, Bajorunaite R, Armitage JO, Bashey A, Burns LJ, et al. Comparison of autologous and allogeneic hematopoietic stem cell transplantation for follicular lymphoma. Blood 2003;102:3521–9.10.1182/blood-2003-04-1205Search in Google Scholar PubMed
©2013 by Walter de Gruyter Berlin Boston