Risk Assessment and Evaluation of Predictions pp 87-103 | Cite as

# Quantiles of Residual Survival

## Abstract

In reliability theory, the lifetime remaining in a network of components after an initial run-in period is an important property of the system. Similarly, for medical interventions residual survival characterizes the subsequent experience of patients who survive beyond the beginning of follow-up. Here we show how quantiles of the residual survival distribution can be used to provide such a characterization. We first discuss properties of the residual quantile function and its close relationship to the hazard function. We then consider parametric estimation of the residual quantile function, focusing on the generalized gamma distribution. Finally, we describe an application of quantiles of residual survival to help describe the effects at the population level of the introduction and sustained use of highly active antiretroviral therapy for the treatment of HIV/AIDS.

## Notes

### Acknowledgements

Data in this manuscript were collected by the Multicenter AIDS Cohort Study (MACS) with centers (Principal Investigators) at The Johns Hopkins Bloomberg School of Public Health (Joseph B. Margolick, Lisa P. Jacobson), Howard Brown Health Center, Feinberg School of Medicine, Northwestern University, and Cook County Bureau of Health Services (John P. Phair), University of California, Los Angeles (Roger Detels), and University of Pittsburgh (Charles Rinaldo). The MACS is funded by the National Institute of Allergy and Infectious Diseases, with supplemental funding from the National Cancer Institute. U01-AI-35042, UL1-RR025005, U01-AI-35043, U01-AI-35039, U01-AI-35040, U01-AI-35041.

Data in this manuscript were collected by the Women’s Interagency HIV Study (WIHS) Collaborative Study Group with centers (Principal Investigators) at New York City/Bronx Consortium (Kathryn Anastos); Brooklyn, NY (Howard Minkoff); Washington, DC Metropolitan Consortium (Mary Young); The Connie Wofsy Study Consortium of Northern California (Ruth Greenblatt); Los Angeles County/Southern California Consortium (Alexandra Levine); Chicago Consortium (Mardge Cohen); Data Coordinating Center (Stephen Gange). The WIHS is funded by the National Institute of Allergy and Infectious Diseases (U01-AI-35004, U01-AI-31834, U01-AI-34994, U01-AI-34989, U01-AI-34993, and U01-AI-42590) and by the Eunice Kennedy Shriver National Institute of Child Health and Human Development (U01-HD-32632). The study is co-funded by the National Cancer Institute, the National Institute on Drug Abuse, and the National Institute on Deafness and Other Communication Disorders. Funding is also provided by the National Center for Research Resources (UCSF-CTSI Grant Number UL1 RR024131).

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