Using Laplace Regression to Model and Predict Percentiles of Age at Death When Age Is the Primary Time Scale
Andrea Bellavia, Andrea Discacciati, Matteo Bottai, Alicja Wolk, Nicola Orsini
2015
American Journal of Epidemiology
Increasingly often in epidemiologic research, associations between survival time and predictors of interest are measured by differences between distribution functions rather than hazard functions. For example, differences in percentiles of survival time, expressed in absolute time units (e.g., weeks), may complement the popular risk ratios, which are unitless measures. When analyzing time to an event of interest (e.g., death) in prospective cohort studies, the time scale can be set to start at
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... irth or at study entry. The advantages of one time origin over the other have been thoroughly explored for the estimation of risks but not for the estimation of survival percentiles. In this paper, we analyze the use of different time scales in the estimation of survival percentiles with Laplace regression. Using this regression method, investigators can estimate percentiles of survival time over levels of an exposure of interest while adjusting for potential confounders. Our findings may help to improve modeling strategies and ease interpretation in the estimation of survival percentiles in prospective cohort studies. age; Laplace regression; survival analysis; survival percentiles; time scale Abbreviation: CI, confidence interval. In today's epidemiologic research, results from time-toevent analysis are commonly reported in terms of increased/ decreased risk of the event of interest in one group of individuals over another. To facilitate interpretation of the results, the estimation of risks may be complemented by time-based measures of association (1-3). A possible way to combine information on risk and time is focusing on the percentiles of survival time (4). Given a follow-up period, the pth percentile of survival is the time t by which p percent of the study participants have experienced the event of interest. The percentiles of survival can be estimated at a univariable level with the nonparametric Kaplan-Meier estimator (5). When multivariable adjustment is required, other methods for estimating survival percentiles have been proposed, primarily consisting of postestimation calculation after fitting of Cox regression or other parametric survival models (6-9). Laplace regression was recently introduced in the epidemiologic literature as an intuitive and flexible method with which to estimate multivariable-adjusted survival percentiles (10). Various reports have suggested that in observational prospective studies, when data are analyzed with Cox proportional hazards regression, attained age at the time of the event should be used as the underlying time scale instead of follow-up time (11) (12) (13) (14) (15) . Given the extreme popularity of the Cox model, using attained age at the event as the primary time scale is becoming the standard way of analyzing time-to-event data. However, the use of attained age has extensive and important consequences for the interpretation and estimation of the survival curve (16, 17) . The presence of delayed entries introduces left-truncation, complicating interpretation of the survival curve, and changes the location of censoring, influencing the number of survival percentiles it is possible to estimate (13, (15) (16) (17) . In this paper, we investigate the implications of changing time scales in the estimation of survival percentiles with Laplace regression. When attained age is chosen as the primary time scale, the method models the percentiles of attained age at the event of interest (such as the median age at event conditionally on the predictors).
doi:10.1093/aje/kwv033
pmid:26093508
fatcat:azfwdku44zafhdt3geunasexym