PARENT SESSION
Oral Session # 13: Statistical Ecology.
Presiding: R Stevens
Monday, August 4. 8:00 AM to 11:30 AM, SITCC Meeting Room 205.

Nonparametric smoothed estimators of population hazard functions.

Riggs, Michael¹, ¹ Department of Statistical Research, RTP, NC, USA

ABSTRACT- Data from prospective studies of the fates of members of a cohort can be used to estimate three interrelated functions: the cohort cumulative hazard function H(t), the cohort hazard rate, h(t), and the cohort cumulative survival probability, S(t). The three functions can be estimated for either the overall risk of death or for multiple competing risks of death from different causes. In this paper, I focus on methods for the estimation of the hazard function from data arising from experimental, quasi-experimental, and observational studies (e.g., monitoring studies). The hazard function is the instantaneous rate of change of the cumulative hazard function, h(t) =d/dt[H(t)] When the survival time variable is age, the plot of h(t) gives the probability of dying as a function of age. Thus the shape of h(t) reveals how the risk of death changes with age in a population or cohort. Moreover, it can be shown that the observed shape of a cohort survival curve (e.g., Kaplan Meier curves) is determined by the underlying hazard function. The practical importance of the hazard function is further demonstrated by the widespread use of parametric (e.g., exponential survival models) and semi-parametric (e.g., Cox regression) survival models to estimate the effects of treatments and covariates on the underlying cohort hazard functions. Unfortunately, a nonparametric maximum likelihood estimator for the hazard function does not exist; instead, a semiparametric smoothed function is generally used to approximate h(t). Three nonparametric methods for obtaining optimally smoothed point and interval estimates of the underlying cohort hazard functions will be discussed. These include splines, kernel density, and penalized likelihood estimators. Examples of the application of these methods to data from experimental and observational ecological studies will be used to illustrate how hazard plots can aid in the interpretation of population survival and risk models.

Key words: survival, hazards, nonparametric, cohort