A Review of Methods to Estimate Cause-Specific Mortality in Presence of Competing Risks

Abstract

Estimating cause‐specific mortality is often of central importance for understanding the dynamics of wildlife populations. Despite such importance, methodology for estimating and analyzing cause‐specific mortality has received little attention in wildlife ecology during the past 20 years. The issue of analyzing cause‐specific, mutually exclusive events in time is not unique to wildlife. In fact, this general problem has received substantial attention in human biomedical applications within the context of biostatistical survival analysis. Here, we consider cause‐specific mortality from a modern biostatistical perspective. This requires carefully defining what we mean by cause‐specific mortality and then providing an appropriate hazard‐based representation as a competing risks problem. This leads to the general solution of cause‐specific mortality as the cumulative incidence function (CIF). We describe the appropriate generalization of the fully nonparametric staggered‐entry Kaplan–Meier survival estimator to cause‐specific mortality via the nonparametric CIF estimator (NPCIFE), which in many situations offers an attractive alternative to the Heisey–Fuller estimator. An advantage of the NPCIFE is that it lends itself readily to risk factors analysis with standard software for Cox proportional hazards model. The competing risks‐based approach also clarifies issues regarding another intuitive but erroneous “cause‐specific mortality” estimator based on the Kaplan–Meier survival estimator and commonly seen in the life sciences literature.

Is anthropogenic cougar mortality compensated by changes in natural mortality in Utah? Insight from long-term studies

“…Radio-telemetry data are well suited to attaining unbiased estimates of net source-specific mortality rates using known-fate competing risk analyses that immediately censor individuals from the at-risk sample once they die of a given cause (Heisey and Fuller, 1985;Heisey and Patterson, 2006). Such data and methods allow for robust inference into the compensatory and additive mortality hypotheses (e.g.…”

Roe deer face competing risks between predators along a gradient in abundance

“…Similarly, an individual captured as a yearling would be reclassified as an adult in May v www.esajournals.org of the subsequent year and then keep its adult status throughout. We initially explored the possibility of applying the non-parametric cumulative incidence function (NPCIFE; Heisey and Patterson 2006), which has recently been used to estimate cause-specific mortality rates for willow ptarmigans (Sandercock et al 2011) and wolves (Liberg et al 2012). However, if sample sizes are small to moderate at the left tail of the age distribution (i.e., left truncation), estimates of survival might be biased downwards (Woodroofe 1985, Tsai 1988.…”

“…All other analyses were performed using the R 2.11.1 software (R Development Core Team 2010). To examine how age, sex and roe deer abundance affected the cause-specific mortality risk, we applied Cox proportional hazard models (Lunn and McNeil 1995, Heisey and Patterson 2006, Murray 2006, and stratified according to cause of mortality as described in Heisey and Patterson 2006. Model selection was based on AICc (Burnham and Anderson 2002).…”

The High Cost of Motherhood: End-Lactation Syndrome in Southern Sea Otters (Enhydra Lutris Nereis) on the Central California Coast, Usa

“…Our analysis accounted for variation in survival caused by differences in age, sex, reproductive status and mean body condition. We employed an instantaneous hazards model for this analysis, treating survival as a continuous process observed at discreet intervals, with the likelihood of survival of an individual animal over a particular time interval given by its cumulative probability of avoiding mortality risks, or hazards, over that interval (Heisey and Patterson 2006). In essence, we can think of the instantaneous "hazards" at any point in time, h(t), as an approximation of the conditional mortality probability over a short interval.…”

“…In essence, we can think of the instantaneous "hazards" at any point in time, h(t), as an approximation of the conditional mortality probability over a short interval. Modeling instantaneous hazards as opposed to modeling survival directly has a number of biological and mathematical advantages, including the fact that instantaneous hazards are independent of time scale, and lead to simple multiplicative models (so called "proportional hazards models") where the relative levels of mortality risk associated with particular covariates can be estimated as hazard ratios (Heisey and Patterson 2006, Heisey et al 2007, Halstead et al 2012. We employed a non-parametric Kaplan-Meier approach (Sinha and Dey 1997) to estimate instantaneous proportional hazards from staggered-entry monitoring data, and then used these to estimate the contribution of various fixed and random effects to survival rates.…”