Reappraising Medfly Longevity: A Quantile Regression Survival Analysis
Koenker, Roger, Geling, Olga, Journal of the American Statistical Association
In this article we explore the usefulness of a quantile regression formulation of reanalyzing a large experimental study that monitored age-specific mortality in a sample of roughly 1.2 million Mediterranean fruit flies. The quantile regression approach appears useful in refining several of the conclusions drawn from the original study including the apparent decline in mortality rates at advanced ages, and the gender crossover effect in survival functions for medflies.
KEY WORDS: Experimental demography; Lehmann treatment effect; Mortality rates; Quantile regression; Survival analysis; Transformation model.
The biology of aging has attained a robust adolescent stage as a scientific discipline and seems destined for a prolonged maturity. The enduring human fascination with "intimations of immortality," nurtured by modern developments in cell biology, provides a powerful impetus for the field. From a statistical vantage point, one of the most exciting recent developments in this emerging field involves large-scale demographic experiments on lower animals designed to explore features of the survival distribution and determinants of longevity. The largest and most influential of these is the work of Carey, Liedo, Orozco, and Vaupel (1992). The primary experiment that these authors described involved monitoring age-specific mortality in a sample of roughly 1.2 million Mediterranean fruit flies (Ceratitis capitata), or medflies. Several findings from this experiment challenged notions that might be regarded as central to the conventional wisdom of population biology, and demography more generally:
* Mortality rates actually declined at the oldest observed ages contradicting the view that aging is an ineluctable, monotone process of senescence. In the most extreme form of the traditional view, the survival distribution is assumed to take the Gompertz form so the mortality rate (hazard) is log-linear. This view is clearly contradicted by the medfly experiments.
* The right tail of the survival distribution was, at least by human standards, remarkably long. By 33 days, 90% of the flies had died, and by 50 days, 99% had died, but 120 (.01%) lived to 86 days and 12 (.001%) lived to 146 days. This finding casts doubt on the common practice of characterizing species-specific maximum life spans, shifting the focus instead to the analysis of tail behavior of the survival distribution. Thatcher (1999) has provided an extended discussion of related evidence for human populations.
* The experiment provided, really for the first time, strong evidence for a crossover in gender-specific mortality rates for a nonhuman population. Carey et al. (1995) reported that female medflies have higher mortality rates than male medflies up to roughly 20 days, whereas from 20-60 days males have higher rates than females and after 60 days the rates are essentially indistinguishable. These results suggest a considerably more complicated view of adaptability of the sexes for survival at various stages of the life cycle than is provided by prior literature.
The statistical analyses used in earlier work on the medfly data are based largely on standard life table methods, as described by, for example, Carey (1993). Life table methods are well adapted for the study of the effects of gender and other discrete covariates on survival and mortality, but are less well suited to investigating the effect of continuous covariates like population density, a variable that has played a significant role in subsequent debate on the interpretation of the experimental results.
In contrast, parametric and semiparametric survival models, while accommodating a broader class of covariates, typically impose stringent conditions on how the covariates are permitted to influence survival prospects. For example, in the accelerated failure time model, covariates are assumed to exert a pure location shift effect on log survival times, whereas in the Cox proportional hazard model, the covariates exert a pure location shift on a transformation of the baseline survival probability evaluated at the random survival time. …