Random forests for survival data: which methods work best and under what conditions?

Few systematic comparisons of methods for constructing survival trees and forests exist in the literature. Importantly, when the goal is to predict a survival time or estimate a survival function, the optimal choice of method is unclear. We use an extensive simulation study to systematically investigate various factors that influence survival forest performance - forest construction method, censoring, sample size, distribution of the response, structure of the linear predictor, and presence of correlated or noisy covariates. In particular, we study 11 methods that have recently been proposed in the literature and identify 6 top performers. We find that all the factors that we investigate have significant impact on the methods' relative accuracy of point predictions of survival times and survival function estimates. We use our results to make recommendations for which methods to use in a given context and offer explanations for the observed differences in relative performance.

Postpartum amenorrhea duration by sex of the newborn in two natural fertility populations.

OBJECTIVES: Postpartum amenorrhea (PA) affects the length of interbirth intervals and thus is intimately related to human life history strategies. PA duration appears to be influenced by maternal energetic status. In humans, as in other mammals, sons are costlier than daughters. Thus, we hypothesize that, in energetically constrained environments, a newborn's sex should be associated with PA duration. METHODS: We analyzed data from two natural fertility populations in which mothers have differing energy budgets: Qom women (n = 121) from a periurban village in Argentina, who have a comparatively calorically dense diet and are sedentary (prepregnancy mean BMI = 24.8 ± 4.5 kg/m2 in 1997), and agropastoral Kaqchikel Maya women (n = 88), who have a comparatively calorically restricted diet and high physical activity levels (mean BMI = 21.8 ± 3.7 kg/m2 ). We predict that (a) mothers of sons exhibit longer PA duration than mothers of daughters and (b) this association between offspring sex and PA duration is stronger in the Maya, who have smaller energy budgets. RESULTS: Maya mothers with sons exhibited estimated mean and median PA durations that were 1.34 times the estimated mean and median PA duration of mothers with daughters (p = 0.02). Among the Qom, mean, and median PA duration did not differ significantly in relation to offspring sex (p = 0.94). CONCLUSIONS: Maya mothers with sons exhibited longer PA duration than those with daughters. This phenomenon was not observed in the well-nourished Qom, possibly due to "buffering" effects from larger energy budgets. Offspring sex may influence birth spacing and maternal life history strategies in energetically constrained environments.

Breastfeeding Duration and the Social Learning of Infant Feeding Knowledge in Two Maya Communities.

Variation in the durations of exclusive breastfeeding (exBF) and any breastfeeding (anyBF) is associated with socioecological factors. This plasticity in breastfeeding behavior appears adaptive, but the mechanisms involved are unclear. With this concept in mind, we investigated whether durations of exBF and anyBF in a rural Maya population covary with markers of a form of socioecological change-market integration-and whether individual factors (individual learning, physiological plasticity) and/or learning from others in the community (social learning, norm adherence) mediate these changes. Using data from 419 mother-child pairs from two Guatemalan Maya villages, we fit a bivariate linear mixed model. The model compared exBF and anyBF among children from households of varying degrees of market integration whose mothers follow what we inferred to be local infant-feeding norms. It controlled for other factors expected to affect breastfeeding durations. We found evidence that exBF is associated with whether mothers follow their population's infant feeding norms, but no evidence that exBF is associated with the household's level of market integration. Conversely, anyBF is significantly associated with the household's market integration, but not with the villages' inferred norms. Because deviations from exBF norms are likely to result in infant mortality and reduced fitness, we hypothesize that the incentive to conform is relatively strong. Relatively greater individual plasticity in anyBF allows mother-child pairs to tailor it to socioecological conditions. Deviations from anyBF norms may be tolerated because they may provide later-life health/fitness payoffs, while posing few risks to infant survival.

Practical considerations when analyzing discrete survival times using the grouped relative risk model.

The grouped relative risk model (GRRM) is a popular semi-parametric model for analyzing discrete survival time data. The maximum likelihood estimators (MLEs) of the regression coefficients in this model are often asymptotically efficient relative to those based on a more restrictive, parametric model. However, in settings with a small number of sampling units, the usual properties of the MLEs are not assured. In this paper, we discuss computational issues that can arise when fitting a GRRM to small samples, and describe conditions under which the MLEs can be ill-behaved. We find that, overall, estimators based on a penalized score function behave substantially better than the MLEs in this setting and, in particular, can be far more efficient. We also provide methods of assessing the fit of a GRRM to small samples.

Application of hidden Markov models to multiple sclerosis lesion count data.

This paper is motivated by the work of Albert et al. who consider lesion count data observed on multiple sclerosis patients, and develop models for each patient's data individually. From a medical perspective, adequate models for such data are important both for describing the behaviour of lesions over time, and for designing efficient clinical trials. In this paper, we discuss some issues surrounding the hidden Markov model proposed by these authors. We describe an efficient estimation method and propose some extensions to the original model. Our examples illustrate the need for models which describe all patients' data simultaneously, while allowing for inter-patient heterogeneity.