A Variation of the Method of Translation to Generate Bivariate and Multivariate Survival Distributions with Competing Risk or Reliability Applications

In the present paper, a variation of the methode of translation is discussed to generate bivariate or multivariate survival distributions starting a given bivariate or multivariate distribution which is not necessarily a life distribution. The new distribution has been called the dual of the given distribution. The duals of several bivariate and multivariate famílies of distributions are obtained, such as FRECHET'S , FARLIE -GUMBEL -MORGENSTERN'S , MARDIA'S and PLACKETT'S , among others. A necessary and sufficient condition is given for a bivariate distribution to be its own dual. Thus the present paper generates several survival distributions in addition to what are already available in the literature. These have important applications in competing risk theory or reliability of engineering systems.     

Discussion on “Instrumental variable estimation of the causal hazard ratio,” by Linbo Wang,Eric Tchetgen Tchetgen,Torben Martinussen,Stijn Vansteelandt

Wang, et al.'s estimator for causal hazard ratios for endogenous treatments makes an important addition to a researcher's toolkit for analyzing censored duration outcomes. Their method complements existing methods in the semiparametric treatment effects literature and suggests useful avenues for future research.     

On the relation between the cause-specific hazard and the subdistribution rate for competing risks data: The Fine–Gray model revisited

The Fine–Gray proportional subdistribution hazards model has been puzzling many people since its introduction. The main reason for the uneasy feeling is that the approach considers individuals still at risk for an event of cause 1 after they fell victim to the competing risk of cause 2. The subdistribution hazard and the extended risk sets, where subjects who failed of the competing risk remain in the risk set, are generally perceived as unnatural . One could say it is somewhat of a riddle why the Fine–Gray approach yields valid inference. To take away these uneasy feelings, we explore the link between the Fine–Gray and cause-specific approaches in more detail. We introduce the reduction factor as representing the proportion of subjects in the Fine–Gray risk set that has not yet experienced a competing event. In the presence of covariates, the dependence of the reduction factor on a covariate gives information on how the effect of the covariate on the cause-specific hazard and the subdistribution hazard relate. We discuss estimation and modeling of the reduction factor, and show how they can be used in various ways to estimate cumulative incidences, given the covariates. Methods are illustrated on data of the European Society for Blood and Marrow Transplantation.     

The effect of intra- and interspecific aggression on patch residence time in Negev Desert gerbils: a competing risk analysis

We observed patch-use behavior by two gerbil species in a fieldsetting and investigated how aggression and intrinsic decision-makinginteract to influence patch residence times. Results were interpretedby using a competing risk analysis model, which uniquely enabledus to estimate the intrinsic patch-leaving decisions independentlyof external interruptions of foraging bouts by aggression. Theexperiment was conducted in two 1-ha field enclosures completelysurrounded by rodent-proof fences and included allopatric (onlyGerbillus andersoni allenbyi) and sympatric (G. a. allenbyiand G. pyramidum) treatments. We predicted that increased foodpatch quality (i.e., habitat quality) should decrease intrinsicpatch-leaving rates and increase rates of aggressive interactionsinvolving the forager feeding in the patch (i.e., the occupantindividual). We also anticipated that increasing populationdensity should result in an increase in the rate of aggressiveinteractions involving the occupant individual. Our resultssupported the first two predictions, indicating a trade-offbetween foraging and aggression. However, the third predictionwas realized only for G. a. allenbyi in allopatry. Furthermore,in allopatry, occupant G. a. allenbyi individuals with highcompetitive ranks were involved in aggressive interactions atlower rates than those with low competitive ranks. However,in sympatry, patch-use behavior of occupant G. a. allenbyi individualswas mainly influenced by aggressive behavior of G. pyramidum,which did not respond to their competitive rank. Thus, it shouldpay less for G. a. allenbyi to be aggressive in sympatric populations.The observed reduction in intraspecific aggression among individualG. a. allenbyi in the presence of G. pyramidum supports thisassertion. We suggest that this reduction likely weakens thenegative effect of intra- and interspecific density on the percapita growth rate of G. a. allenbyi. Because this would changethe slope of the isocline of G. a. allenbyi, it could be animportant mechanism promoting coexistence when habitat selectionis constrained.