Bayesian Joint Estimation of Binary Outcome and Time-to-event Data: Effects of Leaf Quality on Pupal Survival and Time-to-Emergence in the Winter Moth |
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Authors: | Stefan Van Dongen |
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Institution: | (1) Group of Evolutionary Biology, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium |
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Abstract: | Plant–herbivore interactions are complex and affect herbivore fitness components and life history traits in many different
ways. In this paper, we present results from an experiment studying the effects of leaf quality on pupal survival and duration
of pupation (as measured by time-to-emergence) in the winter moth. Because only surviving pupae are at risk of emerging, analysis
of time-to-emergence should exclude the dead pupae. However, due to right censoring, the survival status could not be determined
for each individual. This failure to determine the group of moths at risk of emerging a priori motivated the development of
a joint model of both survival probability and time-to-emergence. We formulate the model in a Bayesian framework and apply
Monte Carlo Markov Chain (MCMC) to obtain posterior distributions. Time-to-emergence is modeled by a Cox Proportional Hazards
(CPH) model where only the surviving pupae are at risk of emergence. Probability of pupal survival was modeled by a Generalized
Linear Mixed Model (GLMM). The censored individuals were included in the analysis as a missing value in the GLMM. The GLMM
then generated prior distributions of survival probabilties—and thus of the probability of being at risk of emergence—for
these 19 individuals, conditional on the model parameters. The CPH model was formulated as a count process and the binary
frailty was incorporated as a zero-inflated Poisson model. Zeros in this model represent the non-survivors. Leaf quality did
not appear to influence time-to-emergence. Pupal survival was affected in a complex and unexpected way showing opposite effects
in males and females. We also explored the robustness of our model against increased levels of censoring. While the degree
of censoring was low in our study (< 1%), we artificially increased it to 67%. Although further study is required to study
the generality of these results in a theoretical framework, our explorations suggest that the newly proposed technique may
be widely applicable in a variety of situations where the identification of the at risk population cannot be done in a straightforward
way.
Received: January 2005 / Revised: June 2005 |
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Keywords: | Cox proportional hazards Fitness Generalized linear mixed model Joint modeling |
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