Modelling variable development using shared frailty models for interval-censored data

Background/Question/Methods

Life history variation is a general feature of many natural systems and is well studied in laboratory experiments, but is rarely included in population models. Other fields, such as survival analysis, have developed models that include similar sources of variation in some time-to-event variable (such as death or failure). Methods exist to fit these models to data, but most assume that exact event times are known. In applying these models to ecological data, we need to account for data that is interval-censored (sampled at regular intervals where exact event times are unknown). We develop a shared frailty Weibull model for time-to-maturation data (days from birth to adulthood), incorporating fixed differences between groups of populations, and two levels of random effects. The data are presumed to be intervals of observation times of newly mature individuals in a single cohort, where the exact maturation time is unknown. There is no widely available software for mixed effects survival analysis for interval censored data, so likelihood calculations were programmed directly in R and a simulation study was conducted under different magnitudes of variation to evaluate model performance and compare power analyses. 

Results/Conclusions

Differences between groups were seen in the scale parameter of the Weibull (λ), which controls the rate of maturation. Shifts in days-to-maturation as small as 0.64 days can be detected with high power under low variance. Under the highest scenarios of variance, larger differences on the scale of 2 days can be detected. Reduced models that lack a complex error structure produce biased estimates of the shape parameter of the Weibull, producing a wider distribution of individual development times, regardless of group, source, or replicate. Using methods developed in this paper for fitting models with a complex error structure to interval censored data, this class of shared frailty models would be applicable in a wide range of ecological systems. Although we have explored time-to-maturation, the methods would be identical for any time-to-event variable, such as survival, oviposition, or onset of disease.