Fully flexible analysis of behavioural sequences based on parametric survival models with frailties: A tutorial

Abstract

Recent automated systems allow collecting continuous data on individual animals with high accuracy over a long time. During this time, animals can be traced across different (discrete) types of behavioural states, with the duration in each state being known. Nevertheless, analyses of such sequences of states or behaviours may prove difficult. Classic Markov-chain methods have limitations in respect to incorporating “memory” (effects of past states), the duration in the states and accounting for dependencies. Dependencies occur in many data sets, where, for example a variety of individuals from different groups are observed and/or when an experiment is divided in different crossover treatment phases. So-called parametric survival analysis with frailties can incorporate aforementioned aspects in one coherent model. The time spent in a specific state (performing a specific behaviour) can be modelled in dependence of the subsequent state (transition probabilities) while incorporating how these transitions are influenced by experimental treatments. In addition, prior states can be used as predictor variables (accounting for past behaviour). Finally, random effects can be included to account for dependencies according to, for example individual identity, group/farm/laboratory or experimental period. Using interactions between random and fixed effects, the within- and between-subject variability of the transition probabilities can be estimated to indicate variation between and consistency within individual subjects (individuality and personality). Moreover, relative hazards describing transitions from one state to several potential follow-up states can be estimated. Behavioural sequences and their modulation by experimental situations can be studied accordingly. Using two exemplary data sets, the data type and structure adequate for parametric survival analysis are introduced and advice is given on how to specify and run such models. Overall, parametric survival analysis with frailties presents a modern and versatile approach that can revive sequential analysis. This will facilitate more detailed use of behavioural data and accordingly detect more subtle aspects of behaviour.