Resumo: Abstract: In many experimental settings, event times are recorded at discrete intervals, e.g. days, and can be viewed as a form of longitudinal repeated-measurement data with the outcome on each day being death or survival. Here we consider such data for groups of individuals, specifically groups of the termite Heterotermes tenuis treated by different isolates of the fungus Beauveria bassiana with 5 replicates of each isolate. The aim is to identify the effective isolates, characterised for example by short LT50s, and also to look for reliable isolates with small replicate variability. We introduce a family of discrete survival models that can incorporate both proportional and additive hazards to describe the mortality history of the groups of termites. These models include an arbitrary piecewise constant baseline hazard and additional parameters are used to characterise the efficacy of the different isolates. Random effect versions of these models are also used to account for the appreciable isolate and replicate variation. In addition, we make links between ordered multinomial models (with ordered categories given by days) and the discrete survival approach using conditional responses over time for the deaths from the number at risk in each time interval, a form of sequential binomial model. In the discrete survival models, including time as a factor gives a baseline discrete hazard function. The ordered multinomial models do not include this and try to capture this time dependence through terms for the ordered time, such as a simple trend. Fitting a continuation ratio sequential binomial model without the time factor and just a simple time trend gives comparable results to the ordered multinomial. In addition, we have explored using different link functions, including logit, cloglog, and clog, for the ordered multinomial models and the discrete survival models, giving very little difference in the results. Different link functions are more interesting in the discrete survival models, where they have an interpretation in terms of the hazards. We can replace the binomial by the quasi-binomial or beta-binomial, and the estimated dispersions are similar to those from an ordered Dirichlet multinomial model. The fitted models can be used to summarise the effectiveness and reliability of the isolates. Furthermore, by using a non-parametric distribution for the isolate random effect, a more formal clustering of similar isolates can be obtained. The models can also be extended to include time-dependent isolate effects, allowing for a more general classification of the efficacy and virulence of the isolates. This study was partially financed by the São Paulo Research Foundation (FAPESP), Brazil. Project Numbers: 2022/11865-1 and 2024/01638-3.
Shortbio: Possui graduação em Engenharia Agronômica pela Universidade de São Paulo (1975), mestrado em Agronomia (Estatística e Experimentação Agronômica) pela Universidade de São Paulo (1978), doutorado em Agronomia (Estatística e Experimentação Agronômica) pela Universidade de São Paulo (1985) e pós-doutorado no Imperial College, Londres (1986-1987). Atualmente, é professora titular da Universidade de São Paulo, no Departamento de Ciências Exatas da ESALQ/USP. Tem experiência na área de Probabilidade e Estatística, com ênfase em Probabilidade e Estatística Aplicadas, atuando, principalmente, em modelos lineares generalizados e extensões. Assumiu os cargos de Incoming-President (2011), President (2012-2013), Outgoing-President (2014) e Chair do Nominating Committee (2015-2016) da International Biometric Society. Doctor Honoris Causa pela Hasselt University, Bélgica em 15/05/2019.