Fitting mixed models to messy longitudinal data: a case study involving estimation of post mortem intervals

Resumo: Non-linear mixed models are useful in many practical longitudinal data problems, especially when they are derived as solutions to differential equations generated by subject matter theoretical considerations. When this underlying rationale is not available, practitioners are faced with the dilemma of choosing a model from the

numerous ones available in the literature. The situation is even worse for messy data where interpretation and computational problems are frequent. This is the case with a pilot observational study conducted at the School of Medicine of the University of São Paulo in which a new method to estimate the time since death (post-mortem interval - PMI) is proposed. In particular, the attenuation of the density of intra-cardiac hypostasis (concentration of red cells in the vascular system by gravity) obtained from a series of tomographic images was observed in the thoraces of 21 bodies of hospitalized patients with known time of death. The images were obtained at different instants and not always at the same conditions for each body, generating a set of messy data. In this context, we consider three ad hoc models to analyse the data, commenting on the advantages and caveats of each approach.