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

*(English)*Zbl 1414.62476Summary: 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.

##### MSC:

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62J12 | Generalized linear models (logistic models) |

62H11 | Directional data; spatial statistics |

##### Keywords:

autopsy; calibration; computed tomography; diagnostics; hypostasis; linear mixed models; post-mortem interval; residual analysis##### References:

[1] | Davidian, M. and Giltinan, D. M. (2003). Nonlinear models for repeated measurement data: An overview and update. Journal of Agricultural, Biological, and Environmental Statistics8, 387–419. |

[2] | Demidenko, E. (2013). Mixed Models: Theory and Applications with R, 2nd ed. New York: Wiley. · Zbl 1276.62049 |

[3] | Dolinak, D., Matshes, E. and Lew, E. O. (2005). Forensic Pathology: Principles and Practice. New York: Elsevier Academic Press. |

[4] | Fávero, F. (1991) Medicina Legal, 12a ed. Belo Horizonte: Villa Rica. |

[5] | Fitzmaurice, G. M., Laird, N. M. and Ware, J. H. (2011). Applied Longitudinal Analysis, 2nd ed. New York: Wiley. · Zbl 1226.62069 |

[6] | Graybill, F. A. and Iyer, H. K. (1994). Regression Analysis: Concepts and Applications. Belmont, CA: Duxbury Press. · Zbl 0868.62056 |

[7] | Harville, D. (1976). Extension of the Gauss–Markov theorem to include the estimation of random effects. The Annals of Statistics4, 384–395. · Zbl 0323.62043 |

[8] | Henderson, C. R. (1975). Best linear unbiased estimation and prediction under a selection model. Biometrics31, 423–447. · Zbl 0335.62048 |

[9] | Ishida, M., Gonoi, W., Hagiwara, K., Takazawa, Y., Akahane, M., Fukayama, M. and Ohtomo, K. (2011). Hypostasis in the heart and great vessels of non-traumatic in-hospital death cases on postmortem computed tomography: Relationship to antemortem blood tests. Legal Medicine (Tokyo)13, 280–285. |

[10] | Kaliszan, M., Hauser, R. and Kernbach-Wighton, G. (2009). Estimation of the time of death based on the assessment of post mortem processes with emphasis on body cooling. Legal Medicine (Tokyo)11, 111–117. |

[11] | Knight, B. (1991). Forensic Pathology, 1st ed. London: Edward Arnold. |

[12] | Laird, N. M. and Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics38, 963–974. · Zbl 0512.62107 |

[13] | Levy, A. D., Harcke, H. T. and Mallak, C. T. (2010). Postmortem imaging: MDCT features of postmortem change and decomposition. American Journal of Forensic Medicine and Pathology31, 12–17. |

[14] | Liang, H., Wu, H. and Zou, G. (2008). A note on the conditional AIC for linear mixed-effects models. Biometrika95, 773–778. · Zbl 1437.62527 |

[15] | Lindsey, J. K. (2004). Statistical Analysis of Stochastic Processes in Time. Cambridge: Cambridge University Press. |

[16] | Lindstrom, M. J. and Bates, D. M. (1990). Nonlinear mixed effects models for repeated measures data. Biometrics46, 673–687. |

[17] | Muggeo, V. M. R., Atkins, D. C., Gallop, R. J. and Dimidjian, S. (2014). Segmented mixed models with random changepoints: A maximum likelihood approach with application to treatment for depression study. Statistical Modelling14, 293–313. |

[18] | Pinheiro, J., Bates, D. M., DebRoy, S. Sarkar, D. and R Core Team (2014). nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1-117. Available at http://CRAN.R-project.org/package=nlme. |

[19] | R Core Team (2014). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Available at http://www.R-project.org/. |

[20] | Sannohe, S. (2002). Change in the postmortem formation of hypostasis in skin preparations 100 micrometers thick. American Journal of Forensic Medicine and Pathology23, 349–354. |

[21] | Sen, P. K., Singer, J. M. and Pedroso-de-Lima, A. C. (2009). From Small Sample to Asymptotic Methods in Statistics. Cambridge: Cambridge University Press. |

[22] | Shiotani, S., Kohno, M., Ohashi, N., Yamazaki, K. and Itai, Y. (2002). Postmortem intravascular high-density fluid level (hypostasis): CT findings. Journal of Computer Assisted Tomography26, 892–893. |

[23] | Singer, J. M., Rocha, F. M. M. and Nobre, J. S. (2017). Graphical tools for detecting departures from linear mixed model assumptions and some remedial measures. International Statistical Review85, 290–324. |

[24] | Thali, M. J., Yen, K., Schweitzer, W., Vock, P., Boesch, C., Ozdoba, C., Schroth, G., Ith, M., Sonnenschein, M., Doernhoefer, T., Scheurer, E., Plattner, T. and Dirnhofer, R. (2003). Virtopsy, a new imaging horizon in forensic pathology: Virtual autopsy by postmortem multislice computed tomography (MSCT) and magnetic resonance imaging (MRI): A feasibility study. Journal of Forensic Sciences48, 386–403. |

[25] | Vaida, F. and Blanchard, S. (2005). Conditional Akaike information for mixed-effects models. Biometrika92, 351–370. · Zbl 1094.62077 |

[26] | Vonesh, E. F. and Chinchilli, V. M. (1996). Linear and Nonlinear Models for the Analysis of Repeated Measurements. · Zbl 0893.62077 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.