Page 19 - Contributed Paper Session (CPS) - Volume 4

CPS2106 Julio M. Singer et al.

A linear mixed model for segmented regression
with smooth transition
2
1
1
Julio M. Singer , Francisco M.M. Rocha , Antonio Carlos Pedroso-de-Lima ,
Giovani, L. Silva , Giuliana C. Coatti , e Mayana Zatz
3
4
4
1 Department of Statistics, University of Sao Paulo
2 Paulista School of Politics, Economics and Business, Federal University of Sao Paulo
3 Department of Mathematics, University of Lisbon

4 Institute of Biosciences, University of Sao Paulo

Abstract
We consider random changepoint mixed segmented regression models
to analyse data obtained from a study conducted to verify whether
treament with stem cells may delay the onset of a symptom of
amyotrophic lateral sclerosis in genetically modified mice. The proposed
models capture the biological aspects of the data, accommodating a
smooth transition between the periods with and without symptoms. An
additional changepoint is considered to avoid negative predicted
responses. Given the non-linear nature of the model, we adapt an
algorithm proposed by Muggeo et al. (2014, Statistical Modelling) to
estimate the fixed parameters and to predict the random effects by fitting
linear mixed models at each step.

Key words
amyotrophic lateral sclerosis; fitting algorithm; mixed models; random effects.

1. Introduction
Amyotrophic Lateral Sclerosis (ALS) is one of the most common adult-
onset motor neuron disease causing a progressive, rapid and irreversible
degeneration of motor neurons in the cortex, brain stem and spinal cord. In
the majority of cases ALS occurs sporadically; in about 10% of the cases it is
caused by familial reasons. No effective treatment is available and cell therapy
clinical trials are currently being tested in ALS affected patients. The SOD1
gene encodes an important antioxidant human enzyme and mutations in
SOD1 represent one of the most frequent causes of ALS.
Among the different animal models for ALS, SOD1 mice are the most used
in pre-clinical studies. After the initial tremor in the limbs they develop muscle
weakness in early adulthood, become fully paralyzed and die. These mice over-
express the human SOD1 gene bearing the G93A mutation, a point mutation
found in familial ALS. Interestingly, in this animal model the disease
progression is different between the genders. Males have a shorter lifespan
and a clinical condition apparently more severe than females and differences

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