Variable selection for generalized linear mixed model by L1 penalization for predicting clinical parameters of ovarian cancer

University essay from Lunds universitet/Matematisk statistik

Author: Lan Hoa Diep; [2021]

Keywords: Mathematics and Statistics;

Abstract: The quantity of biomarkers, which are proteins in this case, in ovarian cancer (OC) tumor and immune tissue regions of interest (ROIs) were measured with the new technology Digital Spatial Profiler (DSP). These measurements were used to construct regression models on the biomarkers to predict for two clinical parameters; tumor type (”Type 1” vs ”Type 2”) and the immune infiltration type (”Cavities” vs ”Dispersed”). The dataset was divided into tumor and immune ROIs to analyze separately. A total of three models were constructed: immune ROI with immune infiltration type, immune ROI with tumor type, and tumor ROI with tumor type. Since there were repeated measurements on the same patient but on different ROIs, logistic linear mixed model with random intercept was used to account for the dependency of ROIs and allow for the intercept to vary between patients. Since there were too many biomarkers to regress on, Lasso was used in combination with mixed model (GLMMLasso) for automatic variable selection. The tuning parameter λ in Lasso was chosen using BIC with some supervision. The model of immune ROI with immune infiltration level included four variables with coefficients that make biological sense and has good fit with both the training and test data. The model of immune ROI with tumor type had three variables that also makes biological sense and fitted the training data well, but not too well for test data. The model of tumor ROI with tumor type had a total of 12 variables but some of the variable coefficients do not make sense biologically. It could probably be optimized by including fewer variables in the model. For any certain conclusion to be made about the predictability of the models, bigger sample size would be needed for refitting as well as testing the models.

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