Modeling Colon Cancer Survival using a Proportional Hazard Mixture Cure Model with Principal Component Covariates

This study explores how gene expression data can help predict the survival times of colon cancer patients. Since the dataset is high-dimensional, Principal Component Analysis (PCA) reduces complexity while retaining essential information. Based on eigenvalue one criteria, proportion of variance accounted for, and scree plot analysis, 60 principal components (PCs) are selected as covariates. These are then used in a Proportional Hazard Mixture Cure Model, applying both Cox and Weibull as baseline models to differentiate between cured and uncured patients over a five-year follow-up period. Maximum Likelihood Estimation (MLE) is applied to estimate the model parameters. The results show that the Cox model provides more reliable estimates, indicated by lower AIC values, higher hazard rates, and statistically significant p-values (<0.05). On the other hand, the Weibull model finds no significant covariates (p-values >0.05), with only the intercept being significant. Furthermore, the Weibull model estimates a 100% cure rate, while the Cox model estimates 56%, suggesting that the Cox model provides a better fit for predicting survival outcomes. By integrating gene expression data into survival modeling, this study offers a more accurate and interpretable way to understand patient outcomes. The findings highlight the Cox mixture cure model as a valuable tool for guiding clinical decisions.