Year: 2020
Type: dissertation
Abstract: The goal of personalized medicine is to give the right treatment to the right patient at the right dose using all we know about the patient. With the increasing availability of biomarkers and prediction models, there is the potential for individualized treatment based on patient specific factors. There are many statistical challenges associated with achieving this goal. One is how to develop and assess good predictions models. Another is how to define a criteria for an optimal treatment when there are multiple outcomes and then how to analyze available data to determine the optimal treatment for each future patient. In Chapter II, we consider the assessment of prediction models using data with missing biomarker values. We propose inverse probability weighted (IPW) and augmented inverse probability weighted (AIPW) estimates of the area under the ROC curve (AUC) and Brier Score to handle the missing data. AIPW is a double-robust method that is robust to the misspecification of either a model for the missingness mechanism or a model for the distribution of the missing variable. We evaluated the performance of IPW and AIPW in comparison with multiple imputation (MI) in simulation studies under missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR) scenarios. We illustrate these methods using an example from prostate cancer. In Chapters III and IV we consider the setting where there is an existing dataset of patients treated with heterogeneous doses and including binary efficacy and toxicity outcomes and patient factors such as clinical features and biomarkers. The goal is to analyze the data to estimate an optimal dose for each (future) patient based on their clinical features and biomarkers. In Chapter III, we propose an optimal individualized dose finding rule by maximizing utility functions for individual patients while limiting the rate of toxicity. The utility is defined as a weighted combination of efficacy and toxicity probabilities. We model the binary efficacy and toxicity outcomes using logistic regression with dose, biomarkers and dose-biomarker interactions. To incorporate the large number of potential biomarkers, we use the LASSO method. We additionally constrain the dose effect to be non-negative for both efficacy and toxicity for all patients. The proposed methods are illustrated using a dataset of patients with lung cancer treated with radiation therapy. In Chapter IV, we extend the approach of Chapter III and propose to use flexible machine learning methods such as random forests and Gaussian processes to build models for efficacy and toxicity depending on the dose and biomarkers. In addition, we allow for dependence between efficacy and toxicity. A copula is used to model the joint distribution of the two outcomes and the estimates are constrained to have non-decreasing dose-efficacy and dose-toxicity relationships. Numerical utilities are assigned to each potential outcome pair, which allow the improvement in the utility due to a change in efficacy to depend on the level of toxicity. For each patient, the optimal dose is chosen to maximize the utility function or the posterior mean of the utility function. We further adjust the utility function with more constraints to incorporate clinical requirements, and consider the uncertainty in the estimation of the utility function in the optimal dose selection. The various models and methods are evaluated in a simulation study and illustrated using data from a lung cancer study.
Author: Pin Li
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3122704744