Heteroscedastic Personalized Regression Unveils Genetic Basis of Alzheimer's Disease Stratified by Cognitive Level

In contemporary medical research, patient heterogeneity plays a pivotal role in comprehending intricate diseases such as Alzheimers disease and various forms of cancer. Specifically, in the genomic analysis of Alzheimers disease, individual patients may exhibit unique causal mutations that significantly influence their therapeutic trajectory. Conventional models that share numerous parameters across all individuals struggle to discern this heterogeneity and identify the influential factors for individuals. To tackle this challenge, we propose an innovative approach called Heteroscedastic Personalized Regression (Het-PR) to estimate the heterogeneity across samples and obtain personalized models for each sample. We demonstrate the effectiveness and robustness of Het-PR through both simulation and real data experiments. In the simulation experiment, we show that Het-PR outperforms other state-of-the-art models in capturing inter-sample heterogeneity. In the real data experiment, we apply Het-PR to Alzheimers data and show that it can identify persuasive selected genetic factors for each individual patient. Interestingly, our results suggest that there might be different associative SNPs for AD patients stratified by different cognitive levels. Author summaryIn medical research, it has been observed that causes of a disease vary significantly among individuals, especially when looking at complex diseases like Alzheimers disease and cancer. For Alzheimers disease, obesity, age, gender, and depression may play different roles across different patients. When studying the genes of Alzheimers patients, we find that each person might have their own unique genetic changes that can affect their treatment. For example, Alzheimers patients with different genetic mutations may respond differently to the same treatment. Traditional research methods often miss these individual differences and cant always pinpoint important personalized factors for each patient, because they usually use one model for all patients. To better understand these differences, weve introduced a new method, Heteroscedastic Personalized Regression (Het-PR), which generates a personalized model for each individual. Our experiments show that Het-PR is more effective than other leading methods in identifying these patient differences and recognizing Alzheimers genetic basis for each patient through both simulation and real data experiments. When we used Het-PR on real Alzheimers data, it helped us spot key genetic factors for each patient. Additionally, in our study, we excitedly find that different genetic markers in Alzheimers patients are possibly based on their cognitive abilities. Software for Heteroscedastic Personalized Regression is available in https://github.com/rong-hash/Het-PR.