Model-Based Optimization of Subgroup Weights for Survival Analysis

Abstract

To obtain a reliable prediction model for a specific cancer subgroup or cohort is often difficult due to the limited number of samples and, in survival analysis, even more due to potentially high censoring rates. Sometimes similar datasets are available for other patient subgroups with the same or a similar disease and treatment, e.g., from other clinical centers. Simple pooling of all subgroups can decrease the variance of the predicted parameters of the prediction models, but also increase the bias due to potential high heterogeneity between the cohorts. A promising compromise is to identify which subgroups are similar enough to the specific subgroup of interest and then include only these for model building. Similarity here refers to the relationship between input and output in the prediction model, and not necessarily to the distributions of the input and output variables themselves. Here, we propose a subgroup-based weighted likelihood approach and evaluate it on a set of lung cancer cohorts. When interested in a prediction model for a specific subgroup, then for every other subgroup, an individual weight determines the strength with which its observations enter into the likelihood-based optimization of the model parameters. A weight close to 0 indicates that a subgroup should be discarded, and a weight close to 1 indicates that the subgroup fully enters into the model building process. MBO (model based optimization) can be used to quickly find a good prediction model in the presence of a large number of hyperparameters to be tuned. Here, we use MBO to identify the best model for survival prediction in lung cancer subgroups, where besides the parameters of a Cox model additionally the individual values of the subgroup weights are optimized. Interestingly, often the resulting models with highest prediction quality are obtained for a mixed weight structure, i.e. both weights close to 0, weights close to 1, and medium weights are optimal, reflecting the similarity of the corresponding cancer subgroups.