| Hierarchical logistic regression models expand conventional logistic regression models by treating some or all model parameters as random instead of fixed. In addition to overcoming convergence problems that may occur in sparse data, hierarchical logistic regression models not only integrate plausible higher-level covariate information into the conventional logistic regression models, but also reflect the uncertainty of parameter effects while this uncertainty is assumed to be zero or constant in the conventional logistic regression models. In applications using the Medicare database, hierarchical logistic regression models could be used for parameter estimation, where differences in adverse outcome rates across states and disease categories are treated as random effects. Here, we focus on the problem of projecting of future numbers of adverse outcomes after surgery in the Medicare population, which would be helpful for budget projections and future resource allocations. We find that the coverage of predictive intervals produced from prediction models that assuming constant regression coefficients across future years did not reflect observed variations as early as three years. To propagate uncertainty about predictions based on models fit to current data sets, we propose a fractional resampling procedure, which is motivated by the idea that hierarchical logistic regression coefficients follow a time-series model instead of being constant over time. Such an approach produces substantial improvements in coverage for predictive intervals for the number of adverse outcomes after glaucoma surgery. The methodology is illustrated through an analysis of HCFA glaucoma surgery data. |
