Hierarchical Conformal Prediction for Clustered Data with Missing Responses // Implements hierarchical conformal prediction for clustered data with missing responses. The method uses repeated cluster-level splitting and within-cluster subsampling to accommodate dependence, and inverse-probability weighting to correct distribution shift induced by missingness. Conditional densities are estimated by inverting fitted conditional quantiles (linear quantile regression or quantile regression forests), and p-values are aggregated across resampling and splitting steps using the Cauchy combination test.