# HCP prediction wrapper for multiple measurements with optional per-patient Bonferroni Wraps `hcp_conformal_region` to produce conformal prediction regions for a collection of measurements, possibly including multiple measurements per individual. Based on the structure of the test dataset, the prediction mode is determined automatically as follows, where $P$ denotes the number of patients (clusters) and $M$ denotes the number of measurements per patient: * P=1,\, M=1 : Predict a single patient with a single measurement. * P=1,\, M\\>1 : Predict a single patient with multiple measurements (e.g., repeated or longitudinal measurements for the same patient). If per-patient simultaneous prediction is desired, optional per-patient Bonferroni calibration can be applied. * P\\>1,\, M=1 : Predict multiple patients, each with a single measurement. Predictions are performed independently at the nominal level $\alpha$, without Bonferroni calibration. * P\\>1,\, M\\>1 : Predict multiple patients, each with multiple measurements. When per-patient simultaneous coverage is desired, a Bonferroni correction can be applied by using an effective level $\alpha / M_p$ for each measurement, yielding Bonferroni-adjusted marginal prediction regions for patient $p$. ```r hcp_predict_targets( dat, test, pid_col = "pid", x_cols, y_grid, alpha = 0.1, bonferroni = FALSE, return_region = FALSE, id_col = "id", y_col = "Y", delta_col = "delta", ... ) ``` ## Arguments - `dat`: Training/calibration data passed to `hcp_conformal_region`. - `test`: A data.frame of test measurements, where each row corresponds to a single measurement. The test data must follow one of the four clustered settings $P=1, M=1$, $P=1, M>1$, $P>1, M=1$, or $P>1, M>1$, where $P$ is the number of patients (clusters) and $M$ is the number of measurements per patient. The data.frame must include a patient identifier specified by `pid_col` and all covariate columns listed in `x_cols`. Repeated values of `pid_col` indicate multiple measurements (e.g., repeated or longitudinal measurements) for the same patient. - `pid_col`: Column in `test` giving the patient (cluster/subject) identifier. Default `"pid"`. - `x_cols`: Covariate column names (e.g., `c("X1")`). - `y_grid`: Candidate y-grid passed to `hcp_conformal_region`. - `alpha`: Nominal miscoverage level in (0,1) passed to `hcp_conformal_region`. - `bonferroni`: Logical; if TRUE, apply per-patient Bonferroni only when a patient has multiple test measurements (i.e., $M_p>1$). If FALSE, always use level $\alpha$. - `return_region`: Logical; if TRUE, return the full region (subset of `y_grid`) for each row. - `id_col, y_col, delta_col`: Column names in `dat` for patient ID, outcome, and missingness indicator. - `...`: Additional arguments forwarded to `hcp_conformal_region` (e.g., `S`, `B`, `combine_B`, `combine_S`, `dens_method`, `prop_method`, `seed`). ## Returns A list with: - **pred**: A data.frame in the same row order as `test`. It contains all columns of `test` plus the effective level `alpha_eff` and the prediction-band endpoints `lo` and `hi` for each measurement. - **region**: If `return_region=TRUE`, a list of length `nrow(test)` where each element is the subset of `y_grid` retained in the prediction region for the corresponding test row; otherwise `NULL`. - **meta**: A list with summary information, including the number of patients `P`, the per-patient measurement counts `M_by_pid`, and the settings `alpha` and `bonferroni`. ## Note When per-patient Bonferroni calibration is enabled and a patient has a large number of measurements (e.g., $M_p > 10$), the effective level $\alpha / M_p$ may be very small, which can lead to extremely wide prediction regions (potentially spanning the entire `y_grid`). This behavior is an inherent consequence of Bonferroni adjustment and not a numerical issue. In longitudinal or panel studies, a cluster corresponds to a single individual (subject), and within-cluster points correspond to multiple time points or repeated measurements on the same individual. In this setting, the time variable `time` can be treated as a generic covariate. In the examples below, time is represented by `X1`. ## Examples ```r ## ------------------------------------------------------------ ## Examples illustrating the four test-data settings: ## (P=1, M=1), (P=1, M>1), (P>1, M=1), and (P>1, M>1) ## ------------------------------------------------------------ set.seed(1) ## training data (fixed across all cases) dat_train <- generate_clustered_mar( n = 200, m = 4, d = 1, x_dist = "uniform", x_params = list(min = 0, max = 10), target_missing = 0.30, seed = 1 ) y_grid <- seq(-6, 6, length.out = 201) ## Case 1: P=1, M=1 (one patient, one measurement) test_11 <- data.frame( pid = 1, X1 = 2.5 ) out_11 <- hcp_predict_targets( dat = dat_train, test = test_11, x_cols = "X1", y_grid = y_grid, alpha = 0.1, S = 2, B = 2, seed = 1 ) out_11$pred ## Case 2: P=1, M>1 (one patient, multiple measurements) test_1M <- data.frame( pid = 1, X1 = c(1, 3, 7, 9) ) out_1M <- hcp_predict_targets( dat = dat_train, test = test_1M, x_cols = "X1", y_grid = y_grid, alpha = 0.1, S = 2, B = 2, seed = 1 ) out_1M$pred ## Case 3: P>1, M=1 (multiple patients, one measurement each) test_P1 <- data.frame( pid = 1:4, X1 = c(2, 4, 6, 8) ) out_P1 <- hcp_predict_targets( dat = dat_train, test = test_P1, x_cols = "X1", y_grid = y_grid, alpha = 0.1, S = 2, B = 2, seed = 1 ) out_P1$pred ## Case 4: P>1, M>1 (multiple patients, multiple measurements per patient) test_PM <- data.frame( pid = c(1,1, 2,2,2, 3,3), X1 = c(1,6, 2,5,9, 3,8) ) out_PM <- hcp_predict_targets( dat = dat_train, test = test_PM, x_cols = "X1", y_grid = y_grid, alpha = 0.1, S = 2, B = 2, seed = 1 ) out_PM$pred ```

hcp_predict_targets function