Improved Parametric Empirical Bayes for Longitudinal Biomarker Analysis

Extends parametric empirical Bayes (PEB) for longitudinal biomarker screening with a time-gap-aware standardization layer, covariate adjustment, and objective-driven multi-marker weighting. The layer models each subject's biomarker history with a random intercept (and an optional random slope) and autocorrelated, gap-scaled residuals, so that prediction uncertainty grows with the time between visits and per-visit specificity is preserved under irregular sampling. Marker weights are learned to optimize a user-selected clinical objective -- maximizing sensitivity at a fixed specificity, extending detection lead time, or a combined objective -- with optional feature selection and a choice of scalar or multivariate combiner. Functions for fitting, prediction, and evaluation (sensitivity, lead time, and specificity at chosen operating points) are provided. A manuscript describing the method is in preparation.

iPEB

Improved Parametric Empirical Bayes for Longitudinal Biomarker Analysis

iPEB extends parametric empirical Bayes (PEB) for longitudinal biomarker screening with three ingredients:

1. a time-gap-aware standardization layer — a random intercept (and optional slope) with autocorrelated, gap-scaled residuals, so prediction uncertainty grows with the time between visits and per-visit specificity is preserved under irregular sampling;
2. objective-driven multi-marker weighting — weights are learned to optimize a user-selected clinical objective rather than to tune opaque penalties; and
3. optional covariate adjustment and feature selection, with an automatically chosen scalar or multivariate combiner.

Installation

# install.packages("remotes")
remotes::install_github("bitansa/iPEB")

Quick start

library(iPEB)

data(ipeb_example)
train <- subset(ipeb_example, split == "train")
test  <- subset(ipeb_example, split == "test")

# Fit for the sensitivity objective at 95% specificity
fit <- ipeb(train, markers = c("m1", "m2", "m3"),
            id = "id", case = "case", time = "time", time_to_dx = "time_to_dx",
            objective = "sensitivity", alpha = 0.95)
fit

# Score and evaluate held-out subjects
scores <- predict(fit, test)
evaluate(fit, test, specificities = c(0.90, 0.95, 0.99))

# One-call fit-and-evaluate
ipeb_run(train, test, markers = c("m1", "m2", "m3"),
         objective = "leadtime", specificities = c(0.90, 0.95, 0.99))

Recovering conventional PEB

Conventional (marginal) PEB is a special case of iPEB: an intercept-only, i.i.d. layer on a single marker (no gap-scaling, no multi-marker weighting). Running it through the same package makes iPEB-versus-PEB comparisons exactly apples-to-apples -- identical layer and thresholding, only the modeling options differ. To score a plain PEB baseline for one marker:

# Conventional PEB: one marker, i.i.d. innovations, intercept-only mean model.
peb <- ipeb(train, markers = c("m1"),
            id = "id", case = "case", time = "time", time_to_dx = "time_to_dx",
            objective = "sensitivity", alpha = 0.95,
            slope = "off", innovation = "iid")
evaluate(peb, test, specificities = c(0.90, 0.95, 0.99))

Turning on innovation = "ar1" and/or slope = "on" for the same data recovers the time-gap-aware iPEB layer, so PEB and iPEB can be compared directly (this is exactly how the baselines are computed in the reproducibility scripts). A fixed multi-marker PEB composite (e.g. a published panel) can be scored the same way by passing that composite as a single marker.

Key options

Sensitivity and lead time are scored per patient over the whole pre-diagnostic trajectory; specificity is scored per visit and calibrated on the training controls, then applied unchanged to new data.

Shiny app

A point-and-click interface to the same engine ships with the package:

iPEB::run_app()

It exposes the objective, operating specificity, slope and innovation switches, covariates, optional feature selection, and evaluation specificities, and runs ipeb()/evaluate() under the hood. A hosted, browser-based version for users without R will be linked here once deployed.

Data format

A long data frame with one row per subject-visit: a subject id, a case indicator (1 = case, 0 = control), a visit-time column, a column giving each visit's days-to-diagnosis, and one column per biomarker. See ?ipeb_example.

Data availability

The lung analysis in the accompanying paper uses PLCO data, which are controlled-access through the NCI Cancer Data Access System (CDAS) under its standard data-use agreement and are not distributed with this package. The bundled ipeb_example dataset is entirely synthetic.

License

MIT © iPEB authors. A manuscript describing the method is in preparation.