Backward Joint Model for the Dynamic Prediction of Both Time-to-Event and Longitudinal Outcomes

Provides tools to fit joint models of multivariate longitudinal data and time-to-event data for dynamic prediction. It allows the joint prediction of both future time-to-event outcomes and future longitudinal outcomes conditional on survival. The models accommodate irregularly measured longitudinal data and competing risks outcomes. The use of the backward joint model enables fast and efficient computation, especially for applications with large sample sizes and many longitudinal variables.

BJM

BJM fits a backward joint model of multivariate longitudinal outcomes and time-to-event data, and uses it to make dynamic predictions: given a patient's longitudinal history up to some prediction_time, predict their risk of an event (and, if desired, their future biomarker values) conditional on survival to that point. The backward joint model formulation keeps fitting and prediction fast, even with large sample sizes and many longitudinal variables, and accommodates irregularly measured longitudinal data and competing risks.

Installation

install.packages("BJM")

To install the development version from source (e.g. a local clone or tarball):

# install.packages("devtools")
devtools::install_local("path/to/BJM")

Quick start

Fitting and prediction is a four-step pipeline: fit a survival sub-model, fit a longitudinal sub-model per biomarker, then combine them to predict event risk and/or future biomarker values.

library(BJM)
data(pbc3)

## 1. Fit the survival sub-model (one row per patient)
data_survival_fitting <- pbc3[!duplicated(pbc3$id), ]

survival_fit_all <- survivalSub(
  data_survival_fitting,
  form_marginal_surv = Surv(years, status3) ~ age + sex,
  form_conditional_cr = status4 ~ years + age + sex
)

## 2. Fit the longitudinal sub-model(s), one per biomarker
long_sub_fixed <- list(
  "serBilir" = serBilir ~ year + age + sex + (years) + (years) * year,
  "albumin"  = albumin  ~ year + age + sex + (years) + (years) * year
)
long_sub_random <- list(
  "serBilir" = ~ year | id,
  "albumin"  = ~ year | id
)
data_fit_all <- list(pbc3[pbc3$status3 == 1, ], pbc3[pbc3$status3 == 1, ])

long_fit_all <- longitudinalSub(data_fit_all, long_sub_fixed, long_sub_random)

## 3. Predict event risk for a patient, using only their history up to
##    prediction_time
survival_variable_all <- list("Tyears1", "Tyears2", "Tyears3", "Tyears4")
survival_trans_function <- list(
  fun1 = function(x) abs(x - 1),
  fun2 = function(x) abs(x - 3),
  fun3 = function(x) abs(x - 5),
  fun4 = function(x) abs(x - 7)
)

data_raw_predict <- pbc3[pbc3$id == 2, ]
data_predict_all <- list(data_raw_predict, data_raw_predict)

risk <- dynamicPrediction(
  data_predict_all, long_fit_all, survival_fit_all,
  prediction_time = 5, horizon = 1, time_variable = "year",
  survival_variable_all, survival_trans_function,
  bandcount1 = 10, bandcount2 = 20
)
risk

## 4. Predict a future biomarker value conditional on survival
bio_pred <- dynamicPredictionBio(
  bio_i = 1, data_predict_all, long_fit_all, survival_fit_all,
  prediction_time = 5, horizon = 1, time_variable = "year",
  survival_variable_all, survival_trans_function,
  bandcount2 = 20, bandcount3 = 50
)
bio_pred$Y_predict

survival_variable_all/survival_trans_function above follow a common convention ("Tyears1", "Tyears2", ..., each the absolute distance from a fixed cut point); survivalTrans(c(1, 3, 5, 7)) builds that same pair for you instead of hand-writing two matching lists. And every data_*_all argument shown above (data_fit_all, data_predict_all, ...) also accepts a single bare data.frame — reused for every biomarker — instead of a repeated list, when all biomarkers share the same measurement data.

predictPlot() and riskPlot() visualize these predictions for a single patient; cmtPlot() plots observed longitudinal trajectories stratified by eventual outcome.

For the full walkthrough — including how to choose the bandcount1/ bandcount2/bandcount3 numerical-integration tuning parameters via a convergence check, and what the input-validation error messages look like — see vignette("BJM-intro", package = "BJM").