Prediction models
In PDRobust: Robust Longitudinal Effects Under Truncation by Death

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  dev = "ragg_png",
  dpi = 192,
  fig.width = 7,
  fig.height = 4.5,
  out.width = "90%",
  fig.align = "center",
  warning = FALSE,
  message = FALSE
)

Introduction

The complete workflow is illustrated as follows. This article focuses on the package's prediction models, including three nuisance models PSPred(), PrinPred() and OutPred().

data -> Mapping() -> DataCheck() -> DataStandard()
     -> prediction / diagnostic / analysis functions

library(PDRobust)
data("BiSample", package = "PDRobust")

map <- Mapping(
  id = "id",
  time = "time",
  treatment = "A",
  survival = "S",
  outcome = "Y",
  baseline_time = 0,
  cutoff_time = 2,
  covariates = c("X1", "X2", "X3", "X4", "X5","X6"),
  interest_vars = c("X1", "X2"),
  y_type = "B"
)

pd_data <- DataStandard(BiSample, map)

head(pd_data)

ps_fo <- A ~ X1 + X3 + X4 + X5 + X6
prin_fo <- S ~ (X1 + X3 + X4 + X5 + X6 ) * A
out_fo <- Y ~ (X1 + X3 + X4 + X5 + X6) * A

Propensity score model

PSPred() returns a numeric vector of propensity score estimation, which is defined as the conditional probability of receiving treatment given the specified covariates. The argument ps_fo specified the propensity score model formula. The argument fit_dat provides the dataset to fit the mode, whereas pred_dat is for propensity score predictions. The argument mapping is the original mapping object at the beginning of the workflow and supplies the relevant structural variable definitions.

The logistic model is fitted only on baseline observations, then used to predict every row of pred_dat. Additional arguments supplied through ... are forwarded to the underlying glm() call, allowing users to customize the model-fitting procedure.

ps <- PSPred(
  ps_fo = ps_fo,
  fit_dat = pd_data,
  pred_dat = pd_data,
  mapping = map
)
head(ps)

Principal score model

PrinPred() estimates cumulative principal score under a specified treatment level and returns a numeric vector. For longitudinal data with multiple time points, the cumulative score combines the estimated survival probabilities across the observed post-baseline times. For data containing a single observed time point, the model is fitted using the complete dataset.

The argument prin_fo, fit_dat, and pred_dat specify the formula, data used to fit the model and the observations where predictions are generated, respectively. The argument mapping is the original argument mapping. The argument a specifies the treatment group under which the principal scores are predicted.

p1 <- PrinPred(
  prin_fo = prin_fo,
  fit_dat = pd_data,
  pred_dat = pd_data,
  a = 1,
  mapping = map
)
head(p1)

Outcome prediction model

OutPred() estimates potential outcomes under a specified treatment level and returns the predictions as a row-aligned numeric vector.

The argument out_fo, fit_dat, pre_dat is the outcome model formula, data used to fit the model and data in which predictions are generated, respectively. The argument mapping is the original argument mapping. The argument a specifies the treatment group under which the outcomes are predicted.

The model-fitting procedure depends on the outcome type specified in mapping. For a continuous outcome, OutPred() fits a linear regression model and returns the conditional means. For a binary outcome, it fits a logistic regression model.

mu0 <- OutPred(
  out_fo = out_fo,
  fit_dat = pd_data,
  pred_dat = pd_data,
  a = 0,
  mapping = map
)

head(mu0)

Tips:

Model-fitting issues such as complete or quasi-complete separation, aliased nuisance-model coefficients, or extreme fitted probabilities may generate warnings. These conditions do not necessarily invalidate the predictions, provided that the fitted model returns a complete, finite, and correctly aligned prediction vector.

In contrast, missing, non-finite, or row-misaligned predictions are treated as errors. Each direct prediction function reports a single standardized warning for each model fit.