Adjust biomarker score with confounder-adjusted risk model

Function for biomarker score with confounder-adjusted risk model

Usage

adjust_score(
  data_set,
  biomarker,
  outcome,
  confounders = NULL,
  k = 2,
  maxit = 1000,
  epsilon = 1e-08,
  CompCase = FALSE,
  xgb_params = NULL,
  validate = FALSE,
  test_size = 0.2,
  seed = 123
)

Arguments

data_set: Data frame containing biomarker, outcome, and confounders.
biomarker: Character, name of biomarker column.
outcome: Character, name of binary outcome column (0/1).
confounders: Character vector of confounder column names (default = NULL).
k: Integer, number of mixture components (default = 2).
maxit: Integer, maximum EM iterations.
epsilon: Numeric, convergence tolerance for EM.
CompCase: Logical, whether to perform complete case analysis (default = FALSE).
xgb_params: Optional list of hyperparameters passed to xgboost::xgb.train. Can override default settings such as max_depth = 3, eta = 0.05, subsample = 0.8, and colsample_bytree = 0.8.
validate: Logical, whether to perform a train/test split. If TRUE, model performance is evaluated on a held-out test set. Validation is only performed when confounders are provided and an xgboost model is fitted.
test_size: Numeric, proportion of data used for the test set. Only used when validate = TRUE. Must be between 0 and 1.
seed: Integer, random seed for reproducibility of the train/test split.

Value

A list containing:

Mixture parameters (mu, sigma, lambda).
Fitted xgboost model object.
Training AUC (train_auc).
Cross-validated AUC from xgboost CV (cv_auc).
Test/validation AUC on held-out data (test_auc, only if validate = TRUE).
Augmented dataset with columns: p_disease (posterior probability from FMM) and adjusted_risk (confounder-adjusted risk score).

Details

This function implements a two-stage modeling pipeline:

Stage 1: Finite Mixture Model (FMM)

Fits a 2-component Gaussian mixture model to the biomarker distribution using the Expectation-Maximization (EM) algorithm (up to maxit iterations, tolerance epsilon).
Estimates component means ($\mu_1, \mu_2$), standard deviations ($\sigma_1, \sigma_2$), and mixing proportions ($\pi$).
Computes the posterior probability of disease for each subject: $$\hat{p}(x) = \frac{\hat{\pi} \cdot N(x|\hat{\mu}_2,\hat{\sigma}_2)}{\hat{\pi} \cdot N(x|\hat{\mu}_2,\hat{\sigma}_2) + (1-\hat{\pi}) \cdot N(x|\hat{\mu}_1,\hat{\sigma}_1)}$$ where $N(x|\mu,\sigma)$ is the Gaussian density.
The resulting p_disease represents the latent probability of disease given the biomarker value.

Stage 2: Confounder-Adjusted Risk Model (xgboost)

Trains a binary logistic xgboost model using predictors: p_disease (from FMM) plus specified confounders.
Model complexity (number of boosting iterations) is selected via cross-validation with early stopping.
Produces an adjusted_risk score in [0,1] for each subject, representing the confounder-adjusted probability of disease.

The disease component is identified using which.max(mu), assuming that higher biomarker values correspond to disease. If this assumption does not hold for your dataset, results may be misleading. A warning is issued if the assumption may not hold.

Examples

n <- 500
set.seed(123)

# outcome
DISEASE <- rbinom(n, 1, 0.35)

# biomarker depends on disease
PTAU <- rnorm(n, mean = 25 + 10 * DISEASE, sd = 8)

# confounders (optional noise)
AGE <- round(rnorm(n, 73, 7))
SEX <- sample(c(0, 1), n, replace = TRUE)
BMI <- rnorm(n, 25, 4)
HTN <- rbinom(n, 1, 0.3)
DM <- rbinom(n, 1, 0.2)

df <- data.frame(PTAU, AGE, SEX, BMI, HTN, DM, DISEASE)

res <- adjust_score(
df,
biomarker = "PTAU", outcome = "DISEASE",
confounders = c("AGE","SEX","BMI","HTN","DM"), validate = TRUE)
#> number of iterations= 704 
#> Setting levels: control = 0, case = 1
#> Setting direction: controls < cases
#> Setting levels: control = 0, case = 1
#> Setting direction: controls < cases
head(res$data[,c("PTAU","p_disease","adjusted_risk")])
#>       PTAU    p_disease adjusted_risk
#> 1 21.99518 3.013220e-22     0.1192439
#> 2 30.50499 7.443839e-10     0.2046204
#> 3 22.24866 1.057691e-21     0.1260243
#> 4 35.72397 3.366296e-04     0.5474330
#> 5 47.78807 9.895697e-01     0.6416051
#> 6 24.29148 4.884413e-20     0.1675190