Fits a Cox proportional hazards regression adjusting for mismatched data using a mixture modeling framework in the secondary analysis setting. The method relies on a two-component mixture model where true matches follow the Cox model and mismatches follow the marginal distribution of the survival outcome. Variance estimates are obtained via Louis' method.
Usage
coxphMixture(
x,
y,
cens,
z,
m.rate = NULL,
safe.matches = NULL,
control = list(),
...
)Arguments
- x
A matrix or data.frame of covariates (design matrix).
- y
A numeric vector of observed time-to-event outcomes.
- cens
A numeric vector indicating censoring status (1 = censored, 0 = event). Note: This is the reverse of the standard
Survobject convention where 1 usually indicates an event.- z
A matrix or data.frame of mismatch covariates (e.g., match scores, blocking variables). Used to model the probability of a mismatch.
- m.rate
An optional numeric value between 0 and 1 specifying the assumed overall mismatch rate upper bound. If provided, the mismatch indicator model is constrained such that the average estimated mismatch rate does not exceed this bound.
- safe.matches
A logical vector indicating records known to be correct matches (TRUE). These records are fixed as matches (probability 1) during estimation. Defaults to all FALSE.
- control
An optional list of control parameters. Parameters can also be passed directly via
....louis.k: Number of Monte Carlo iterations for variance estimation (default: 1000).max.iter: Maximum EM iterations (default: 1000).cmax.iter: Maximum iterations for the constrained optimization subroutine (default: 1000).tol: Convergence tolerance (default: 1e-4).init.beta: Initial estimates for outcome model coefficients.init.gamma: Initial estimates for mismatch model coefficients.fy: Pre-calculated marginal density of the response. If NULL, estimated non-parametrically.
- ...
Additional arguments passed to
control.
Value
An list of results:
- coefficients
Estimated coefficients for the outcome model (beta).
- m.coefficients
Estimated coefficients for the mismatch model (gamma).
- var
Variance-covariance matrix of the estimates.
- linear.predictors
Linear predictors for the outcome model.
- means
Column means of the covariate matrix
x.- n
Number of observations.
- nevent
Number of events.
- match.prob
Posterior probabilities that each observation is a correct match.
- objective
Value of the negative log pseudo-likelihood at each iteration.
- converged
Logical indicating if the algorithm converged.
- Lambdahat0
Estimated baseline cumulative hazard.
- gLambdahat0
the baseline cumulative hazard for the marginal density of the response variable (using Nelson-Aalen estimator)
References
Bukke, P., Ben-David, E., Diao, G., Slawski, M., & West, B. T. (2025). Cox Proportional Hazards Regression Using Linked Data: An Approach Based on Mixture Modelling.
Examples
library(survival)
set.seed(123)
n <- 200
# Generate covariates
x_cov <- seq(-3, 3, length = n)
d_cov <- rep(0:1, each = n/2)
X <- cbind(d_cov, x_cov, x_cov * d_cov)
# True parameters
b <- c(-1.5, 1, 0.5)
sigma <- 0.25
mu <- X %*% b
y <- exp(drop(mu)) * rweibull(n, shape = 1/sigma)
# Censoring
cens <- (y >= 1.5)
y[cens] <- 1.5
# Generate mismatch errors
ps <- rbeta(n, 4.5, 0.5)
logit_ps <- log(ps / (1 - ps))
mp <- cbind(1, logit_ps)
gamma_true <- c(-0.5, 1)
m <- 1 - rbinom(n, prob = plogis(mp %*% gamma_true), size = 1)
yperm <- y
shuffled_ix <- sample(which(m == 1))
yperm[shuffled_ix] <- yperm[sample(shuffled_ix)]
# Fit model
fit <- coxphMixture(x = X, y = yperm, cens = as.numeric(cens),
z = matrix(logit_ps, ncol = 1),
control = list(max.iter = 50))
print(fit)
#> Call:
#> NULL
#>
#> Outcome Model Coefficients:
#> d_cov x_cov
#> 7.005 -4.377 -2.899
#>
#> Mismatch Model Coefficients:
#> [1] 0.9644
#>
#> Likelihood ratio test (model=outcome) not available due to pseudo-likelihood.
#> n= 200 , number of events= 144
summary(fit)
#>
#> Call:
#> NULL
#>
#> --- Outcome Model (Cox PH) ---
#> coef exp(coef) se(coef) z Pr(>|z|)
#> d_cov 7.00547 1102.65118 0.66757 10.494 < 2e-16 ***
#> x_cov -4.37692 0.01256 0.37763 -11.590 < 2e-16 ***
#> -2.89911 0.05507 0.61015 -4.751 2.02e-06 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> --- Hazard Ratios & Confidence Intervals ---
#> exp(coef) exp(-coef) lower .95 upper .95
#> d_cov 1.103e+03 9.069e-04 2.980e+02 4.080e+03
#> x_cov 1.256e-02 7.959e+01 5.994e-03 2.634e-02
#> 5.507e-02 1.816e+01 1.666e-02 1.821e-01
#>
#> --- Mismatch Indicator Model ---
#> Estimate Std. Error z value Pr(>|z|)
#> [1,] 0.9644 0.1566 6.158 7.37e-10 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Average Estimated Correct Match Rate: 0.8789
#> Events: 144 / Total: 200
#> Iterations: 24
#>