Competing risks analysis of correlated failure time data

Abstract

We develop methods for competing risks analysis when individual event times are correlated within clusters. Clustering arises naturally in clinical genetic studies and other settings. We develop a nonparametric estimator of cumulative incidence, and obtain robust pointwise standard errors that account for within-cluster correlation. We modify the two-sample Gray and Pepe-Mori tests for correlated competing risks data, and propose a simple two-sample test of the difference in cumulative incidence at a landmark time. In simulation studies, our estimators are asymptotically unbiased, and the modified test statistics control the type I error. The power of the respective two-sample tests is differentially sensitive to the degree of correlation; the optimal test depends on the alternative hypothesis of interest and the within-cluster correlation. For purposes of illustration, we apply our methods to a family-based prospective cohort study of hereditary breast/ovarian cancer families. For women with BRCA1 mutations, we estimate the cumulative incidence of breast cancer in the presence of competing mortality from ovarian cancer, accounting for significant within-family correlation.

Figure 1

Biases for the cumulative incidence functions by percentile of the standardized cumulative incidence function $F_1^{\ast }(t)$ when μ₁ = 0.1 and μ₂ = 0.1 for different cluster sizes m and correlation coefficient φ. Results were based on 10,000 replications.

Figure 2

ESEs, RSEs, and NSEs by percentile of the standardized cumulative incidence function $F_1^{\ast }(t)$. Results were based on 10,000 replications.

Figure 3

Power of the landmark test at t₉₀ (the 90% quantile of the normalized subdistribution function), the Gray test, and the Pepe–Mori test for value of the frailty parameter φ. Results were based on 10,000 replications. The baseline hazard rates are: (A) $h_1^{(0)}(t)=0.10$ and $h_1^{(1)}(t)=0.25$, (B) $h_1^{(0)}(t)=0.10$ and $h_1^{(2)}(t)=0.20\times \sqrt{t}$, (C) $h_1^{(0)}(t)=0.10$ and $h_1^{(2)}(t)=0.02\times t$, and (D) $h_1^{(1)}(t)=0.15$ and $h_1^{(2)}(t)=0.02\times t$.

Figure 4

Cumulative incidence of breast cancer in BRCA1 mutation-positive women, and corresponding pointwise 95% confidence intervals.