Analysis of Generalized Semiparametric Regression Models for Cumulative Incidence Functions with Missing Covariates

Abstract

The cumulative incidence function quantifies the probability of failure over time due to a specific cause for competing risks data. The generalized semiparametric regression models for the cumulative incidence functions with missing covariates are investigated. The effects of some covariates are modeled as non-parametric functions of time while others are modeled as parametric functions of time. Different link functions can be selected to add flexibility in modeling the cumulative incidence functions. The estimation procedures based on the direct binomial regression and the inverse probability weighting of complete cases are developed. This approach modifies the full data weighted least squares equations by weighting the contributions of observed members through the inverses of estimated sampling probabilities which depend on the censoring status and the event types among other subject characteristics. The asymptotic properties of the proposed estimators are established. The finite-sample performances of the proposed estimators and their relative efficiencies under different two-phase sampling designs are examined in simulations. The methods are applied to analyze data from the RV144 vaccine efficacy trial to investigate the associations of immune response biomarkers with the cumulative incidence of HIV-1 infection.

Keywords: Competing risks; Inverse probability weighted complete-case; RV144 vaccine efficacy trial; Semiparametric regression model; Time-varying effects; Two-phase sampling.

Figure 1

Comparison of the Full, IPW, CC estimators for η₀(t) under model (23) with n = 700 based on 1000 simulations under sampling designs I, II and III moving from the left panels to the right panels. Figures (a), (b) and (c) show biases of the estimates under designs I, II and III, respectively. Similarly, Figures (d), (e) and (f) show empirical standard errors of the estimates and Figures (g), (h) and (i) show coverage probabilities of 95% confidence intervals.

Figure 2

Comparison of the Full, IPW, CC estimators for η₀(t) under model (24) with n = 700 based on 1000 simulations under sampling designs I, II and III moving from the left panels to the right panels. Figures (a), (b) and (c) show biases of the estimates under designs I, II and III, respectively. Similarly, Figures (d), (e) and (f) show empirical standard errors of the estimates and Figures (g), (h) and (i) show coverage probabilities of 95% confidence intervals.

Figure 3

Estimated coefficient functions under model (25) for k = 1 (an HIV-1 near the A244 vaccine-insert) and for k = 2 (an HIV-1 far from the A244 vaccine-insert). Figures (a) shows the IPW estimate of η_k0(t) and (b) shows the IPW estimate of η_k1(t) for the antibody response biomarker R_i (IgG-A244V1V2), along with 95% pointwise confidence intervals.

Figure 4

Estimated cumulative incidence functions under model (25) for k = 1 (an HIV-1 near the A244 vaccine-insert) and for k = 2 (an HIV-1 far from the A244 vaccine-insert). Figures (a), (b) and (c) show F̂_k(t|X_i, Z_i) at the first (Q₁), second (Q₂) and third quartile (Q₃) of observed antibody response biomarker R_i (IgG-A244V1V2) at each level of behavioral risk score groups (Low, Medium, High), respectively.

Figure 5

Comparison of the Full, IPW, CC estimators for η_k0(t) and η_k1(t) for the RV144 data simulation under (25) for k = 1 with s₀ = 0.03, n = 8198 and approximately 98% censoring based on 500 simulations. Figures (a), (b) show biases of the estimates, Figures (c) and (d) show empirical standard errors of the estimates and Figures (e), (f) show coverage probabilities of 95% confidence intervals for η_k0(t) and η_k1(t).

Figure 6

Comparison of the Full, IPW, CC estimators for η_k0(t) and η_k1(t) for the RV144 data simulation under (25) for k = 2 with s₀ = 0.03, n = 8198 and approximately 98% censoring based on 500 simulations. Figures (a), (b) show biases of the estimates, Figures (c) and (d) show empirical standard errors of the estimates and Figures (e), (f) show coverage probabilities of 95% confidence intervals for η_k0(t) and η_k1(t).