In the context of time‐to‐event analysis, a primary objective is to model the risk of experiencing a particular event in relation to a set of observed predictors. The Concordance Index (C‐Index) is a statistic frequently used in practice to assess how well such models discriminate between various risk levels in a population. However, the properties of conventional C‐Index estimators when applied to left‐truncated time‐to‐event data have not been well studied, despite the fact that left‐truncation is commonly encountered in observational studies. We show that the limiting values of the conventional C‐Index estimators depend on the underlying distribution of truncation times, which is similar to the situation with right‐censoring as discussed in Uno et al. (2011) [On the C‐statistics for evaluating overall adequacy of risk prediction procedures with censored survival data. Statistics in Medicine 30(10), 1105–1117]. We develop a new C‐Index estimator based on inverse probability weighting (IPW) that corrects for this limitation, and we generalize this estimator to settings with left‐truncated and right‐censored data. The proposed IPW estimators are highly robust to the underlying truncation distribution and often outperform the conventional methods in terms of bias, mean squared error, and coverage probability. We apply these estimators to evaluate a predictive survival model for mortality among patients with end‐stage renal disease.
Purpose The aims of this study were to develop a scoring model that predicts the effects of withdrawing inhaled corticosteroids (ICSs) from triple therapy and to examine its adaptability when applied to assess the effect of adding ICSs to dual bronchodilators patients with chronic obstructive pulmonary disease (COPD). Patients and Methods A scoring model was developed using the IMPACT study dataset, consisting of 2389 COPD patients treated with triple therapy before enrollment (ICS withdrawal dataset). The developed model consisted of COPD duration, Acute exacerbation history, Sex, Pulmonary function tests, blood Eosinophil count, and Race (CASPER) and was used to predict composite events of moderate-to-severe exacerbation, all-cause mortality, and pneumonia. Treatment heterogeneity was assessed using Cox interaction analyses. The CASPER model was applied to 540 COPD patients treated with dual bronchodilator before enrollment (ICS addition dataset). Validity was assessed using Harrell’s C-index, time-dependent receiver operating characteristic curves, and calibration plots. Results The cumulative incidence of the composite event was 60.1% over 12 months in the ICS withdrawal dataset. Cox interaction analyses revealed that ICS was different according to race and blood eosinophil counts. The hazard ratios (HRs) for dual bronchodilator compared with triple therapy were 1.318 (95% confidence interval (CI)=1.170–1.485; P -value <0.001) in whites and 0.922 (95% CI = 0.712–1.195; P -value=0.541) in other races. The treatment effect was different in the eosinophil count ≥0.3 group (HR = 1.586; 95% CI = 1.274–1.975) and in the eosinophil count = 0.1–0.3 group (HR = 1.211; 95% CI = 1.041–1.408), but it was same in the eosinophil count <0.1 (HR = 1.009; P -value=0.940). The CASPER model performed well with good discrimination and calibration, which were superior to the prediction based on exacerbation history and blood eosinophil count. Conclusion The presented CASPER model might be able to predict and compare the risk of composite events when dual bronchodilator or triple therapy is administered to COPD patients.
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