Predicting the restricted mean event time with the subject's baseline covariates in survival analysis

Abstract

For designing, monitoring, and analyzing a longitudinal study with an event time as the outcome variable, the restricted mean event time (RMET) is an easily interpretable, clinically meaningful summary of the survival function in the presence of censoring. The RMET is the average of all potential event times measured up to a time point τ and can be estimated consistently by the area under the Kaplan-Meier curve over $[0, \tau ]$. In this paper, we study a class of regression models, which directly relates the RMET to its "baseline" covariates for predicting the future subjects' RMETs. Since the standard Cox and the accelerated failure time models can also be used for estimating such RMETs, we utilize a cross-validation procedure to select the "best" among all the working models considered in the model building and evaluation process. Lastly, we draw inferences for the predicted RMETs to assess the performance of the final selected model using an independent data set or a "hold-out" sample from the original data set. All the proposals are illustrated with the data from the an HIV clinical trial conducted by the AIDS Clinical Trials Group and the primary biliary cirrhosis study conducted by the Mayo Clinic.

Reply to M. Horiguchi et al

“…3 After adjusting for stratification factors, the RMST was 1.5 months lower in the pazopanib arm compared with paclitaxel arm (80% CI, 22.7 to 20.3 months; unadjusted one-sided P 5.96, on the basis of a truncation time of 17.9 months). This is stronger evidence for the superiority of paclitaxel than using the proportional hazards approach, which had a P value of .89.…”

To maintain or not, that is the question

“…Using the area between the Kaplan-Meier curves, the time to next chemotherapy was prolonged by an average of only 2Á8 months [95% confidence interval (CI) 1Á0-4Á6] in the first 48 months of follow-up. The confidence intervals were obtained by a perturbation resampling method based on data reconstructed from the Kaplan-Meier curves (Guyot et al, 2012;Tian et al, 2014). Rituximab maintenance increased the PFS by an average of 5Á5 months (95% CI 3Á6-7Á5) during the first 48 months, but PFS events included asymptomatic lymph node growth detected by routine imaging.…”

Women's Health Initiative estrogen plus progestin clinical trial

“…6 Nevertheless, several authors agreed that times using HRs may pose difficulty in interpreting clinical results. [6][7][8][9] Indeed, results that are statistically significant within a large sample size may not translate into a significant clinical difference. 10,11 Restricted mean survival time (RMST) is a measure of mean survival from time 0 to a specified time point.…”

“…In contrast to HRs obtained in Cox proportional hazards analysis, RMST does not require proportional hazards assumptions. [7][8][9] Royston and Parmar 7,8 proposed estimating and reporting RMST and expressing treatment effects as the difference in RMST between studied randomized arms at a suitable follow-up time point. Time difference in the onset of events should not be evaluated by HRs.…”

“…6 Rather, difference in RMST is used as a measure to determine interpretable differences in treatment effects (complementing the information provided by HRs) to ensure a correct interpretation of the intervention. [7][8][9] To assess the clinical effects of CEE/MPA combination on postmenopausal women in the WHI study, 1 we proposed to determine differences in RMST 7,8 for the outcomes of the WHI study (invasive breast cancer, coronary heart disease, stroke, pulmonary embolism, colorectal cancer, and hip fracture) between placebo and CEE/MPA at 5.2-year follow-up.…”