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. 2014 Apr;15(2):222-33.
doi: 10.1093/biostatistics/kxt050. Epub 2013 Nov 29.

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

Lu Tian  1 , Lihui Zhao, L J Wei
Affiliations

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

Lu Tian et al. Biostatistics. 2014 Apr.

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.

Keywords: Accelerated failure time model; Cox model; Cross-validation; Hold-out sample; Personalized medicine; Perturbation-resampling method.

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Figures

Fig. 1.
Fig. 1.
KM estimates of the survival functions of the two randomized groups based on the ACTG 320 data.
Fig. 2.
Fig. 2.
KM estimate of the overall patient survival function based on the PBC data.
Fig. 3.
Fig. 3.
Estimated subject-specific restricted mean survival time (solid curve) over the score, and its 95% pointwise (dashed curve) and simultaneous confidence intervals (shaded region). The dotted line is the 45formula image reference line. The survival function of the censoring time C is estimated locally (a) and based on the entire sample (b).
Fig. 4.
Fig. 4.
KM estimates of the survival functions of the four strata divided by quartiles of the scores based on the PBC data.
See this image and copyright information in PMC

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