Statistical issues in survival analysis (Part XVVVVVVII)
January 15, 2025
In this paper the authors proposed prognostic accuracy measures for recurrent event data. They did so by developing semiparametric estimators for making inferences about the prognostic accuracy measures that accommodate recurrent events. Usually a Poisson process is used for the recurrent events, however, there could be unobserved heterogeneity. One way that this could be accounted for is by use of random effects (frailities) in the model. Therefore, their proposed estimators of accuracy measures were based on a semiparametric frailty model.
The authors came up with updated true positive fraction, TPF, and false positive fraction, FPF, rates. Also they extended the definition of the PPV and the NPV. The estimation was conducted with a semiparametric mixed Poisson model, which as they said is commonly used to analyze recurrent event data with inter-individual variation. The model also incorporated a random effect (frailty) component to the Poisson model where they estimated a conditional, subject-specific intensity. They assumed the frailty followed a gamma distribution with mean of 1 and variance of theta. For model estimation they used an algorithm proposed by Klein and Nielsen (Klein, 1992 and Nielsen et al., 1992).
They evaluated the finite sample performance of the proposed estimators through their series of simulation studies with varying degrees of unobserved heterogeneity of the recurrent event process. They generated recurrent event times from a proportional intensity model. The accuracy
parameters were fairly close to their true values in terms of the coverage probabilities. They also found negligible bias under frailty misspecification. They also evaluated their methods on a real dataset to treat CF where they used FEV as a biomarker. They evaluated their versions of ROC, AUC, PPV, and NPV curves. Their measures give clinicians a measures to evaluate risk in terms of recurrent events.
In their summary they note their measures are not appropriate when the data have missing information. They suggested imputation could be done but they haven’t yet assessed the robustness of such method. Also, they had not considered time-varying markers in their design, which they suggested shall also be explored.
Written by,
Usha Govindarajulu, PhD
Keywords: survival, prognostic marker, recurrent events, semiparametric, mixed model, frailty
References
R Dey, D E Schaubel, J A Hanley, P Saha-Chaudhuri, Time-dependent prognostic accuracy measures for recurrent event data, Biometrics, Volume 80, Issue 4, December 2024, ujae150, https://doi.org/10.1093/biomtc/ujae150
Klein J. P. (1992). Semiparametric estimation of random effects using the Cox model based on the EM algorithm Biometrics, 48, 795–806
Nielsen G. G., Gill R. D., Andersen P. K., Sørensen T. I. (1992). A counting process approach to maximum likelihood estimation in frailty models. Scandinavian Journal of Statistics, 19, 25–43.
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