Abstract
In epidemiological and clinical studies, the restricted mean lifetime is often of direct interest quantity. The differences of this quantity can be used as a basis of comparing several treatment groups with respect to their survival times. When the factor of interest is not randomized and lifetimes are subject to both dependent and independent censoring, the imbalances in confounding factors need to be accounted. We use the mixture of additive hazards model and inverse probability of censoring weighting method to estimate the differences of restricted mean lifetime. The average causal effect is then obtained by averaging the differences fitted values based on the additive hazards models. The asymptotic properties of the proposed method are also derived and simulation studies are conducted to demonstrate their finite-sample performance. An application to the primary biliary cirrhosis (PBC) data is illustrated.
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References
Breslow, N.E., Day, N. Statistical Methods in Cancer Research, Volume I, The Design and Analysis of Cohort Studies. IARC., Lyon, 1987
Chen, P.Y., Tsiatis, A.A. Causal inference on the difference of the restricted mean lifetime between two groups. Biometrics, 57: 1030–1038 (2001)
Cox, D.R. Regression models and life tables (with discussion). Journal of the Royal Statistical Society, Series B, 34: 187–220 (1972)
Dickson, E.R., Grambsch, P.M., Fleming, T.R., Fisher, L.D., Langworthy, A. Prognosis in primary biliary cirrhosis: model for decision making. Hepatology, 10: 1–7 (1989)
Ding, J., Wang, J.L. Modeling longitudinal data with nonparametric multiplicative random effects jointly with survival data. Biometrics, 64: 546–556 (2008)
Fleming, T.R., Harrington, D.P. Counting Processes and Survival Analysis. Wiley, New York, 1991
Karrison, T. Restricted mean life with adjustment for covariates. Journal of the American Statistical Association, 82: 1169–1176 (1987)
Lin, D.Y., Ying, Z.L. Semiparametric analysis of the additive risk model. Biometrika, 81: 61–71 (1994)
Mantel, N. Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemotherapy Reports, 50: 1623–1670 (1966)
Murtaugh, P.A., Dickson, E.R., VanDam, G.M., Malinchoc, M., Grambsch, P.M., Langworthy, A.L., Gips, C.H. Primary biliary cirrhosis: prediction of short-term survival based on repeated patient visits. Hepatology, 20: 26–134 (1994)
Peto, R., Peto, J. Asymptotically efficient rank invariant test procedures. Journal of the Royal Statistical Society: Series A (General), 135: 185–198 (1972)
Pollard, D. Empirical Processes: Theory and Applications. CA: IMS, Hayward, 1990
Robins, J.M. Information recovery and bias adjustment in proportional hazards regression analysis of randomized trials using surrogate markers. In: Biopharmaceutical Section, American Statistical Association, 1993, 24: 3.
Robins, J.M. Robust estimation in sequentially ignorable missing data and causal inference models. In: Bayesian Statistical Science Section, American Statistical Association, 2000, 1999: 6–10.
Robins, J.M., Rotnitzky, A. Recovery of information and adjustment for dependent censoring using surrogate markers. AIDS epidemiology, 297–331 (1992)
Rubin, D.B. Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66: 688–701 (1974)
Rubin, D.B. Inference and missing data. Biometrika, 63: 581–592 (1976)
Rubin, D.B. Bayesian inference for causal effects: The role of randomization. The Annals of Statistics, 6: 34–58 (1978)
Shows, J.H., Lu, W., Zhang, H.H. Sparse estimation and inference for censored median regression. Journal of Statistical Planning and Inference, 140: 1903–1917 (2010)
Tibshirani, R. The lasso method for variable selection in the cox model. Statistics in Medicine, 16: 385–395 (1997)
Zhang, H.H., Lu, W. Adaptive lasso for cox’s proportional hazards model. Biometrika, 94: 691–703 (2007)
Zhang, M., Schaubel, D.E. Estimating differences in restricted mean lifetime using observational data subject to dependent censoring. Biometrics, 67: 740–749 (2011)
Zucker, D.M. Restricted mean life with covariates: modification and extension of a useful survival analysis method. Journal of the American Statistical Association, 93: 702–709 (1998)
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The authors thank the Editor, an associate editor and two referees for their insightful comments and suggestions that greatly improved the article.
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This research was partly supported by the National Natural Science Foundation of China (11671268, 11771431 and 11690015), the Key Laboratory of RCSDS, CAS (2008DP173182).
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Li, Q., Zhang, Bx. & Sun, Lq. Estimating Differences in Restricted Mean Lifetime Using Additive Hazards Models under Dependent Censoring. Acta Math. Appl. Sin. Engl. Ser. 37, 17–34 (2021). https://doi.org/10.1007/s10255-021-0987-y
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DOI: https://doi.org/10.1007/s10255-021-0987-y