Nonparametric Predictive Inference With Combined Data Under Different Right-Censoring Schemes
Tóm tắt
This article presents nonparametric predictive inference (NPI) for meta-analysis in which multiple independent samples of lifetime data are combined, where different censoring schemes may apply to the different samples. NPI is a frequentist statistical approach based on few assumptions and with uncertainty quantified via lower and upper probabilities. NPI has the flexibility to deal with a mixture of different types of censoring, mainly because the inferences do not depend on counterfactuals, which affect several inferences for more established frequentist approaches. We show that the combined sample, consisting of differently censored independent samples, can be represented as one sample of progressively censored data. This allows explicit formulas for the NPI lower and upper survival functions to be presented that are generally applicable. The approach is illustrated through an example using a small data set from the literature, for which several scenarios are presented.
Tài liệu tham khảo
Augustin, T., and F. P. A. Coolen. 2004. Nonparametric predictive inference and interval probability. J. Stat. Plan. Inference, 124, 251–272.
Balakrishnan, N. 2007. Progressive censoring methodology: an appraisal (with discussions). TEST, 16, 211–296.
Balakrishnan, N., and R. Aggarwala. 2000. Progressive censoring: Theory, methods, and applications. Boston, MA: Birkha.
Balakrishnan, N., E. Beutner, and E. Cramer. 2010. Exact two-sample nonparametric confidence, prediction, and tolerance intervals based on ordinary and progressively type-II right censored data. TEST, 19, 68–91.
Bordes, L. 2004. Non-parametric estimation under progressive censoring. J. Stat. Plan. Inference, 119, 171–189.
Borenstein, M., L. V. Hedges, J. P. T. Higgins, and H. Rothstein. 2009. Introduction to meta-analysis. Chichester, UK: Wiley.
Burke, M. 2011. Nonparametric estimation of a survival function under progressive type-I multistage censoring. J. Stat. Plan. Inference, 141, 910–923.
Coolen, F. P. A. 2006. On nonparametric predictive inference and objective Bayesianism. J. Logic Language Information, 15, 21–47.
Coolen, F. P. A. 2011. Nonparametric predictive inference. In International encyclopedia of statistical science, ed. M. Lovric, 968–970. Berlin, Germany: Springer.
Coolen, F. P. A., P. Coolen-Schrijner, and K. J. Yan. 2002. Nonparametric predictive inference in reliability. Reliability Eng. System Safety, 78, 185–193.
Coolen, F. P. A., and K. J. Yan. 2004. Nonparametric predictive inference with right-censored data. J. Stat. Plan. Inference, 126, 25–54.
Coolen-Maturi, T. 2014. Nonparametric predictive pairwise comparison with competing risks. Reliability Eng. System Safety, in press.
Coolen-Maturi, T., P. Coolen-Schrijner, and F. P. A. Coolen. 2011. Nonparametric predictive selection with early experiment termination. J. Stat. Plan. Inference, 141, 1403–1421.
Coolen-Maturi, T., P. Coolen-Schrijner, and F. P. A. Coolen. 2012c. Nonparametric predictive multiple comparisons of lifetime data. Commun. Stat. Theory Methods, 41, 4164–4181.
Coolen-Schrijner, P., T. A. Maturi, and F. P. A. Coolen. 2009. Nonparametric predictive precedence testing for two groups. J. Stat. Theory Pract., 3, 273–287.
De Finetti, B. 1974. Theory of probability. London, UK: Wiley.
Hill, B. M. 1968. Posterior distribution of percentiles: Bayes’ theorem for sampling from a population. J. Am. Stat. Assoc., 63, 677–691.
Hill, B. M. 1988. De Finetti’s theorem, induction, and An, or Bayesian nonparametric predictive inference (with discussion). In Bayesian statistics 3, ed. J. M. Bernando, M. H. DeGroot, D. V. Lindley, and A. Smith, 211–241. New York, NY: Oxford University Press.
Hill, B. M. 1993. Parametric models for an: Splitting processes and mixtures. J. R. Stat. Soc. Ser. B (Methodological), 55, 423–433.
Kaplan, E. L., and P. Meier. 1958. Nonparametric estimation from incomplete observations. J. Am. Stat. Assoc., 53, 457–481.
Maturi, T. A. 2010. Nonparametric predictive inference for multiple comparisons. PhD thesis, Durham University, Durham, UK. https://doi.org/www.npi-statistics.com
Maturi, T. A., P. Coolen-Schrijner, and F. P. A. Coolen. 2010a. Nonparametric predictive comparison of lifetime data under progressive censoring. J. Stat. Plan. Inference, 140, 515–525.
Maturi, T. A., P. Coolen-Schrijner, and F. P. A. Coolen. 2010b. Nonparametric predictive inference for competing risks. J. Risk Reliability, 224, 11–26.
Nelson, W. 1982. Applied life data analysis. New York, NY: Wiley.
Shafer, G. 1976. A mathematical theory of evidence. Princeton, NJ: Princeton University Press.
Volterman, W., and N. Balakrishnan. 2010. Exact nonparametric confidence, prediction and tolerance intervals based on multi-sample type-II right censored data. J. Stat. Plan. Inference, 140, 3306–3316.
Volterman, W., N. Balakrishnan, and E. Cramer. 2012. Exact nonparametric meta-analysis for multiple independent doubly type-II censored samples. Comput. Stat. Data Anal., 56, 1243–1255.
Volterman, W., N. Balakrishnan, and E. Cramer. 2014. Exact meta-analysis of several independent progressively type-II censored data. Appl. Math. Model., 38, 949–960.
Walley, P. 1991. Statistical reasoning with imprecise probabilities. London, UK: Chapman & Hall.
Weichselberger, K. 2001. Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung I. Intervallwahrscheinlichkeit als umfassendes Konzept. Heidelberg, Germany: Physika.
Yan, K. J. 2002. Nonparametric predictive inference with right-censored data. PhD thesis, Durham University, Durham, UK. https://doi.org/www.npi-statistics.com