Abstract
The paper investigates diagnostic procedures for the specification of common hazard models in duration analysis. It is shown that under mixed hazard specifications the survival functions of different subgroups cannot cross. A nonparametric test for the crossing of two survival functions is provided and its applications in duration analysis are discussed. In particular, the proportional hazard model with unobserved heterogeneity (PHU) is investigated, and procedures are developed to test whether given data are consistent with the PHU model and whether they contain unobserved heterogeneity within the PHU specification. Examples in which crossing survivals are of substantive concern are discussed, including the dynamics of infectious diseases and the demand for vaccination.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
American Academy of Pediatricians (1992).Red Book. Washington, D.C.
Andersen, P.K. (1982). Testing goodness of fit of Cox’s regression and life model.Biometrics 38, 67–77.
Anderson, R., and May, R. (1991).Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press.
Bailey, N. (1975).The Mathematical Theory of Infectious Diseases, 2nd edn. Hafner Press.
Castillo-Chavez, C. (1989).Mathematical and Statistical Approaches to Aids Epidemiology. New York and Heidelberg: Springer Verlag.
Conover, W.J. (1967). The distribution functions of Tsao’s truncated Smirnov statistics.The Annals of Mathematical Statistics 38, 1208–1215.
Cox, D.R. (1972). Regression models and life tables (with discussion).Journal of the Royal Statistical Society, B 34, 187–220.
Cox, D.R., and Oakes, D. (1984).Analysis of Survival Data. London: Chapman and Hall.
Farewell, V.T. (1986). Mixture models in survival analysis: Are they worth the risk?The Canadian Journal of Statistics 14, 257–262.
Fleming, Th.R., O’Fallon, J.R., O’Brien, P.C., and Harrington, D.P. (1980). Modified Kolmogorov-Smirnov test procedures with application to arbitrarily right-censored data.Biometrics 36, 607–625.
Fleming, Th.R., and Harrington, D.P. (1981). A class of hypothesis tests for one and two sample censored survival data.Communications in Statistics A 10, 763–794.
Geoffard, P., and Philipson, T. (1995). The empirical content of canonical models of infectious disease.Biometrika 82, 110–113.
Harter, H.L., and Owen, D.B. (1970).Selected Tables in Mathematical Statistics, vol. 1. Chicago: Markham.
Hawkins, D.L., and Kochar, S.C. (1991). Inference for the crossing point of two continuous cdf’s.The Annals of Statistics 19, 1626–1638.
Kalbfleisch, J.D., and Prentice, R.L. (1980).The Statistical Analysis of Failure Time Data. New York: Wiley.
Lancaster, T. (1990).The Econometric Analysis of Transition Data. Cambridge, UK: Cambridge Univ. Press.
Lin, D.Y., Wei, L.J., and Ying, Z. (1993). Checking the Cox model with cumulative sums of martingale-based residuals.Biometrika 80, 557–572.
Mosler, K. (1995). Testing whether two distributions are stochastically ordered or not. In: H. Rinne/B. Rüger/H. Strecker eds., Grundlagen der Statistik und ihre Anwendungen, Festschrift für Kurt Weichselberger, Heidelberg: Physica, pp. 149–155.
Philipson, T. (1997). Private vaccination and public health: An empirical examination for U.S. measles.Journal of Human Resources 31, 611–630.
Rothan, S.A.M., and Gideon, R.A. (1996) A two-sample distribution-free scale test of the Smirnov type,Communications in Statistics—Simulation 25, 785–800.
Schmid, F., and Trede, M. (1996). Testing for first order stochastic dominance in either direction.Computational Statistics 11, 165–173.
Schoenfeld, D. (1980). Chi-squared goodness-of-fit tests for the proportional hazards regression model.Biometrika 67, 145–153.
Schumacher, M. (1984). Two-sample tests of Cramér-von Mises- and Kolmogorov-Smirnov-type for randomly censored data.International Statistical Review 52, 263–281.
Tsao, C.K. (1954). An extension of Massey’s distribution of the maximum deviation between two sample cumulative step functions.The Annals of Mathematical Statistics 25, 587–592.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mosler, K., Philipson, T. Specification analysis in mixed hazard models and a test of crossing survival functions. Statistical Papers 40, 37–54 (1999). https://doi.org/10.1007/BF02927109
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02927109