Parametric Survival Models

Harrell, Frank E.

doi:10.1007/978-3-319-19425-7_18

Frank E. Harrell Jr.⁸

Part of the book series: Springer Series in Statistics ((SSS))

205k Accesses
6 Citations

Abstract

The nonparametric estimator of S(t) is a very good descriptive statistic for displaying survival data. For many purposes, however, one may want to make more assumptions to allow the data to be modeled in more detail. By specifying a functional form for S(t) and estimating any unknown parameters in this function, one can

1.
easily compute selected quantiles of the survival distribution;
2.
estimate (usually by extrapolation) the expected failure time;
3.
derive a concise equation and smooth function for estimating S(t), Λ(t), and λ(t); and
4.
estimate S(t) more precisely than S _KM(t) or S _Λ(t) if the parametric form is correctly specified.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 64.99; Price excludes VAT (USA)

Softcover Book: USD 84.99; Price excludes VAT (USA)

Hardcover Book: USD 129.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

J. Buckley and I. James. Linear regression with censored data. Biometrika, 66:429–36, 1979.
Article MATH Google Scholar
C. Cox. The generalized f distribution: An umbrella for parametric survival analysis. Stat Med, 27:4301–4313, 2008.
Article MathSciNet Google Scholar
C. Cox, H. Chu, M. F. Schneider, and A. Muñoz. Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Stat Med, 26:4352–4374, 2007.
Article MathSciNet Google Scholar
D. R. Cox. Regression models and life-tables (with discussion). J Roy Stat Soc B, 34:187–220, 1972.
MATH Google Scholar
D. R. Cox and E. J. Snell. A general definition of residuals (with discussion). J Roy Stat Soc B, 30:248–275, 1968.
MathSciNet MATH Google Scholar
R. B. D’Agostino, M. L. Lee, A. J. Belanger, and L. A. Cupples. Relation of pooled logistic regression to time dependent Cox regression analysis: The Framingham Heart Study. Stat Med, 9:1501–1515, 1990.
Article MATH Google Scholar
M. Glasser. Exponential survival with covariance. J Am Stat Assoc, 62:561–568, 1967.
Article Google Scholar
S. M. Gore, S. J. Pocock, and G. R. Kerr. Regression models and non-proportional hazards in the analysis of breast cancer survival. Appl Stat, 33:176–195, 1984.
Article Google Scholar
J. E. Herndon and F. E. Harrell. The restricted cubic spline hazard model. Comm Stat Th Meth, 19:639–663, 1990.
Article MathSciNet Google Scholar
J. E. Herndon and F. E. Harrell. The restricted cubic spline as baseline hazard in the proportional hazards model with step function time-dependent covariables. Stat Med, 14:2119–2129, 1995.
Article Google Scholar
S. L. Hillis. Residual plots for the censored data linear regression model. Stat Med, 14:2023–2036, 1995.
Article Google Scholar
P. Hougaard. Fundamentals of survival data. Biometrics, 55:13–22, 1999.
Article MATH Google Scholar
J. D. Kalbfleisch and R. L. Prentice. The Statistical Analysis of Failure Time Data. Wiley, New York, 1980.
MATH Google Scholar
C. Kooperberg and D. B. Clarkson. Hazard regression with interval-censored data. Biometrics, 53:1485–1494, 1997.
Article MATH Google Scholar
C. Kooperberg, C. J. Stone, and Y. K. Truong. Hazard regression. J Am Stat Assoc, 90:78–94, 1995.
Article MathSciNet MATH Google Scholar
G. P. S. Kwong and J. L. Hutton. Choice of parametric models in survival analysis: applications to monotherapy for epilepsy and cerebral palsy. Appl Stat, 52:153–168, 2003.
MathSciNet MATH Google Scholar
J. F. Lawless. Statistical Models and Methods for Lifetime Data. Wiley, New York, 1982.
MATH Google Scholar
M. A. Nicolaie, H. C. van Houwelingen, T. M. de Witte, and H. Putter. Dynamic prediction by landmarking in competing risks. Stat Med, 32(12):2031–2047, 2013.
Article MathSciNet Google Scholar
M. C. Pike. A method of analysis of certain class of experiments in carcinogenesis. Biometrics, 22:142–161, 1966.
Article Google Scholar
J. Stare, F. E. Harrell, and H. Heinzl. BJ: An S-Plus program to fit linear regression models to censored data using the Buckley and James method. Comp Meth Prog Biomed, 64:45–52, 2001.
Article Google Scholar
C. J. Stone, M. H. Hansen, C. Kooperberg, and Y. K. Truong. Polynomial splines and their tensor products in extended linear modeling (with discussion). Ann Stat, 25:1371–1470, 1997.
Article MathSciNet MATH Google Scholar
T. Therneau and P. Grambsch. Modeling Survival Data: Extending the Cox Model. Springer-Verlag, New York, 2000.
Book Google Scholar
S. Wellek. A log-rank test for equivalence of two survivor functions. Biometrics, 49:877–881, 1993.
Article MathSciNet MATH Google Scholar

Download references

Author information

Authors and Affiliations

Department of Biostatistics, School of Medicine Vanderbilt University, Nashville, TN, USA
Frank E. Harrell Jr.

Authors

Frank E. Harrell Jr.
View author publications
You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Harrell, F.E. (2015). Parametric Survival Models. In: Regression Modeling Strategies. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-19425-7_18

Download citation

DOI: https://doi.org/10.1007/978-3-319-19425-7_18
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19424-0
Online ISBN: 978-3-319-19425-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

Publish with us

Policies and ethics