Skip to main content
SpringerLink
Log in

Influence diagnostics for polyhazard models in the presence of covariates

  • Original Article
  • Published:
Statistical Methods and Applications Aims and scope Submit manuscript

Abstract

In this paper, we present various diagnostic methods for polyhazard models. Polyhazard models are a flexible family for fitting lifetime data. Their main advantage over the single hazard models, such as the Weibull and the log-logistic models, is to include a large amount of nonmonotone hazard shapes, as bathtub and multimodal curves. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. A discussion of the computation of the likelihood displacement as well as the normal curvature in the local influence method are presented. Finally, an example with real data is given for illustration.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aarset MV (1987) How to identify a bathtub hazard rate. IEEE Trans Reliab 36:106–108

    Article  MATH  Google Scholar 

  • Barlow WE, Prentice RL (1988) Residual for relative risk regression. Biometrika 75:65–74

    Article  MATH  MathSciNet  Google Scholar 

  • Basu S, Basu AP, Mukhopadhyay C (1999) Bayesian analysis for masked system failure data using non-identical Weibull Models. J Stat Plan Inference 78:255–275

    Article  MATH  MathSciNet  Google Scholar 

  • Bennet S (1983) Log-logistic regression models for survival data. Appl Stat 32:165–171

    Article  Google Scholar 

  • Berger JO, Sun D (1993) Bayesian analysis for the poly-Weibull distribution. J Am Stat Assoc 88:1412–1418

    Article  MATH  MathSciNet  Google Scholar 

  • Cook RD (1986) Assesment of local influence (with discussion). J R Stat Soc 48(2):133–169

    MATH  Google Scholar 

  • Cook RD, Peña D, Weisberg S (1988) The likelihood displacement: a unifying principle for influence. Commun Stat Theory Methods 17:623–640

    Article  Google Scholar 

  • David HA, Moeschberger M (1978) The theory of competing risks. MacMillan, New York

    MATH  Google Scholar 

  • Davison AC, Louzada-Neto F (2000) Inference for the poly-Weibull model. Statistician 49:189–196

    Google Scholar 

  • Díaz-García JA, Galea M, Leiva-Sánchez V (2004) Influence diagnostics for elliptical multivariate linear regression models. Commun Stat Theory Methods 32:625–641

    Article  Google Scholar 

  • Doornik J (1996) Ox: an object-oriented matrix programming language. International Thomson Business Press.

  • Escobar LA, Meeker WQ (1992) Assessing influence in regression analysis with censored data. Biometrics 48:507–528

    Article  MATH  MathSciNet  Google Scholar 

  • Fahrmeir L, Tutz G (1994) Multivariate statistical modelling based on generalized linear models. Springer, New York

    MATH  Google Scholar 

  • Galea M, Riquelme M, Paula GA (2002) Diagnostics methods in elliptical linear regression models. Braz J Probab Stat 14:167–184

    MathSciNet  Google Scholar 

  • Klein JP, Moeschberger ML (1997) Survival analysis: techniques forcensored and truncated data. Springer, New York

    Google Scholar 

  • Kuo L, Yang TY (2000) Bayesian reliability modeling for masked system lifetime. Stat Probab Lett 47:229–241

    Article  MATH  MathSciNet  Google Scholar 

  • Lee SY, Lu B, Song XY (2006) Assessing local influence for nonlinear structural equation models with ignorable missing data. Comput Stat Data Anal 50:1356–1377

    Article  MathSciNet  Google Scholar 

  • Lesaffre E, Verbeke G (1998) Local influence in linear mixed models. Biometrics 54:570–582

    Article  MATH  Google Scholar 

  • Louzada-Neto F (1999) Polyhazard models for lifetime data. Biometrics 55:1281–1285

    Article  MATH  Google Scholar 

  • McCullagh P, Nelder JA (1989) Generalized Linear Models, 2nd edn. Chapman and Hall, London

    MATH  Google Scholar 

  • Meeter CA, Meeker WQ (1994) Optimum accelerated life tests with a nonconstant scale parameter. Technometrics 36:71–83

    Article  MATH  Google Scholar 

  • Mudholkar GS, Srivastava Dk, Kollia GD (1996) A generalization of the Weibull distribution with application to the analysis of survival data. J Am Stat Assoc 91:1575–1583

    Article  MATH  MathSciNet  Google Scholar 

  • O‘Hara Hines RJ, Lawless JF, Carter EM (1992) Diagnostics for a cumulative multinomial generalized linear model with application to grouped toxicological mortality data. J Am Stat Assoc 87:1059–1069

    Article  Google Scholar 

  • Ortega EMM (2001) Influence analysis and residual in generalized log-gamma regression models. Doctor Thesis, Department of Statistics, University of São Paulo, Brasil (in Portuguese)

  • Ortega EMM, Bolfarine H, Paula GA (2003) Influence diagnostics in generalized log-gamma regression models. Comput Stat Data Anal 42:165–186

    Article  MathSciNet  MATH  Google Scholar 

  • Ortega EMM, Cancho VG, Bolfarine H (2006) Influence diagnostics in exponentiated-Weibull regression models with censored data. Stat Oper Res Trans 30:171–196

    MathSciNet  Google Scholar 

  • Paula GA (1993) Assessing local influence in restricted regressions models. Comput Stat Data Anal 16:63–79

    Article  MATH  MathSciNet  Google Scholar 

  • Paula GA (1995) Influence residuals in restricted generalized linear models. J Stat Comput Simul 51:63–79

    MathSciNet  Google Scholar 

  • Pettit AN, Bin Daud I (1989) Case-weight measures of influence for proportional hazards regression. Appl Stat 38:51–67

    Article  Google Scholar 

  • Shyur H, Elsayed AE, LuxhHj JT (1999) A general model for accelerated life testing with time-dependent covariates. Naval Res Logist 46:303–321

    Article  MATH  MathSciNet  Google Scholar 

  • Therneau TM, Grambsch PM, Fleming TR (1990) Martingale-based residuals for survival models. Biometrika 77:147–60

    Article  MATH  MathSciNet  Google Scholar 

  • Thomas W, Cook RD (1990) Assessing influence on predictions from generalizes linear models. Technometrics 32:59–65

    Article  MathSciNet  Google Scholar 

  • Williams DA (1984) Residuals in generalized linear model diagnostic using the deviance and single case deletion. Appl Stat 36:181–191

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ESALQ, Universdade de São Paulo, Piracicaba, Brazil

    Juliana B. Fachini & Edwin M. M. Ortega

  2. Departamento de Ciências Exatas, USP, Av. Pádua Dias 11 - Caixa Postal 9, 13418-900, Piracicaba, São Paulo, Brazil

    Edwin M. M. Ortega

  3. DEs, Universidade Federal São Carlos, São Carlos, Brazil

    Francisco Louzada-Neto

Authors
  1. Juliana B. Fachini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edwin M. M. Ortega
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Francisco Louzada-Neto
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Edwin M. M. Ortega.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fachini, J.B., Ortega, E.M.M. & Louzada-Neto, F. Influence diagnostics for polyhazard models in the presence of covariates. Stat Meth Appl 17, 413–433 (2008). https://doi.org/10.1007/s10260-007-0067-3

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10260-007-0067-3

Keywords

Search

Navigation