Diagnostic plots to reveal functional form for covariates in multiplicative intensity models

P. M. Grambsch, Terry M Therneau, T. R. Fleming

Research output: Contribution to journalArticle

125 Citations (Scopus)

Abstract

We show how plots based on the residuals from a proportional hazards model may be used to reveal the correct functional form for covariates in the model. A smoothed plot of the martingale residuals was suggested for this purpose by Therneau, Grambsch, and Fleming (1990, Biometrika 77, 147160); however, its consistency required that the covariates be independent. They also noted that the plot could be biased for large covariate effects. We introduce two refinements which overcome these difficulties. The first is based on a ratio of scatter plot smooths, where the numerator is the smooth of the observed count plotted against the covariate, and the denominator is a smooth of the expected count. This is related to the Arias goodness-of-fit plot (1988, Journal of the American Statistical Association 83, 204-212). The second technique smooths the martingale residuals divided by the expected count, using expected count as a weight. This latter approach is related to a GLM partial residual plot, as well as to the iterative methods of Hastic and Tibshirani (1990, Biometrics 46, 1105-1016) and Gentleman and Crowley (1991, Biometrics 47, 1283-1296). Applications to survival data sets are given.

Original languageEnglish (US)
Pages (from-to)1469-1482
Number of pages14
JournalBiometrics
Volume51
Issue number4
DOIs
StatePublished - 1995
Externally publishedYes

Fingerprint

Diagnostic Plot
Biometrics
biometry
Proportional Hazards Models
Covariates
Multiplicative
Count
Martingale Residuals
Weights and Measures
Iterative methods
Hazards
Residual Plots
Scatter diagram
Numerator
Proportional Hazards Model
Survival Data
Denominator
Goodness of fit
methodology
Model

Keywords

  • Augmented partial residuals
  • Cox model
  • Partial residuals
  • Proportional hazards model

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Public Health, Environmental and Occupational Health
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Statistics and Probability

Cite this

Diagnostic plots to reveal functional form for covariates in multiplicative intensity models. / Grambsch, P. M.; Therneau, Terry M; Fleming, T. R.

In: Biometrics, Vol. 51, No. 4, 1995, p. 1469-1482.

Research output: Contribution to journalArticle

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