Abstract
SUMMARY Nonproportional hazards can often be expressed by extending the Cox model to include time varying coefficients; e.g., for a single covariate, the hazard function for subject i is modelled as exp { fl(t)Zi(t)}. A common example is a treatment effect that decreases with time. We show that the function /3(t) can be directly visualized by smoothing an appropriate residual plot. Also, many tests of proportional hazards, including those of Cox (1972), Gill & Schumacher (1987), Harrell (1986), Lin (1991), Moreau, O'Quigley & Mesbah (1985), Nagelkerke, Oosting & Hart (1984), O'Quigley & Pessione (1989), Schoenfeld (1980) and Wei (1984) are related to time-weighted score tests of the proportional hazards hypothesis, and can be visualized as a weighted least-squares line fitted to the residual plot.
Keywords
MathematicsStatisticsEconometrics
Affiliated Institutions
Related Publications
Explaining heterogeneity in meta-analysis: a comparison of methods
Exploring the possible reasons for heterogeneity between studies is an important aspect of conducting a meta-analysis. This paper compares a number of methods which can be used ...
Maximum likelihood fitting using ordinary least squares algorithms
Abstract In this paper a general algorithm is provided for maximum likelihood fitting of deterministic models subject to Gaussian‐distributed residual variation (including any t...
A Linear Spatial Correlation Model, with Applications to Positron Emission Tomography
Abstract A simple spatial-correlation model is presented for repeated measures data. Correlation between observations on the same subject is assumed to decay as a linear functio...
Publication Info
- Year
- 1994
- Type
- article
- Volume
- 81
- Issue
- 3
- Pages
- 515-526
- Citations
- 5332
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
5332
OpenAlex
Cite This
Patricia M. Grambsch,
Terry M. Therneau
(1994).
Proportional hazards tests and diagnostics based on weighted residuals.
Biometrika
, 81
(3)
, 515-526.
https://doi.org/10.1093/biomet/81.3.515
Identifiers
- DOI
- 10.1093/biomet/81.3.515