### Abstract

Adjusted variable plots are useful in linear regression for outlier detection and for qualitative evaluation of the fit of a model. In this paper, we extend adjusted variable plots to Cox's proportional hazards model for possibly censored survival data. We propose three different plots: a risk level adjusted variable (RLAV) plot in which each observation in each risk set appears, a subject level adjusted variable (SLAV) plot in which each subject is represented by one point, and an event level adjusted variable (ELAV) plot in which the entire risk set at each failure event is represented by a single point. The latter two plots are derived from the RLAV by combining multiple points. In each point, the regression coefficient and standard error from a Cox proportional hazards regression is obtained by a simple linear regression through the origin fit to the coordinates of the pictured points. The plots are illustrated with a reanalysis of a dataset of 65 patients with multiple myeloma.

Original language | English (US) |
---|---|

Pages (from-to) | 73-90 |

Number of pages | 18 |

Journal | Lifetime Data Analysis |

Volume | 2 |

Issue number | 1 |

State | Published - 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Applied Mathematics
- Medicine(all)

### Cite this

*Lifetime Data Analysis*,

*2*(1), 73-90.

**Adjusted Variable Plots for Cox's Proportional Hazards Regression Model.** / Hall, Charles B.; Zeger, Scott L.; Bandeen-Roche, Karen J.

Research output: Contribution to journal › Article

*Lifetime Data Analysis*, vol. 2, no. 1, pp. 73-90.

}

TY - JOUR

T1 - Adjusted Variable Plots for Cox's Proportional Hazards Regression Model

AU - Hall, Charles B.

AU - Zeger, Scott L.

AU - Bandeen-Roche, Karen J.

PY - 1996

Y1 - 1996

N2 - Adjusted variable plots are useful in linear regression for outlier detection and for qualitative evaluation of the fit of a model. In this paper, we extend adjusted variable plots to Cox's proportional hazards model for possibly censored survival data. We propose three different plots: a risk level adjusted variable (RLAV) plot in which each observation in each risk set appears, a subject level adjusted variable (SLAV) plot in which each subject is represented by one point, and an event level adjusted variable (ELAV) plot in which the entire risk set at each failure event is represented by a single point. The latter two plots are derived from the RLAV by combining multiple points. In each point, the regression coefficient and standard error from a Cox proportional hazards regression is obtained by a simple linear regression through the origin fit to the coordinates of the pictured points. The plots are illustrated with a reanalysis of a dataset of 65 patients with multiple myeloma.

AB - Adjusted variable plots are useful in linear regression for outlier detection and for qualitative evaluation of the fit of a model. In this paper, we extend adjusted variable plots to Cox's proportional hazards model for possibly censored survival data. We propose three different plots: a risk level adjusted variable (RLAV) plot in which each observation in each risk set appears, a subject level adjusted variable (SLAV) plot in which each subject is represented by one point, and an event level adjusted variable (ELAV) plot in which the entire risk set at each failure event is represented by a single point. The latter two plots are derived from the RLAV by combining multiple points. In each point, the regression coefficient and standard error from a Cox proportional hazards regression is obtained by a simple linear regression through the origin fit to the coordinates of the pictured points. The plots are illustrated with a reanalysis of a dataset of 65 patients with multiple myeloma.

UR - http://www.scopus.com/inward/record.url?scp=0030325217&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030325217&partnerID=8YFLogxK

M3 - Article

C2 - 9384650

AN - SCOPUS:0030325217

VL - 2

SP - 73

EP - 90

JO - Lifetime Data Analysis

JF - Lifetime Data Analysis

SN - 1380-7870

IS - 1

ER -