The data for this example were taken from a heart failure analysis, and the primary results of this analysis can be seen in the form of the parameter estimates (or more commonly as the hazard ratios). After fitting the model, it was determined that the key predictor variables influencing survival probability include age (HR=1.047, 95% CI=[1.028,1.067]), a low ejection fraction (HR=2.159, 95% CI=[1.167,4.231]), high blood pressure (HR=1.632, 95% CI=[1.062,2.485]), and high serum creatine (HR=2.226, 95% CI=[1.391,3.534]). Intuitively, these results seem to fit with the general understanding of the risk factors associated with heart failure (in other words, older patients with poor heart and kidney function, and increased blood pressure are at a higher risk of heart failure than others who may be younger, with better heart or kidney function, or with lower blood pressure).
The residual graphs generated by this analysis suggest that the assumptions upon which Cox proportional hazards regression relies had not been violated. A lack of trend in the scaled Schoenfeld residuals suggests that the proportional hazards assumption was not grossly violated for the analysis of this data, and the deviance residuals vs. covariate plots indicate that there were no immediately apparent outliers in the data to be removed. There was a slight trend in the plot of deviance residuals vs linear predictor/HR, but this was likely due to the high prevalence of censored data within the sample (ratio of censored observations to events = 2.1146 and the ratio of censored observations to total observations = 0.6789) and not indicative of any violation of the linearity assumptions for the model.
Interestingly, a number of predictor variables failed to achieve “significance” (those with confidence intervals for their hazard ratios that included 1) including sex, smoking status, and diabetes. The authors from which the data for this example were obtained suggest that the reason for this may be due to the fact that these factors are often considered predictors of the early stages of heart failure, while the individuals in this study represent a population exhibiting advanced stages of heart failure.
