57. Segmented Cox Regression (60 Patients)

Cox regression assesses time to events, like death or cure, and the effects of predictors like comorbidity and frailty. If a predictor is not significant, then time-dependent Cox regression may be a relevant approach. It assesses whether the predictor interacts with time. Time dependent Cox has been explained in Chap. 56. The current chapter explains segmented time-dependent Cox regression. This method goes one step further and assesses, whether the interaction with time is different at different periods of the study.

Primary question: is frailty a time-dependently changing variable in patients admitted to hospital for exacerbation of chronic obstructive pulmonary disease (COPD).

A simulated data file of 60 patients admitted to hospital for exacerbation of COPD is given underneath. All of the patients are assessed for frailty scores once a week. The frailty scores run from 0 to 100 (no frail to very frail)

The above table gives the first 42 patients of 60 patients assessed for their frailty scores after 1, 2 and 3 weeks of clinical treatment. It can be observed that in the first week frailty scores at discharge were 15–20, in the second week 15–32, and in the third week 14–24. Patients with scores over 32 were never discharged. Frailty scores were probably a major covariate of time to discharge. The entire data file is in extras.springer.com, and is entitled “chapter57segmentedcox”. We will first perform a simple time dependent Cox regression. Start by opening the data file in SPSS.

For analysis the statistical model Cox Time Dependent in the module Survival is required.

The above table shows the result: frailty is not a significant predictor of day of discharge. However, patients are generally not discharged from hospital until they are non-frail at a reasonable level, and this level may be obtained at different periods of time. Therefore, a segmented time dependent Cox regression may be more adequate for analyzing these data.

For analysis the statistical model Cox Time Dependent in the module Survival is again required.

The above table shows that the independent variable, segmented frailty variable T_COV_, is, indeed, a very significant predictor of the day of discharge. We will, subsequently, perform a multiple segmented time dependent Cox regression with treatment modality as second predictor variable.

The above table shows that both the frailty (variable T_COV_) and treatment (variable 3) are very significant predictors of the day of discharge with hazard ratios of 0,942 and 1,424. The new treatment is about 1,4 times better and the patients are doing about 0,9 times worse per frailty score point. If treatment is used as a single predictor unadjusted for frailty, then it is no longer a significant factor.

The p-value of treatment (variable 3) has risen from p = 0,0001 to 0,070. Probably, frailty has a confounding effect on treatment efficacy, and after adjustment for it the treatment effect is, all of a sudden, a very significant factor.

Cox regression assesses time to events, like death or cure, and the effects on it of predictors like treatment efficacy, comorbidity, and frailty. If a predictor is not significant, then time dependent Cox regression may be a relevant approach. It assess whether the time-dependent predictor interacts with time. Time dependent Cox has been explained in Chap. 56. The current chapter explains segmented time dependent Cox regression. This method goes one step further and assesses whether the interaction with time is different at different periods of the study. It is shown that a treatment variable may be confounded with time dependent factors and that after adjustment for it a statistically significant treatment efficacy can be demonstrated.

More background, theoretical and mathematical information of segmented Cox regression is given in Statistics applied to clinical studies 5th edition, Chap. 31, Springer Heidelberg Germany, 2012, from the same authors.