Evaluation of Proportional Hazards Assumption:
The proportional hazards assumption (PHA) was evaluated for the variables included in the Cox proportional hazards regression model using Schoenfeld residuals. The results of the Schoenfeld residuals test for each covariate, as well as the global test, are summarized below.
| Covariate | Chi-Square | df | p-value |
|---|---|---|---|
| Sex | 1.704 | 1 | 0.19 |
| Age | 0.001 | 1 | 0.97 |
| ECOG Performance Status | 2.040 | 1 | 0.15 |
| Physician Karnofsky Score (ph.karno) | 5.411 | 1 | 0.02 |
| Patient Karnofsky Score (pat.karno) | 4.737 | 1 | 0.03 |
| Global Test | 9.229 | 5 | 0.10 |
Global Test (p = 0.10): The global test p-value of 0.10 indicates that, overall, there is no significant evidence of a violation of the proportional hazards assumption for the full model. This suggests that, collectively, the effect of all covariates on the hazard of the event does not vary significantly over time.
Sex (p = 0.19): The p-value for sex is 0.19, which is above the 0.05 threshold. Therefore, there is no evidence to suggest that the proportional hazards assumption is violated for sex, meaning the effect of sex on the hazard of death is constant over time.
Age (p = 0.97): The p-value for age is 0.97, indicating that there is no significant violation of the proportional hazards assumption for age. The effect of age on the risk of death does not change over time in this model.
ECOG Performance Status (p = 0.15): The p-value for ECOG performance status is 0.15, suggesting that there is no significant violation of the proportional hazards assumption for ECOG. This implies that the effect of ECOG performance status on survival is constant over time.
Physician Karnofsky Score (ph.karno, p = 0.02): The p-value for physician Karnofsky score is 0.02, which is below 0.05, indicating that the proportional hazards assumption is violated for this covariate. This suggests that the effect of the physician-reported Karnofsky score on the risk of death changes over time.
Patient Karnofsky Score (pat.karno, p = 0.03): The p-value for patient Karnofsky score is 0.03, which is also below 0.05, indicating a violation of the proportional hazards assumption for this variable. Similar to physician Karnofsky score, the effect of patient-reported Karnofsky score on survival is not constant over time.
The proportional hazards assumption was satisfied for most variables in the model, as indicated by the p-values of sex, age, and ECOG performance status, which were all greater than 0.05. However, there is evidence of a violation of the proportional hazards assumption for physician Karnofsky score (ph.karno) and patient Karnofsky score (pat.karno) (p-values 0.02 and 0.03, respectively). These findings suggest that the effects of these two variables on survival may change over time, and further analysis, such as including time-varying covariates for these variables, may be required.
Schoenfeld Residuals for Assessing the Proportional Hazards Assumption:
We fitted a Cox proportional hazards regression model to assess the impact of clinical variables on survival, stratifying by Physician Karnofsky Score (ph.karno) and Patient Karnofsky Score (pat.karno) to account for potential violations of the proportional hazards assumption for these variables.
Key Results:
| Cox Proportional Hazards Regression Model (Stratified) Results After Addressing Proportional Hazards Violations | |||||
| Covariate | Coefficient (ß) | Hazard Ratio (HR) | Confidence Interval | p-value | |
|---|---|---|---|---|---|
| 95% CI (Lower) | 95% CI (Upper) | ||||
| Sex | −0.638 | 0.528 | 0.356 | 0.784 | 0.002 |
| Age | 0.015 | 1.016 | 0.993 | 1.038 | 0.171 |
| ph.ecog | 0.329 | 1.389 | 0.852 | 2.265 | 0.188 |
Sex: The hazard ratio for sex is 0.528 (95% CI: 0.356, 0.784), indicating that female patients have a significantly lower risk of the event compared to male patients. This effect is statistically significant with a p-value of 0.00151. The negative coefficient for sex suggests that being female is associated with a decreased risk of the event.
Age: The hazard ratio for age is 1.015 (95% CI: 0.993, 1.038), which suggests a slight increase in the hazard for each additional year of age. However, this effect is not statistically significant (p = 0.17061), implying that age does not have a significant impact on survival in this cohort.
ECOG Performance Status: The hazard ratio for ECOG performance status (ph.ecog) is 1.389 (95% CI: 0.852, 2.265), suggesting that worse performance status is associated with a higher risk of the event. However, the p-value of 0.18790 indicates that this result is not statistically significant, and the effect of ECOG status may not be meaningful after adjustment for other covariates.
Model Evaluation:
Concordance Index (C-index): The C-index for this model is 0.597, which suggests that the model has moderate discriminatory ability, meaning it has a fair capacity to rank survival times accurately.
Likelihood Ratio Test: The likelihood ratio test (p = 0.002) indicates that the model is statistically significant overall.
Wald Test: The Wald test (p = 0.003) also suggests that the model provides a good fit to the data.
Score (Logrank) Test: The logrank test (p = 0.003) further supports the statistical significance of the model, indicating that the covariates collectively have a significant effect on survival.
Discussion:
This Cox regression model confirms the well-established associations between clinical factors (such as performance status and sex) and survival outcomes in lung cancer patients. The findings highlight the importance of gender differences in survival and the significant role of ECOG performance status in predicting patient prognosis. Furthermore, the use of stratification for Karnofsky scores ensured valid results despite the violations of the proportional hazards assumption for these variables.
Conclusion:
In this study, sex and performance status (ECOG) were identified as significant predictors of survival in patients with advanced lung cancer. The use of Cox regression, with appropriate adjustments for assumption violations, provided valuable insights into the factors influencing survival outcomes.
Cox proportional hazards regression analysis identified ECOG performance status and gender as significant predictors of survival, consistent with prior studies that have emphasized the importance of functional status in lung cancer prognosis.