Moving beyond the Cox proportional hazards model in survival data analysis: a cervical cancer study

Time-varying associations of patient and tumor characteristics with cancer survival: an analysis of SEER data across 14 cancer sites, 2004-2017

PURPOSE

Surveillance, Epidemiology, and End Results (SEER) cancer registries provides information about survival duration and cause of death for cancer patients. Baseline demographic and tumor characteristics such as age, sex, race, year of diagnosis, and tumor stage can inform the expected survival time of patients, but their associations with survival may not be constant over the post-diagnosis period.

METHODS

Using SEER data, we examined if there were time-varying associations of patient and tumor characteristics on survival, and we assessed how these relationships differed across 14 cancer sites. Standard Cox proportional hazards models were extended to allow for time-varying associations and incorporated into a competing-risks framework, separately modeling cancer-specific and other-cause deaths. For each cancer site and for each of the five factors, we estimated the relative hazard ratio and absolute hazard over time in the presence of competing risks.

RESULTS

Our comprehensive consideration of patient and tumor characteristics when estimating time-varying hazards showed that the associations of age, tumor stage at diagnosis, and race/ethnicity with risk of death (cancer-specific and other-cause) change over time for many cancers; characteristics of sex and year of diagnosis exhibit some time-varying patterns as well. Stage at diagnosis had the largest associations with survival.

CONCLUSION

These findings suggest that proportional hazards assumptions are often violated when examining patient characteristics on cancer survival post-diagnosis. We discuss several interesting results where the relative hazards are time-varying and suggest possible interpretations. Based on the time-varying associations of several important covariates on survival after cancer diagnosis using a pan-cancer approach, the likelihood of the proportional hazards assumption being met or corresponding interpretation should be considered in survival analyses, as flawed inference may have implications for cancer care and policy.

Effect of marital status on the survival outcomes of cervical cancer: a retrospective cohort study based on SEER database

BACKGROUND

Cervical cancer is the fourth most common malignant tumor troubling women worldwide. Whether marital status affects the prognosis of cervical cancer is still unclear. Here, we investigate the prognostic value of marital status in patients with cervical cancer based on the seer database.

MATERIAL/METHODS

The demographic and clinical data of patients with cervical cancer were extracted from the Surveillance, Epidemiology, and End Results (SEER) database from 1975 to 2017. Patients were divided into two groups (married and unmarried) according to marital status, and then the clinical characteristics of each group were compared using the chi-square test. Propensity score matching (PSM) was used to reduce differences in baseline characteristics. The overall survival (OS) and cervical cancer-specific survival (CCSS) were assessed by the Kaplan-Meier method, univariate and multivariate Cox regression models, and stratified analysis. Moreover, univariate and multivariate competing risk regression models were performed to calculate hazard ratios (HR) of death risk.

RESULTS

A total of 21,148 patients were included in this study, including 10,603 married patients and 10,545 unmarried patients. Married patients had better OS(P < 0.05) and CCSS (P < 0.05) compared to unmarried patients, and marital status was an independent prognostic factor for both OS (HR: 0.830, 95% CI: 0.798-0.862) and CCSS (HR: 0.892, 95% CI: 0.850-0.937). Moreover, after eliminating the competing risk, married patients (CCSD: HR:0.723, 95% CI: 0.683-0.765, P < 0.001) had a significantly decreased risk of death compared to unmarried patients. In stratified analysis, the married patients showed better OS and CCSS than the unmarried patients diagnosed in 1975-2000 and 2001-2017.

CONCLUSIONS

Being married was associated with a favorable prognosis of cervical cancer, and marital status was an independent prognostic factor for cervical cancer.

Individual dynamic prediction and prognostic analysis for long-term allograft survival after kidney transplantation

Background

Predicting allograft survival is vital for efficient transplant success. With dynamic changes in patient conditions, clinical indicators may change longitudinally, and doctors’ judgments may be highly variable. It is necessary to establish a dynamic model to precisely predict the individual risk/survival of new allografts.

Methods

The follow-up data of 407 patients were obtained from a renal allograft failure study. We introduced a landmarking-based dynamic Cox model that incorporated baseline values (age at transplantation, sex, weight) and longitudinal changes (glomerular filtration rate, proteinuria, hematocrit). Model performance was evaluated using Harrell’s C-index and the Brier score.

Results

Six predictors were included in our analysis. The Kaplan–Meier estimates of survival at baseline showed an overall 5-year survival rate of 87.2%. The dynamic Cox model showed the individual survival prediction with more accuracy at different time points (for the 5-year survival prediction, the C-index = 0.789 and Brier score = 0.065 for the average of all time points) than the static Cox model at baseline (C-index = 0.558, Brier score = 0.095). Longitudinal covariate prognostic analysis (with time-varying effects) was performed.

Conclusions

The dynamic Cox model can utilize clinical follow-up data, including longitudinal patient information. Dynamic prediction and prognostic analysis can be used to provide evidence and a reference to better guide clinical decision-making for applying early treatment to patients at high risk.

Dynamic risk prediction of BK polyomavirus reactivation after renal transplantation

Purpose

To construct a dynamic prediction model for BK polyomavirus (BKV) reactivation during the early period after renal transplantation and to provide a statistical basis for the identification of and intervention for high-risk populations.

Methods

A retrospective study of 312 first renal allograft recipients was conducted between January 2015 and March 2022. The covariates were screened using univariable time-dependent Cox regression, and those with P<0.1 were included in the dynamic and static analyses. We constructed a prediction model for BKV reactivation from 2.5 to 8.5 months after renal transplantation using dynamic Cox regression based on the landmarking method and evaluated its performance using the area under the curve (AUC) value and Brier score. Monte-Carlo cross-validation was done to avoid overfitting. The above evaluation and validation process were repeated in the static model (Cox regression model) to compare the performance. Two patients were presented to illustrate the application of the dynamic model.

Results

We constructed a dynamic prediction model with 18 covariates that could predict the probability of BKV reactivation from 2.5 to 8.5 months after renal transplantation. Elder age, basiliximab combined with cyclophosphamide for immune induction, acute graft rejection, higher body mass index, estimated glomerular filtration rate, urinary protein level, urinary leukocyte level, and blood neutrophil count were positively correlated with BKV reactivation, whereas male sex, higher serum albumin level, and platelet count served as protective factors. The AUC value and Brier score of the static model were 0.64 and 0.14, respectively, whereas those of the dynamic model were 0.79 ± 0.05 and 0.08 ± 0.01, respectively. In the cross-validation, the AUC values of the static and dynamic models decreased to 0.63 and 0.70 ± 0.03, respectively, whereas the Brier score changed to 0.11 and 0.09 ± 0.01, respectively.

Conclusion

Dynamic Cox regression based on the landmarking method is effective in the assessment of the risk of BKV reactivation in the early period after renal transplantation and serves as a guide for clinical intervention.

Dynamic Prediction of Survival after Curative Resection of Gastric Adenocarcinoma: A landmarking-based analysis

BACKGROUND

Accurate estimation of survival and recurrence are important to inform decisions regarding therapy and surveillance. We sought to design and validate a dynamic prognostic model for patients undergoing resection for gastric adenocarcinoma.

METHODS

Patients who underwent curative-intent surgery for gastric adenocarcinoma between 2000 and 2020 were identified using a multi-institutional database. Landmark analysis was used to create dynamic OS and DFS prediction models. Model performance was internally cross-validated via bootstrap resampling.

RESULTS

Among 895 patients, 507 (57.2%) patients underwent partial gastrectomy (n = 507, 57.2%) while 380 (42.8%) had total gastrectomy. Median tumor size was 40 mm (IQR: 25-65), most tumors were located in the antrum (n = 344, 39.5%) and infiltrated the subserosa (T3 tumors: n = 283, 31.9%) or serosa (T4 tumors: n = 253, 28.5%); lymph node metastasis occurred in 528 (59.1%) patients. Median OS and DFS were 17.5 (IQR: 7.5-42.8) and 14.3 months (IQR: 6.5-39.9), respectively. The impact of age, sex, preoperative comorbidities, tumor size and location, extent of lymphadenectomy and total number of lymph nodes examined, Lauren class, T and N category, postoperative complications, and tumor recurrence varied over time (all p < 0.05). An online tool to predict dynamic OS and DFS based on patient survival relative to time survived was developed and made available for clinical use. Discrimination ability of OS and DFS was excellent (C-index: 0.84 and 0.86, respectively) and calibration plots revealed good prediction.

CONCLUSIONS

An online dynamic prognostic tool was developed and validated to predict OS and DFS following resection of gastric adenocarcinoma. Landmark analysis to predict long-term outcomes based on follow-up time may be helpful to surgeons and patients.

Development and application of a dynamic prediction model for esophageal cancer

Background

Current prediction models of esophageal cancer (EC) are limited to predicting at a specific time point, and ignore changes in hazard ratios of predictive variables, known as time-varying effects. Our study aimed to investigate variables with time-varying effects in EC and to develop a prediction model that can update the 5-year predicted dynamic overall survival (DOS) probability during the follow-up period.

Methods

Firstly, the clinicopathological information and survival data of 4,541 patients with EC was obtained from the Surveillance, Epidemiology, and End Results (SEER) database between 2007 and 2011 for modeling. Secondly, the time-varying effect of variables was assessed and the dynamic prediction model was developed based on the proportional baselines landmark supermodel.

Results

Here, we found that age at diagnosis, sex, location of primary tumor, histological type, chemotherapy, surgery, and T stage showed significant time-varying effects on overall survival. Thirdly, the prediction model was validated by an internal SEER validation cohort and a Chinese patient cohort, respectively, and achieved promising results as follows: area under the curve (AUC) =0.733 (internal validation) and 0.864 (external validation). The heuristic shrinkage factor was 0.995. Finally, several clear cases were selected as examples for model application to map the patient’s 5-year DOS curves and to respectively demonstrate the impact of different variables’ time-varying effect on survival.

Conclusions

Overall, our results suggest that the existence of time-varying effect highlights the importance of updating the predicted survival probability during the follow-up period. Moreover, this prediction model can be used to assist doctors in making more-individualized treatment decisions based on a dynamic assessment of patient prognosis.

Dynamic prediction and analysis based on restricted mean survival time in survival analysis with nonproportional hazards

BACKGROUND AND OBJECTIVE

In the process of clinical diagnosis and treatment, the restricted mean survival time (RMST), which reflects the life expectancy of patients up to a specified time, can be used as an appropriate outcome measure. However, the RMST only calculates the mean survival time of patients within a period of time after the start of follow-up and may not accurately portray the change in a patient's life expectancy over time.

METHODS

The life expectancy can be adjusted for the time the patient has already survived and defined as the conditional restricted mean survival time (cRMST). A dynamic RMST model based on the cRMST can be established by incorporating time-dependent covariates and covariates with time-varying effects. We analyzed data from a study of primary biliary cirrhosis (PBC) to illustrate the use of the dynamic RMST model, and a simulation study was designed to test the advantages of the proposed approach. The predictive performance was evaluated using the C-index and the prediction error.

RESULTS

Considering both the example results and the simulation results, the proposed dynamic RMST model, which can explore the dynamic effects of prognostic factors on survival time, has better predictive performance than the RMST model. Three PBC patient examples were used to illustrate how the predicted cRMST changed at different prediction times during follow-up.

CONCLUSIONS

The use of the dynamic RMST model based on the cRMST allows for the optimization of evidence-based decision-making by updating personalized dynamic life expectancy for patients.