Moving Beyong The Cox Proportional Hazards Model When The Proportional Hazards Assumption Is In Doubt

BackgroundThree gynecologic cancers(cervical cancer,endometrial cancer,ovarian cancer)still affect women's life and health with a high mortality even in the rapidly development of medical technology today.Therefore an appropriate prognosis model and precision predicting model specifically for three cancers would be useful and clinically benefical.Endometrial cancer(EC)is the major malignant tumor in three gynecologic cancers,accounting 20%to 30%.In Europe and the United States,its incidence had became the first one in 2016.The new cases in the United States had exceeded cervical and ovarian cancer.And the incidence in developing countries has increased significantly in recent years.According to WHO,cervical cancer is the fourth most frequent cancer in women with an estimated 527,624 new cases in 2012 representing 7.9%of all female cancers and 265,672 deaths(7.5%of all female cancer).Although in recent years,the incidence in developed countries is declining,in some developing countries still ranked first in 2015.Approximately 90%the 270,000 deaths from cervical cancer in 2015 occurred in low-and middle-income countries.Ovarian cancer(OC)in the incidence of gynecological malignancies ranked second,mortality ranked first in the world,about 19 million new cases each year.Epidemiological studies have shown that women has 1.4%risk to suffer from ovarian cancer.Because ovarian cancer was deep in pelvic,lack of early symptoms and effective screening methods,only having 45%survival rate.It has been the most difficult to diagnosis and cure,the worst prognosis in gynecological malignancies.The most common regression modeling framework to explore prognostic factors and to estimate survival probabilities is fitting a Cox proportional hazards(PH)model.However,hazard ratio frequently varies with time in fact when the PH assumption is not satisfied.In such situation,a single hazard ratio(averaged hazard ratio over the follow-up)from the Cox PH model may result misleading conclusions when analyzing the time-varying covariates.Buckley-James model,one of the accelerated failure time model is a linear regression model for right censored data which presented by Buckley in 1979.It seems to be superior to Cox PH model in some studies.Trinquart et al.have advocated restricted mean survival time(RMST)difference as a summary statistic to evaluate intergroup effects whether evidence of non-proportionality of hazards was identified or not.Therefore,we used these two models to explore the relationship between prognostic factors and survival time.However,the hazard radio from the Cox PH model and the RMST difference are summary measures,could not show the hazard ratio in different time point.Cox suggested that the Etended Cox model can be constructed using the interaction term of time function and time dependent co variate to explore the relative risk ratio at different time points.Patients after diagnosis of cancer may pay more attention to the probability of "w" years'survival or mortality.The value of "W" here is often asked by the question "How long will I live?" or "what's the probability to be alive after the next "w" years from now?" Furthermore,the question maybe not only asked at the start of the treatment,but also asked anytime of the follow-up visits.This question emphasis the dynamic use of predictive models.Houwelingen designed the proportional baselines landmark supermodel based the Cox PH model taking into account time-varying effects.So we can use this model to obtain individual death rate after an arbitrary time point during follow-up.ObjectiveTo explore the the prognosis factors varying over time on overall survival and to obtain the 5-year dynamic survival for cervical cancer,endometrial cancer,ovarian cancer patients from SEER data.Using the Cox proportional hazards model,AFT model,generalized linear model based on RMST difference,extended Cox model,and PBLS model in dynamic prediction to give some statistical suggestions that could assess risks and predict survival probability for the clinical researches and patients when the proportional hazards assumption failed.MethodsThe outcome in this analysis was all-cause mortality from any type of death.Univariate analysis.The Kaplan-Meier curves was graphed to describe overall survival and the Log-rank test was used to test the significance between the curves.Then the univariable and multivariable Cox PH models were used to estimate HRs and 95%confidence intervals(CIs).Through the Grambsch-Themeau proportional hazards test,we found some factors violated the PH assumption.So,we used the AFT model to find the relationship between prognostic factors and survival time.We chose a restricted survival time,then computed the pseudo-value for each observation,finally fitted a generalized linear model(GLM)to assess the prognostic factors.As for the extended Cox model,we constructed Cox model with interaction between covariates and a time function to reflect the time-varying effect.For dynamic prediction analysis,we facilitated the proportional baselines landmark supermodel to obtain the 5-year dynamic survival rate.AIC?C-index?AUC were used to give the model's performance.All analyses employed the R(version 3.2.4)software and the significance level was 0.05.ResultsThree major gynecologic cancer mainly were married,white women.Age at diagnosis in endometrial cancer and ovarian cancer patients were elder than cervical cancer's.No differences were found the year of diagnosis.The FIGO stage I in endometrial cancer and cervical cancer patients were more than other stages,while FIGO stage III in ovarian cancer were the most.Lymph node metastasis occurred less than 30%in three cancers.As for radiotherapy,fewer endometrial carcinoma underwent,following by cervical cancer.Ovarian cancer was not included in the this study.More than 90%patients of ovarian cancer and endometrial cancer received the surgery treatment,cervical cancer is lower than 70%.The differentiation from high to low,malignant degree from low to high were:endometrial cancer,cervical cancer,ovarian cancer.The histology for endometrial cancer and ovarian cancer were mainly adenocarcinoma,while the cervical cancer mainly squamous cell carcinoma.The number of patients registered in the west was equal to the east.Cervical cancer easily occurred in the cervical.Ovarian cancer easily occurred in bilateral.For marital status,women(divorced,widowed,separated)has high risk to death compared with married women.Unmarried women was more complex.There was no difference between unmarried ladies and married women with endometrial cancer.Unmarried ladies with cervical cancer has significant higher survival rate than married.The hazard rate for unmarried and married women with ovarian cancer changed over time.The more age at diagnosis was,the lower the survival rate was.The hazard rate for age at diagnosis in cervical cancer had a time-varying effect.Different races had different survival rates,while there was no statistically difference between white and other ethnic groups with ovarian cancer.FIGO staging was higher,the lower survival rate it was.FIGO staging of endometrial carcinoma of the hazard ratio had a declined trend.Patients with lymph node metastasis had lower survival rate than that of patients without lymph node metastasis.The hazard ratio in endometrial cancer increased before than decreased,cervical cancer has s declined trend,and ovarian cancer remains the same.Surgery for three major gynecological malignant tumor is a protective factor.Dynamic prediction found that PBLS model can reflect the 5-year survival rate at different time points,while the Cox proportional hazards models can not reflect the changing process.We used five models to analyze three cancer patients.Extended Cox model showed the best performance among these models from C-index and AIC,following by the RMST model(in the cervical cancer),the AFT model,the Cox proportional hazards model,and the dynamic predictive.But in the AUC value,the dynamic prediction showed the better than the Cox proportional hazards model.So it is recommended to explore the risk factors for women with three cancer in the United States by using the extended Cox model,the RMST model to the cervical cancer and the AFT model to the other two.To predict the 5-year dynamic survival rate using the PBLS model.The dynamic prediction not only explored the prognostic factors,but also to predict the w year survival rate in different time points.ConclusionMarriage status,age at diagnosis,race,FIGO staging,lymph node metastasis,radiotherapy,surgery and so on affecting the femalel malignancy cancer survival.We firstly used PBLS model to predict 5-year survival rate in different time point for three major gynecologic malignant tumor.We also refer alternative models taking into account time-varying factors when the PH assumption isn't satisfied.