Research And Application In Medical Studies Of Semiparametric Accelerated Failure Time Mixture Cure Model

Background:With the advancements in technology and improvements of medical quality,“long-term survivors” are common in medical studies which mean a fraction of population will not or never experience the event of interest even given enough follow-up time and often behave as longer censorting time.The phenomenon is common in oncological clinical trials or reasearches about other chronic diseases.However,an unstated assumption of typical survival analyses such as proportional hazard models(cox model)and accelerated failure time models is that every single subject will eventually experience the event of interest,given enough follow-up time.In order to take the situation above into account,classical survival models have been extended to cure models and the mixture cure models(MCM)are considered to be more feasible.The MCM belongs to the class of two-part models that considers jointly the modeling where the population is a mixture of two groups,the cured(incidence)and the uncured(latency).Generally,the cured is analyzed by logistic regression and the uncured is analyzed by different survival models,such as cox,parametirc survival analysis and so on.The two most frequently used are fully parametric models and semiparametric proportional hazards mixture cure models(PHMC).Neverthless,these two models also have their own liminations: the former is limited by the identification of survival distributions and the latter assumes the dataset should obey proportional hazard assumption(PH assumption).What’s more,recently in survival analyses,semiparametric accelerated failure time model is regarded as an alternative to cox model due to the two advantages: the model can not only be applied regardless of survival distributions,but also without PH assumption.And compared with cox model,it is feasible for higher-censoring data.Taking the conditions above into account,development of mixture cure models based on semiparametric accelerated failure time model is of much practice value.In addition,at present,majority of simulation studies are still based on an exponential or weibull distribution for the distribution of event times which assume the hazard is stable,monotonically increasing or decreasing.However,in medical studies,at least one turning point is observed in the underlying hazard function which means the survival distribution may be composed of two or more simple distributions.Taking this situation into account,Crowther et al.firstly introduced mixture weibull distribution into a simulation study in order to generate more complex medical plausible survival data in 2012.However,the survival data with proportional structure was not suitable for studies focusing on accelerated failure time models.Therefore,it is of potential theoretical and practice value to develop new simulation methods which can generate more complex plausible survival data for accelerated failure time model and exploring the reasonability and feasibility of mixture cure models combined with the semiparametric accelerated failure time model.Objective:Considering the phenomenon “long-term survivors”,this study aimed to develop accelerated failure time mixture cure model(AFTMC)and explored the performance in different scenarios based on a weibull distribution or mixture weibull distribution compared with the other four common parametric mixture cure models,which is expected to provide methodological support for analyses of data with cured subjects.Further,we introduced mixture survival distribution into simulation methods for accelerated failure time models in order to provide methodological support for survival simulations.Method:For the purposes above,the whole study adopted data simulation,model building,model assessment and case study,respectively.Data simulation: The Monte Carlo method was used to generate two covaries,one was a binary variable and the other one was a contingous variable.The survival time t and the cure indicator Y representing whether a subject was cured or not were simulated by an accelerated failure time model and a logistic model,respectively.Noteablely,the event times were simulatied on the basis of a simple distribution(weibull distribution)or a complex distribution(mixture weibull distribution).Further,combined with the cure indicator and censoring times,the final survival times T and the status indicator D were acquired.The censoring times obeyed uniform distribution and the limits were got by simulaton iteration.In addition,different scenarios were set: different sample size: based on weibull distribution: 200,500;based on mixture weibull distribution: 200,500,1000;different cure rate: 0.2,0.4,0.6;different uncured censoring rate: 0.05,0.15 and there were 30 scenarios in total.Model building and assessment: Five statistical methods including AFTMC,Exponential Mixture Cure Model(EXPMC),Weibull Mixture Cure Model(Web MC),Lognormal Mixture Cure Model(Log NMC)and Loglogistic Mixture Cure Model(LLog MC)were compared in terms of accuracy and precesion.The performance of models was assessed by relative bias and mean squared error(MSE)from accuracy perspective as well as by standard error(SE)and 95% confidence interval capture rate from precision perspective.Case study: All of case studies were derived from two clinical trials sponsored by Eastern Cooperative Oncology Group(ECOG)and compared appropriateness of different models by analyzing the effect of high-dose Interferon Alpha-2b on relapse and overall survival of high-risk melanoma following surgery.Results:Results of simulation study:Weibull distribution: Generally,Web MC and EXPMC had the best performance in terms of accuracy and precesion,followed by AFTMC where the performance was slightly different compared with the previous two and Log NMC as well as LLog MC had the worst performance.In addition,along with the uncure censoring rate increased,especially in sample with smaller sample size,AFTMC performed better than Web MC 和 EXPMC with smaller relative bias,MSE and SE.The reason was that we generated survival times based on weibull distribution which was consistent with Web MC and EXPMC and different from Log NMC and LLog MC.Mixture weibull distribution: Generally,AFTMC had the best performance from both accuracy and precision perspective,followed by Web MC,EXPMC,LLog MC,Log NMC,respectively.The advantage of AFTMC was even more pronounced along with increasing cure rate and uncured censoring rate.Only when the cure rate was lower than 0.6 and the uncensored cure rate equaled to 0.05,Web MC and EXPMC have good performance similar to AFTMC.In addition,generally sample size,cure rate and uncured censoring rate also had influence on models’ performance,especially on parametric models: 1.Along with increase of cure rate,the accuary and precision of parameter estimation of latency slightly reduced;2.Along with increase of uncured censoring rate,the accuary and precision of parameter estimation within both parts signifcantly reduced;3.Along with increase of samplesize,performance of every single model got better in each simulation scenario;When sample size was smaller and the uncured censoring rate was equal to 0.15,the MSE of parameters within the cured part in parametric models was estimated to behave as giant value exceeding one thousand on avarage and the value increased greatly as the cure rate increased.However,this situation did not appear in AFMMC;5.When the sample size was small,cure rate was 0.6 and the total censoring rate was 0.75,all of the five methods did not very well.Results of case studies:Further,two case studies derived from two clinical trials sponsored by ECOG were applied to assess the performance of AFTMC and the other four parametric models.The first study was to explore the impact of high-dose interferon Alpha-2b on overall survival(OS)of high-risk melanoma and the results showed that the adjutant therapy could increase cure rate significant statistically with an OR value equaled to 0.118.The second was to explore the impact of high-dose interferon Alpha-2b on relapse of high-risk melanoma and the results showed that this therapy had no impact on relapse of patients suffered from high-risk melanoma.In addition,survival times in both studies obeyed the mixture weibull distribution and the results of goodness to fit measured by Akaike information criterion(AIC)manifested that AFTMC had the best performance.Conclusion:In summary,AFTMC perform well in analyses with long term data regardless of survival distributions and the results have good reliability and stability.What’s more,the model is feasible for data with high censoring rate.In addition,uncured censoring rate has significant influence on cure models,especially on parameter estimation of incidence and cure models are not feasible for sample with small sample size and high uncured censoring rate.