Analytical Strategies And Study Of Subgroup Identification For Failure Time Data With A Cured Fraction

BackgroundSome failure time data come from patients may consists of some subjects who are cured and others who are uncured.The data typically have heavy censoring at the end of the follow-up period,and a traditional survival analysis would not always be appropriate,yet a great deal of literatures indicated that non-statistical professional researchers would still choose the traditional Cox's PH model or AFT model for analysis.At present,there are many studies on subgroup identification,involving outcomes such as quantification,classification and survival.But the emphasis is on how to identify subgroups without paying attention to the method of testing for the existence of subgroups.According to the literature available at present,if the survival time of the treatment does not show significant improvement,how to test whether there is a benefit subgroup in the treatment is still rare.The mixture cure model and the K index for assessing the prognosis accuracy may provide some theoretical references for testing the existence of subgroups of survival data.ObjectiveWhen there is a cured fraction in the survival data,we intend to compare the performances of the Cox proportional hazard model with the proportional hazard mixture cure model(PHMC model)and the AFT model with the accelerated failure time mixture cure model(AFTMC model)respectively by Monte Carlo simulation.Simulation results are illustrated by real example.Based on the calculation method of K index,we intend to construct a test statistic to test whether there is a subgroup when the treatment does not show obvious benefit,and then use a small number of'biomarkers associated with subgroup to establish a subgjroup cdiscriminant model to determine the subgroup identity of each patient.MethodsEstimated biases,MSE,Confidence interval capture rate and K index were used to evaluate goodness of fit of Cox proportional hazard model and PHMC model,AFT model and AFTMC model.Based on the K index of the AFT model and AFTMC model,we construct a statistic of Ksub to test whether the survival data exists in a subgroup.When there is a subgroup,we construct the statistic of Koff to find the optimal time point for distinguishing subgroups,and determine the subgroup identity of each patient,and then establish a subgroup discriminant model.ResultsComparison of Cox proportional hazard model and PHMC model:when the cured rate is 0,the estimated bias,Confidence interval capture rate,and K index of the PHMC model are close to the Cox's PH model,but the MSE of the PHMC model is slightly larger than the Cox's PH model.When survival data has a substantial proportion of subjects being cured,the absolute value of Bias in the PHMC model is always smaller than the Cox's PH model,the Confidence interval capture rate of the PHMC model is always closer to the acceptable range than the Cox s PH model,and the K index of the PHMC model is always greater than the Cox's PH model.Comparison of AFT model and AFTMC model:when the cured rate is 0,estimated bias,MSE,Confidence interval capture rate,and K index of AFTMC model are similar to AFT model.When survival data has a substantial proportion of subjects being cured,the absolute value of Bias and MSE of the AFTMC model are always smaller than the AFT model,the Confidence interval capture rate of the AFTMC model is always closer to the acceptable range than the AFT model,and K index of the AFTMC model is always larger than the AFT model.The type I error of Ksub is basically controlled within 0.05.With the increase of the censored rate,the type I error tend to increase.The power can be maintained at a high level in most cases,but when the sample size is small,the cured rate is low,and the censored rate is high,the power of Ksub is not high.As the cured rate increases,the power of Ksub is gradually increasing.When the cured rate is fixed,the power of Ksub is gradually decreasing as the censored rate increases.After finding the optimal time point(T(off))for distinguishing subgroups with Koff,Method 3 can accurately and stably predict the subgroup identity of patients in the four customized methods.Method 3 has the highest average accuracy(86.8%)and average sensitivity(82.5%),and the smallest fluctuation range of accuracy and sensitivity(standard deviation=4.1%,5.3%).Although its average specificity is lower than the other methods,its value is not low(89.7%)and the fluctuation range is small(standard deviation is 6.7%),so Method 3 can be relatively accurate to predict that the patient belongs to the non-benefit subgroup.In the four discriminant models corresponding to the four customized methods,Model 3 can effectively discriminate the subgroup identity of patients,with the highest average sensitivity(93.1%),the smallest fluctuation range of sensitivity(standard deviation is 6.7%),the highest average specificity(77.5%),the smallest fluctuation range of specificity(standard deviation is 7.2%),the highest average accuracy(82.7%),the smallest fluctuation range of accuracy(standard deviation is 5.1%),the largest average AUC(87.6%),and the smallest fluctuation range of AUC(standard deviation is 3.3%).ConclusionWe concluded that the PHMC model and the AFTMC model do not have obvious advantages for analyzing survival data without a cured fraction.But when subjects exist in the data,who will never experience the event of interest,it is recommended to use the PHMC model or AFTMC model for analysis,which may need relatively larger sample size.If the survival time of the treatment does not show a significant improevement,Ksub can be used to test whether there is a subgroup.If there is a subgroup,we use Koff to find the optimal time point T(off)to distinguish the subgroup,and use Method 3 to identify the subgroup identity of patients:when the survival time of the patient is greater than T(off),the patient is considered to be in the benefit subgroup(Yi = 0),and can be cured.When the survival time of the patient is less than or equal to T(off)and a failure event occurs(?i= 1),the patient is considered to be in the non-benefit subgroup(Yi = 1).When the survival time of the patient is less than or equal to T(off)and is in the censored status(?i= 0),if the patient's P(Yi = 0|Xi)is greater than the predicted average cured rate,it is considered to be in the benefit subgroup(Yi = 0),otherwise it belongs to the non-benefit subgroup(Yi = 1).And based on Method 3,a subgroup discriminant model(Model 3)can be established.