Assessing Noninferiority With Time-to-event Data Via The Method Of Nonparametric Covariance

BackgroundNoninferiority trials using active control, in particular, those with endpoints such asmortality and/or non-irreversible morbidity have become increasingly popular since theethic of placebo-controlled trials has been challenged. Developing a test treatment whichhas advantages in toxicity, cost, and/or administration might be desirable, even if it wereslightly less effective than the active control. Statistical methods for assessingnoninferiority of a new test treatment to an active control have been well developed forbinary and continuous endpoints and to a lesser degree for time-to-event data withcensoring. The most commonly used method for assessing noninferiority withtime-to-event data is the Cox proportional hazard model which is a semi-parametricmethod. However, The Cox proportional hazard model is based on the assumption that thehazard ratio for two groups of subjects is constant over time. If the data does not satisfyproportional hazard assumption, using Cox proportional hazard model to analyze the datais not acceptable.Nonparametric methods are very useful tools in clinical trials since they are generallyrobust and need fewer assumptions as compared to their parametric and semi-parametriccounterparts. To establish one-sided noninferiority of a new treatment to the standard oneon survival responses, authors have investigated non-parametric stastistical method basedon different theories (such as survival function at a single time poin,median survival,average hazard ratio, bootstrap approximations and so on). Although there are severalnonparametric method available for assessing noninferiority with time-to-event data inclinical trials, these approaches are only applicable to survival (time-to-event) data withoutadjustment for predictive covariates that have influence on the primary outcome. Whenthere are predictive covariates that have influence on the primary outcome, there is still notproper statistical method to test the non-inferiority of survival data.In this study, we investigate the non-parametric covariance approach for assessing thenon-inferiority based on time-to-event data. We derive the hypotheses and statistics fornon-inferiority based on survival data from the non-parametric covariance methodproposed by Tangen and Koch. Furthermore, simulations are preformed to investigate thetype I error and power of the non-parametric covariate-adjusted test and the unadjusted counterparts. The results are compared with the corresponding ones of Cox proportionalhazard model. In addition, the application of the non-parametric covariance method isillustrated by an example. Last but not least, a discussion is given.MethodsFirst of all, we extended the nonparametric covariance approach of Tangen and Koch to anoninferiority setting with time-to-event data. The expected value of the difference inregression coefficient of treatment can be estimated by weighted least squares (WLS)linear regression. Then we constructed the hypotheses and statistics for non-inferiority testbased on survival data by using the estimate of regression coefficient and non-inferioritymargin.Secondly, in order to investigate the performance of the method of nonparametriccovariance in terms of Type1error rate and power, we generated the survival times basedon the approach by Bender et al.Thirdly, to evaluate this nonparametric covariance model vs. the classical semi-parametricCox proportional hazards regression model, simulations in terms of the Type1error rateand power were performed and compared. What's more, an application of thenon-parametric method to pemetrexed, a recently approved drug for first-line treatment ofnon small lung cancer, was illustrated.Finally, we summarized and refined the proceed of nonparametric covariance model inassessing the non-inferiority based on time-to-event data. And we will providestandardized SAS macro code for application.ResultsSimulations illustrate that the covariate-adjusted nonparametric model and Coxproportional hazards regression model are comparable in terms of the Type1error rate.The nonparametric method preserves the Type1error rate and appears to be more robustwhen compared with the Cox proportional hazards regression model. The efficiency of theCox proportional hazards regression model depends on the proportional hazardsassumption and is sensitive to the impact of covariates. The adjusted and unadjustedtreatment effects may not have the same interpretation, and sometimes even differentresults may be obtained from the adjusted and unadjusted analyses using a Coxproportional hazards regression model. Contrarily, the nonparametric covariance model requires no assumptions beyond randomization of subjects to treatments and censoring tobe non-informative and independent of treatment assignment. Besides, similarinterpretation of the treatment parameter is maintained across different specifications ofcovariates.Furthermore, we considered the uncertainty of the estimate of the active control's effect innoninferiority. We demonstrated that the Type1error rate is inflated for both methodswhen the constancy assumption is violated. However, the Cox proportional hazardsregression model is more sensitive to the reduction of the effect of active control in thenoninferiority trial.The results also show that when the covariates have an effect on survival, thecovariate-adjusted nonparametric model increases the power in the noninferiority trial.However, for the Cox proportional hazards regression model in the noninferiority trial,adjustment for the covariate would decrease the efficiency, especially when the regressioncoefficient is between0and the noninferiority margin.The results of nonparametric covariance model with single covariate were similar with thatwith multiple covariates. This suggested that the nonparametric ANCOVA approach isgenerally stable and reliable.ConclusionsThe nonparametric covariance model does not require proportional hazard assumption andcan test the non-inferiority of survival data with adjustment of important covariates. It is avaluable alternative tool for assessing treatment effect in a noninferiority trial when theoutcome is time-to-event data with censoring. Although the nonparametric covariancemodel and Cox proportional hazards regression model may have different assumptions andoperational characteristics, the two methods are mutually supportive in terms of estimationand hypothesis testing. However, it should be noted that the nonparametric modelcannotevaluate "treatment x covariate" interactions nor can it provide the estimate for the effectof the covariates. The Cox proportional hazards regression model, in general, is moreversatile when subpopulation-specific estimates are required. The complementary use ofboth methods would provide more interpretable and robust results.