| BackgroundThe multiple comparison problem is very common in clinical trials, and it is not very easy to resolve. For example, the researchers often need to evaluate the efficacy and safety of a drug simultaneously by using no less than two endpoints. However, it is even impossible that the treatment drug is superior to the control drug on all endpoints, with the improvement of medical technology. In most cases, the treatment drug may be superior to the control drug just on some endpoint. Most of the clinical trials are designed to test whether the treatment drug is non-inferior to the control drug on all endpoint, and superior to the control drug on at least one endpoint. Until now, the testing methods of the superiority and non-inferiority problem had not accounted for the correlation between each two endpoints, which will make the power lower in turn.In addition, clinical safety data, usually reported as clinically manifested adverse events (AEs), are routinely collected throughout all clinical trials; the volume of reported AEs is typically large in a trial. For some new drug, we can’t predict how many AEs will occur in the clinical trial. As many types of adverse events can occur on one patient, and the same type of adverse event can occur on the same patient for more than once with many visits(for example:sometimes, A patient will feel uncomfortable with his stomach for a short time when administering some drug. Some patients will feel uncomfortable in the beginning period of taking the drug, and will not fell uncomfortable with his stomach in future. While some patients will feel uncomfortable with his stomach frequently after having the drug). This type of data is longitudinal data, the different AE are correlated with each other, and it is not independent between different visits. If the data are analyzed ignoring this, then the type I error will be increased by doing so, and it is still very difficult to analyze the safety data. Until now, there is no optimal way to deal the high-dimensional, expected and unexpected clinical AEs and statistical methods for the analysis of clinical Aes data mostly remain descriptive. One of the challenging issues when analyzing safety data with multiple clinical AEs is that whether multiplicity adjustment should be applied. Adjusting for multiplicity using standard classical multiple comparison methods such as Bonferroni procedure to control the type I error may make it more difficult to spot the harm caused by the product; On the other hand, no adjustment at all may yield a high proportion of AEs that are falsely claimed to be associated with the product. With this dilemma, the classical multiple comparison method will be not appropriate to be used to control FWER, and the Bayesian method will be a good choice to treat such problems.ObjectiveThis objective is to do research on the testing method about superiority and non-inferiority problem while accounting for the correlation relationship between each endpoint; meanwhile, do research on the testing method about the adverse events with more than one following-up visits.MethodFor m endpoints, we set the superiority critical values and non-inferiority critical values firstly, then estimate the sample convariance matrix through the sample data. Take the superiority critical value and sample convariance matrix as the simulation parameters, then generate N random samples independently by using the Monte Carlo method in computer. Set a series of nominal a’, and Calculate the corresponding (100-α)%confidence intervals for each a’. Calculate the proportion of samples P(a’) which meet the following conditions:all the lower bounds of the (100-α’)%confidence intervals are larger than non-inferiority critiacal values and at least one of lower bounds is greater than the superiority critaical values, and select the appropriate nominal a’to make the above ratio P(a’) closest to the significant level α (usually α=0.05) set by the researchers. Denoted it as a, calculate the (100-α)%confidence intervals of the samples in clinical trials, and compare the lower bound of this confidence intervals with the superiority critical values and non-inferior critical values. If all the lower bound of this (100-α)%confidence intervals are larger than non-inferiority critical values and at least one is greater than superiority critical value, then reject the null hypothesis and regard that the test drug is non-inferior and superior to the control drug on the m endpoints; otherwise, accept the null hypothesis. Since the adverse events occurred in some clinical trial can be classified into different body systems, suppose we have done K follow-up visits and all the adverse events can be classified into B body systems. Sign the j th class adverse event in the b th body system as Abj, we consider the correlation between the various adverse events, and the correlation between different visits to evaluate whether the incidence rate of some adverse event in the test group is higher than in the control group. The logarithm of odds ratio of the incidence rate in the adverse event Abj between the test group and the control group is signed as θbj, and take θbj as a random variable by using Bayesian method. We assume that θbj in the same body system have the same prior distribution corresponding that different adverse events can be classified into different body systems, and θbj in different body system have different prior distribution. So θbj have a multi-level prior distribution, then get the posterior distribution of θbj and make decision accordingly.ResultsThe simulation study demonstrated that the reported method in this paper can control the type I error rate in the superiority and non-inferiority problem, while make the power higher when the non-inferior margins are close to zero. Further more, the proposed method in this paper can not only tell us that whether the treatment drug is superior and non-inferior to the control drug, but also tell us that which endpoints are superior and how much superior they are.Through simulation studies we explore the nature of the Bayesian method proposed in this paper to evaluate of the adverse events in clinical trials. The simulation studies show that the expected proportion of the false-positive events in the total number of positive events (average) can be controlled in the pre-set level by this method. The expected number of false events is found to have an increasing trend with the increase of the incidence rate of adverse events in the control group and OR value; the expected number of false negative events tends to decrease.ConclusionIn clinical trials, if the non-inferiority critical value is relatively small, it is suggested that the testing methods for superiority and non-inferiority problem in this paper to be used due to it has a higher power. To evalueate the adverse events in clinical trials with more than one following up visits, we can use the Bayesian approach proposed in this paper, and the evaluation results can be submitted to the relevant decision-making departments as a reference. |
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