Sample Sizesestimation And Group Sequential Design In Bioequivalence Studies

Objective: Bioequivalence study is an important part of the evalution of the consistency between quality and efficacy of generic drugs.When someone prepares to launch a bioequivalence study,the study design and the sample size are the inportant problems which should be solved.These problems require an accurate estimation of the geometric mean ratio between reference drugs and test drugs and intrasubjet variation of the drugs.In the first part,this paper studys the sample size under different parameter settings used different formulas or Monte Carlo simulation according to whether the drug is a highly variable drugs.Meanwhile this paper compiles the SAS macro %BE_SSE,and this paper hopes this macro can provide reference for sample size estimation in pratical study.In the second part,the properties of fix design and two group sequential design based on partial replicated design and reference scaled average bioequivalence are studied and compared.Methods: Firstly,for sample size estimation,this paper divides the drugs into the common generic drugs and highly variable drugs.For common generic drugs,this paper compares three formulas consisted of Owen's Q function,non-central t distribution and an approximate formula called Chow's approximate formula.For highly variable drugs,this paper takes Monte Carlo simulation into consideration,this paper combines that method with different bioequivalence evaluation regulation recommended.Secondly for group sequential designs in bioequivalence,this paper studys and compares the statistical properties for fix design and two group sequential designs called BE-Pocock50 and BE-OBF50(the information is cumulated until 50%,this paper conducts an interim analysis)using Monte Carlo simulation under the partial replicated design and reference scaled average bioequivalence.Results:Firstly the sample size of bioequivalence was estimated,for common generic drugs,the sample size under 2x2 crossover design was calculated and compared by Owen's Q function,non-central t distribution and CHOW's approximate formula.The sample size estimated by the three methods increases with the increase of CV.When GMR = 1,the sample size is the smallest for three methods.As GMR moves to the bioequivalence boundary of 0.80 or 1.25,the sample size will gradually increase.The sample size required for GMR = 0.95 and GMR = 1.05 is slightly different in terms of numbers,because the logarithm is not symmetrical about 0.Although the non-central t distribution isan approximation method,the estimated sample size under different parameter configurations is consistent with that estimated by Owen's Q function.The sample size estimated by Chow's approximation formula is greater than or equal to that estimated by the other two methods under the same parameter configurations,but when the variation is small(CV ? 15%)and GMR is between 0.90 and 1.10.The approximation method is completely consistent with the sample size estimated by the other two methods.Sample size estimation of highly variable drugs needs to be divided into different designs and simulated by bioequivalence evaluation method recommended by regulatory authorities to obtain sample size estimation.Under the same parameter configuration,the sample size required by FDA and CFDA is less than or equal to the sample size required by EMA.And the sample size is the smallest when GMR = 1.The closer GMR is to the boundary of bioequivalence limits,the more sample size demand increases.When GMR is in the range of 0.95-1.05,the sample size remains unchanged or increases with the increase of CV.When GMR is not in the above range,the sample size first increases with the increase of CV(between 45% and 55%)and then decreases with the continuous increase of CV.Sample sizes under different drug parameters can be obtained by using the SAS macro program %BE_SSE developed in this study.Secondly,the group sequential design under the bioequivalence of highly variable drugs was studied.In the fix design,when study ignores the point estimation constraint,the type I error will inflate.However study takes the point estimation into consideration,the type I error reduces gradually with the increase of CVconversely.the minimum type I error can be lower than 1%.The relationship of type I error and CV in two GSD methods is consistent with that in fix design.And the power for these three designs from largest to smallest is BE-Pocock50,BE-OBF50 and fix design.Even though study found that the inflation of the type I error is upto6.24% at CV equal to 30% and 40% for BE-Pocock50,nevertheless BE-Pocock50 still show some merits-the probability of going into stage2 is lower than 50%,that means the average mean is lower than fix design.For BE-OBF50,when CV is larger than 70% it shows the same condition with BE-Pocock50.So when researchers launch a bioequivalence study,they can take BE-Pocock50 and BE-OBF50 into consideration.Conclusions: To accurately estimate the sample size of bioequivalence studies,it is necessary to have a thorough understanding of the design,intra-individual variation coefficient and geometric mean ratio of drugs.In practice,for the sake of accuracy and convenience,non-central t distribution formula is recommended to estimate sample size for common generic drugs.For highly variable drugs,Monte Carlo simulation is recommended to estimate sample size.In this paper,SAS macro program% BE_SSE is compiled.Sample size can be obtained by directly inputting the corresponding parameters,but attention should be paid to the requirements of the regulatory authorities for the minimum sample size.For highly variable drugs bioequivalence,this paper recommend the BE-Pocock50 as an alternative design for the single stage design mainly.Meanwhile for larger actual CV,this paper can also use the BE-OBF50.Because it's often assumed that the drug is bioequlvant.The inflation of type I error can be ignored.Nobody likes to study a drug that inbioequivalene.Additionally,when this paper uses the GSD under the highly variable drugs bioequivalence,this paper should note that the inflation factor,and the nominal ? level.