BIOEQUIVALENCE STANDARDIZED Singer Júlia Chinoin Pharmaceutical and Chemical Works Ltd, Hungary

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1 BIOEQUIVALENCE STANDARDIZED Singer Júlia Chinoin Pharmaceutical and Chemical Works Ltd, Hungary As the attention of pharmaceutical companies focused towards generic drugs, the design and analysis of bioequivalence studies - aimed to demonstrate bioequivalence between the generic and original drug product - have gained an increasing importance over the past decade. Their usual 2x2 cross-over design is suitable for standardization because ICH and FDA guidelines prescribe clearly the procedures to be applied. The SAS application presented comprises all the steps which involve statistics during a bioequivalence study: 1. Sample size evaluation 2. Evaluation of pharmacokinetic parameters from the raw data 3. Internal pilot study for an eventual correction of the sample size (assessing only the coefficient of variation, without affecting type I and type II error) 4. Lists for individual data 5. Graphs for individual plots of plasma concentration versus time 6. Lund s test for outliers 7. GLM for parametric evaluation (of logarithmically transformed data) and the calculation of confidence intervals 8. Nonparametric confidence intervals This application has the advantages specific to standardization: keeping the same data structure for all studies and doing always the same steps shortens considerably the time needed for the evaluation of a study and can be easily used even by nonstatisticians. The tables and lists have the same format for each study and this enhances the search in the final report. 1. Sample size evaluation The formulas (1) used are:

2 [( α, 2 2) ( β 22, 2) ][ / ln( 125. )] n t n + t n CV 2 2 [( α, 2 2) ( β 22, 2) ][ / ln( 125. ln θ) ] 2 2 n t n + t n CV and n [ t( α, 2n 2) + t( β 22, n 2) ][ CV / ln( 08. ln θ) ] 2 2 for θ=1 for θ>1 for θ<1 where θ denotes the anticipated ratio of the geometric means of the two formulations. This application has an interface suggesting to the user which kind of previous knowledge he needs to plan the study: The critical succes factor widget is divided into three zones: the domain of highly variable drugs is marked with red as a warning. 2. Pharmacokinetic parameters are evaluated in the usual manner: trapezoidal approximation for AUC and t max, C max calculated from the raw data without any interpolation. 3. The possibility of an internal pilot study (2) is included. The same model is fitted as in the final evaluation (proc glm) but the only printed result is the coefficient of

3 variation calculated from ANOVA residuals. In this way (without assessing the proportion of geometric means) the type I error does not increase (computer simulations were done to prove that type I error does not change considerably). 4. Lists for individual data are prepared by proc report. 5. Graphs are produced by proc gplot. 6. Lund s test is the only test for detecting outliers which is accepted by the guidelines (3). This test fits again the same model as in the final evaluation and it chooses the observation with the largest studentized residual (4). The code of this macro is: %macro lund(dsname,varname,clsvar,mod); data bioekvi; set &dsname; logauc=&varname; proc glm data=bioekvi outstat=ki1 noprint; class &clsvar; model logauc = &mod; output out=ki residual=res stdr=std; data b; set ki; studres=res/std; set ki1; if _type_= ERROR then do; call symput( dgf,left(put(df,3.))); proc univariate data=b noprint; var studres; output out=ki2 n=n max=max; options linesize=70 pagesize=54; file print; set ki2; alfa=0.01; n1=&dgf; f=finv(1-alfa/n,1,n1-1); value=sqrt(n1*f/(n1-1+f)); call symput( mmax,left(put(max,9.6))); if max<value then do; put / The max. of studentized residual = max ; / upper limit = value 5.3 At level alfa no outlier detected ; else do;

4 put / The max. of studentized residual = max ; / upper limit = value 5.3; put / max is an outlier at level alfa; file print; set b; if studres>=&mmax then do; put / The max. of the studentized residual is attained at subject: subject; %mend lund; In case of an outlier significant at level 0.01 the final evaluation is performed with and without the outlier. 7. The parametric evaluation of the logaritmically transformed parameters is done by proc glm in the following way: proc glm data=&dsname outstat=out1; class sequence subject PERIOD treat; model logauc = sequence PERIOD treat subject(sequence); test h=sequence e=subject(sequence); lsmeans treat/out=out2; estimate Test vs. Reference treat -1 1; Two SAS datasets are created (out1 containing the mean square errors and the degrees of freedom and out2 containing the least-square means of the two treatment groups) which enable the calculation of the confidence limits and their back-transformation to the original scale. 8. Nonparametric confidence intervals are evaluated applying the Hodges-Lehman method (5). The macro uses proc sql to create all the differences possible between the two groups distinguished by their sequence number. The code is the following (maybe it is not the shortest but the simplest way to implement the Hodges-Lehman method): %macro numobs(dsn); %global num; if 0 then set &dsn nobs=count; call symput( num,left(put(count,8.))); stop; %mend numobs; %macro numobs1(dsn); %global num1; if 0 then set &dsn nobs=count; call symput( num1,left(put(count,8.))); stop; %mend numobs1; %macro tmax(dsname);

5 */ data c (rename=(tmax=tmax1)); /* az elso periodus kivalasztasa set &dsname; where period=1; data b (rename=(tmax=tmax2)); set &dsname; where period=2; proc sort data=c; by subject; proc sort data=b; by subject; data c; merge c b; by subject; data d; set c; y1=tmax1-tmax2; y2=tmax1-tmax2; data e; set d; where sequence=1; %numobs(e); data f; set d; where sequence=2; %numobs1(f); proc sql; create table cross as select e.y1,f.y2 from e e, f f ; quit; data f; set cross; z=y1-y2; proc univariate data=f noprint; var z; output out=ki median=median n=m; data nez; set ki; c=&num1*&num/2-probit(0.95)* sqrt(&num1*&num*(&num1+&num+1)/12); c=floor(c); cc=m-c; call symput( med,left(put(median,6.2)));

6 call symput( clim1,left(put(c,3.))); call symput( clim2,left(put(cc,3.))); proc sort data=f out=g; by z; file print; set g; if _n_=&clim1 then do; m=&med/2; z=z/2; put / The estimated median of difference (test-reference) is: m; put / The lower limit of 90% confidence interval: z; if _n_=&clim2 then do; z=z/2; put The upper limit of 90% confidence interval: z; %mend tmax; The drawbacks of this application are the same as for every standardization: it cannot be applied for more complicated design and it isn t flexible to changes. If the new individual bioequivalence approach will be implemented (the draft version (6) of the FDA guideline is now available) this application will have to be extended. References [1] Hauschke D, Steinijans VW, Diletti E, Burke M: Sample size determination for bioequivalence assessment using a multiplicative model. Journal of Pharmacokinetics and Biopharmaceutics, 20: , [2] Peace KE: Discussion for interim analysis and sample size reestimation. Drug Information Journal, 27: , [3] Guidance. Statistical Procedures for Bioequivalence Studies Using a Standard Two-Treatment Crossover Design, Office of Generic Drugs, Division of Bioequivalence, 1992 [4] Lund RE: Tables for an approximate test for outliers in linear models. Technometrics, Vol. 17, pp , [5] Hauschke D, Steinijans VW, Diletti E: A distribution-free procedure for the statistical analysis of bioequivalence studies. International Journal of Clinical Pharmacology, Therapy and Toxicology, 28: 72-78, [6] In Vivo Bioequivalence Studies Based on Population and Individual Bioequivalence Approaches. Draft Guidance. U.S. Department of Health and Human Services. FDA. Center for Drug Evaluation and Research (CDER)