A PROCEDURE FOR DOCUMENTING AND ASSESSING BIOEQUIVALENCE A. ARDIA, C. MONTORO, N. ORLANDO

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1 ~. A PROCEDURE FOR DOCUMETIG AD ASSESSIG BIOEQUIVALECE A. ARDIA, C. MOTORO,. ORLADO ABSTRACT Bioequivalence comparative trials are conducted to demonstrate that the bioavailability of new formulations (one or more) of a standard drug does not differ from the original one or that new forms of administration (one or more) do not differ from the actually marketed formulation. The most widely used experimental procedures follows the cross-over scheme in which each subject receives each of the forms of the studied caupound over the course of the study in an order of administration such to generate a design constituted by a series of Latin squares. In alternative, not all of the formulations are given to the same subject but at least two of them conducting in such a way to an incomplete block design. Main response variables on which assessment is based are AUC (area under curve), Cmax (peak level) - observed or log-transformed values - and tmax (time to peak level). Several statistical methods have been developed and proposed to deal with the problem of "proving" the " pratical equality" of two parameters. We present a procedure, completely written in SAS, menu-driven, for producing a complete documentation of a bioequivalence trial. The output gives the list of the observations, of the response variables with descriptive statistics and table and exits of the statistical analysis. THE BIOEQUIVALECE PROBLEM When a new formulation of a drug is proposed, it is necessary to demonstrate that it is essentially equivalent to the standard formulation. Although it is possible to distinguish many kinds of equivalence - chemical, biological, therapeutic - it is the latter that chiefly concerns us. A direct demonstration of the therapeutic equivalence of two different formulations would require a large number of clinical trials. However if we assume that two formulations which produce the same blood-level profile over time give the same therapeutic effect, the problem of proving the "pharmacokinetic" or "bioavailability" equivalence is simplified. AIM OF A BIOEgUIVALECE TRIAL The aim of a bioequivalence trial is to prove that the bioavailability of a formulation does not differ from that of the standard by more than a prespecified value: in particular all the regulatory authorities agree that for equivalence to be claimed, two products should not differ by more than ± 20\ in mean bioavailability. '317

2 SUITABLE DESIGS: Since it' has been observed that even in a selected relatively hclllloqenous- group, the response (time taken for the drug to reach blood or urine levels) is quite variable, any design which eliminates the variations between subjects variation fra. the caaparison being made is an efficient one, even though --efficiency does not necessarily 1mply validity. Among such efficient designs, which are characterized by the use of each subject more than once, the most widely used are: - the cross-over design, for two formulations - the latin square and the incomplete randomized blocks for more than two formulations, the latter being useful when the number of adm1 nistrations on the same subject is less than the formulations under study. RBSPClIfSB In each subject after each administration the drug concentration in the blood and urine is measured at fixed times thus giving rise to a curve over t1meof which the quantities of interest are: - Area under curve (AUe) (i.e. integral of the blood levels over time) that gives information about the average concentration over the interval examined Maximum concentration ( 0Dax, or peak, and time to 0IIax) that contain information about the rate and extent of absorption. Instead of the original values of Aue and Cmax, their logs are usually analyzed. STATISTICAL AALYSIS AUe -0I\aX Several approaches have been proposed. In our procedure we have adopted two of them that meet the requirements of the regulatory agencies, one in the field of hypothesis testing and the other in the confidence interval approach. The adequate statistical hypothesis system for the proposed problem can be stated as: S1 Ra M~ SLc, or M~ Me: 8 1: Lo < < Uo M$ where M., Ms are respectively the means formulation L is the lower limit, usually 0.80 U is the upper limit, usually 1.20 ME Its of ~ Uo the new and the standard FDA requirements 378

3 or for loq-transformed data S,. [.H,,: hu-_ lls) S L H1 : L < (lle- ll,)< u or (lla- "S)~ U where lle= 109 M. 116= 109' M5 L = 109 L.. U = log Uo Assuminq that 109 transformed values follow the normal distributions with constant variance S2, they can be tested followinq the procedure proposed by Hauck and Anderson. First calculated the quantities XE - 'is- t ( L + V) T = S J(2/n) where X are the sample means (in the 109 scale) n is the size of each qroup S the error standard deviation calculated from the appropriate AOVA with degrees of freedom g I. and v - ~. 6 = S J(2/n) r = Fv (ITI - 6) - Fv ( -ITI - 6) where F is the distribution function of the Student's ~ with g deqrees of freedom. Bence decide for the bioequivalence if p < a not for HI otherwise. Alternatively the corrispoddtnq confidence interval approach can be used, followinq the criteria qiven by Westlake and accepted aa a standard evaluation by the FDA. On this basis for 109' transformed data the confidence interval for the difference is calculated as where lle D2 S lq (--- ) S D1 lls D1 1(1S J(1/n) - (Xs - Xe,) D2 = 1(2S J(l/n) - (Xs- XE.) 1(1' 1(2 are as such the inteqral of the t- distribution from 1(,. to 1(1 with the appropriate deqrees of freedom is (1~) with the constraint and bioequivalence accepted if, takinq antiloqs, L "s S lleo :S U lls 379

4 If data are not 109 transformed limits of confidence have to be expressed as percent o.fxs and compared with Land U. Kock's non parametric analysis for a cross-over design is usually adopted for two formulations. For more than two formulations Friedman's two-way non parametric scheme is applied both on treatments and periods. THE PROCEDURE The procedure uses the SAS AE, FSP, GRAPH, STAT and BASICS' products. It is completely menu-driven, largely adopts the PROC BUILD and DISPLAY of the AE module and is illustrated in the flow-chart. " The main menu proposes the foreseen operations. Data acquisition is performed by a data-entry created with the FSEDIT procedure of FSP. Statistical analysis adopts the PROC GLM whereas the bioequivalence assessment is ac;hieved by means of DATA STBP- BASICS module. The outputs are as follows: '.", s: - TABLES 1 - Individual blood/urine drug concentration observed in each subject subdivided by treatment with the means and standard deviations at the foot. - TABLES 2 - Pharmacokinetic parameters AUC - cmax (original and logtransformed) and tmax for each patient subdivided by treatment with mean and standard deviation at the foot. TABLES 3 Statistical Analysis - AUC and Cmax AHOVA according to the experimental design (PROC GLM Type III SS). - TABLES 4 - Statistical Analysis - t max Koch's non parametric test for cross-over design or Friedman's test for a two-way scheme applied both to periods and treatmen' (PROC PAR1WAY - PROC MRAK). - TABLES 5 - Bioequivalence assessment. Table summing up the mean values of the pharmacokinetic parameters AUC and Croax (original and log) and comparison of the new formu1ation(s) to the standard: Confidence Intervals (Westlake criteria). As regards the original data, the values in the table refer to the magnitude of the interval of the difference with the standard. As regards the logarithms, the value in the table correspond to the confidence interval of the ratio between the new and the standard formulation Hauck and Anderson test: the value in the table refers to the result of the test in terms of P value. 380

5 REFERECES 1. Anderson S. and Hauck W.W. A new procedure for testinq equivalence in comparative bioavailability and other clinical trials. Comm. Stat. A12: (1983). 2. FDA bioequivalence task force report conclusion. The pink Sheet, February 15: (1988). 3. Friedman and Milton. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Am. Statist. Assoc. 32: (1937). 4. Grizzle J.E. The two-period chanqe-over desiqn and its use in clinical trials. Biometrics 21: (1965). 5. Kirkwood T.B.L.Bioequivalence testinq - a need to rethink. Biometrics 37: (1981). 6. Koch G.G. The use of non-parametric methods in the statistical analysis of the two-period chanqe-over desiqn. Biometrics 28: (1972). 7. Mandallaz D. and Mau J. Comparison of different methods for decision-makinq in bioequivalence assessment. Biometrics 37: (1981). 8. Metzler C.M. Bioavailability - a problem in equivalence. Biometrics 30: (1974). 9. Westlake W. J.. Syrmnetric confidence intervals for bioequivalence trials. Biometrics 32: (1976). 10. Westlake W.J. Response to bioequ!valence testinq - a need to rethink. Biometrics 37: (1981). 11. Westlake W.J. Statistical aspects of comparative bioavailability trials. Biometrics 35: (1979). 381

6 TABLE 1/1 COCETRATIO ( TREATMET STADARD SUBJECT SEQ o TIMES MEA S.D. TABLE 1/2 COCETRATIO ( TREATMET EW SUBJECT SEQ TIMES o U 12 MEA S.D. 382

7 TABLE 2/J. PllAlllfACOKDIETICS PA1IAMETERS STADARD StIIIJECT CIIAX LOG AUC LOG SEQ CIIAX AUC MEAS sm TABLE 2/2 PHARMACOKIETICS PA1IAMETERS TREATMET: EW SUBJECT CMAX LOG A U C LOG TMAX SEQ CMAX A U C l2 MEAS sm 383

8 TABLE 5. BIOEQUIVALECE AALYSIS OBSERVED VALUES LOG - TRAF VALUES TREATMET MEAS (ARITM. IF OBS. - GEOM. IF LOG) SYMMETRIC COFIDECE ITERVAL (WESTLAKE) A VS B RHO-VALUE () (HAUCK TEST) SSE (A) STADARD (B) TEST ' AUC.... CMAX AUC CMAX d!i '" TYPE I ERROR ALPHA=O.05 SSE = AOVA ERROR STADARD DEV (D.F... BIOEQUIVALECE ACCEPTED IF RHO = ALPHA

9 COCETRATIO :1 M ::f 5 4 S 3~~~~~~~~~~~~~~~~~~~~~~~ o so TIM E TREATMT -~ EW 4-+-& STADARD 385

10 PROGRAM o. 1 2 I Edi t SAS d"ta set ; DATI. TEST! Co-and... ~ Screen 1 PROTOCOL O. DESCRIPTIO TREA"""", PATIET O. "i'!m Obs II--- C. """"""" -- PERIOD T I III S TOTAL o. OF PATIET - TREATMETS A (STADARD) c= - I Edi t SAS 'data set ; DATI. TESTl Screen PATIEKT O. T'" SEQ<mICE -- PERIOD 386

11 , S~lect Option ==~ Press ED to return. I - I 1. DEFIITIO OF A EW PROTOCOL BIOEQUIVALECE 2. EDITIG A OLD PROTOCOL 3. LISTIG OF EXISTIG PROTOCOLS 4. REPORT AD STAT. : CROSS"'{)VER 5. : LATI SQUARE & BIBD, 6. BIOEQ. ASSESSMET : CROSs"'{)VER, 7. : LATI SQUARE & BIBD J ~ 3 I 4,'S I 6,~ 1 " Text Editor f TABLES 1-2 "-'"..., Col ' PROTOCOL HO. DESCRIPTIO AD MODEL - (see enclosures) : &:PROT- D."..or - AlIA 6ALl- PI\O'lOOOL \ --, f TABLES i' AOYA - PROC GLM i" O PARAMETRIC TEST "ER1-- % OW< -- " k: I AlJC LOG_CMAX :',-. LDG_AUC i: I J " t: " ~ ri.er2--.er3--.-.': i TABLE 5!' (see enclosures) r' f ~ I 387