Pharmaceutical Research, Vol. 15, No. 2, 1998
`
`Resaerch Paper
`
`Why Rate of Absorption Inferences in
`Single Dose Bioequivalence Studies are
`Often Inappropriate
`
`Rodney P. Basson,112 Atalanta Ghosh,1’3
`Benito J. Cerimele,l Karl A. DeSante,1 and
`Daniel C. HoWeyl
`
`Received A ugust 25, 1997; accepted October 3], 1997
`Pumose. Peak drug concentration (Cmax) measures the extremity of
`drug exposure and is a secondary indicator of the extent of absorption
`after area under the concentration time curve (AUC). Cmax serves as the
`indicator of absorption rate in bioequivalence (BE) studies in the US
`(l ). The use of Cm“, not the time to Cm,X(Tm,,), as the metric to assess
`absorption rate causes erratic inferences in BE studies, and incorrect
`conclusions for some. We can improve BE efficiency (i,e_, get the
`answer right
`the first
`time), by properly analyzing the time to
`Cmax(Tmax) instead of Cm“.
`Methods. We have previously redirected attention to Tmax as the
`unconfounded absorption rate variable, instead of Cm“, and have
`called for equally spaced sampling times during the suspected absorp—
`tion phase to improve the performance of the rate metric (2). Equal
`spacing converts Tmax easily into a count variable and we illustrated an
`appropriate statistical analysis for counts. This paper provides some
`measurement theory concepts to help judge which is the more appro-
`priate analysis, and also provides parametric confidence limits for Tm“
`treatment differences. Three separate BE studies are then analyzed by
`both methods.
`Results. By focusing on the differences in conclusiOns, or inferences,
`this paper identifies three major issues with the current FDA “recom-
`mended” analysis of BB studies. First, Cm“, a continuous variable
`peak-height or extent measure has usurped me’s function and per-
`forms erratically as a substitute measure for the rate of absorption. Sec
`ond, Tm”, should be analyzed as a discrete attribute, not as a
`continuous variable. Third, since several extent measures (AUC, Cm“),
`not one, are actually being analyzed, an adjustment for multiple testing
`is mandatory if we are to maintain the size of the test at the desired ot
`level (i 3), and not inadvertently use a narrower bioequivalence win~
`dow than is intended. These actions all can have serious unintended
`consequences on inferences, including making inappropriate ones.
`
`KEY WORDS: bioequivalence; absorption rate; Tmax; absorption
`process rate; measurement theory; inference.
`
`INTRODUCTION
`
`Generic competition in human drugs is a laudable public
`interest goal with which, in principle, few disagree. A finding
`of bioequivalence (BE) serves as a surrogate for therapeutic
`identity (1), so a BE evaluation (BEE) process that is fair and
`efficient should foster generic drug competition. Because com—
`panies use BEE to also assess formulation changes during drug
`development, an efficient process grounded in statistically
`
`‘ Lilly Laboratory for Clinical Research, Eli Lilly and Company, Indi-
`anapolis, Indiana 46285.
`1 To whom correspondence should be addressed.
`3 To whom a request for the confidence interval macro program should
`be addressed.
`
`sould science is important. BB is customarily evaluated in viva
`in healthy subjects, by comparing both the rate and the extent
`of drug absorption of a test formulation with a reference formu—
`lation. The area under the concentration time curve from time
`zero to time t (AUCM, where t is the last measurable time point)
`and similarly the area under the curve from time zero to time
`infinity (AUCOE) are both accepted as uncontaminated mea—
`sures of the extent of absorption. The situation for rate is in a
`state of confusion. There are drugs whose plasma concentra-
`tions are plateaued, where the concept of rate of absorption is
`not well defined, and ought therefore not be calculated. In reg-
`ular time—concentration profiles, data on time to peak absorp-
`tion, Tm,“ are typically collected but with irregular sampling
`schemes. Such data beg the question, and are not routinely
`amenable to proper statistical evaluation (3). The continuous
`variable Cm“, the highest observed concentration, and undeni—
`ably also a measure of extent, has quietly usurped the function
`of Tmax and performs as a surrogate measure for the rate of
`absorption. A formulation problem that Cmax is uniquely quali-
`fied to evaluate is ‘dose-dumping’ , Le. reaching an unsafe con—
`centration, and retaining it to evaluate safety peripherally for
`that purpose, is not in dispute. When in addition to Chm, Tmax is
`analyzed, often it too'is regarded as a continuous variable.
`There are consequences to all these actions, and we illustrate
`how erratic, error prone rate inference can afflict BEE by way
`of several pertinent examples.
`
`METHODS
`
`Absorption Phase Sampling Times
`
`To assess the rate of absorption we advocate the use of
`equal spacing of the sampling times from time zero (or other
`suitable initial time) until approximately two or three times the
`expected peak concentration time (or other suitable absorption
`phase restricted time interval) to collect pertinent rate data. For
`example,,a drug which has a Tmax of approximately 30 minutes
`in fasted subjects, and a similar short elimination half-life, is
`easily densely sampled every fifteen minutes for the first two
`hours (nine samples) and with diminishing frequency thereafter
`through eight hours. An equal sampling interval through the
`absorption phase ensures that a subject’s Tmax in hours multi—
`plied by the sampling frequency per hour is always a positive
`integer. These integer counts tell how long the absorption
`process takes to reach maximum concentration for each sub—
`ject, so they encapsulate the process rate (2).
`
`Measurement Theory
`
`Measurement Theory (MT) is a branch of applied mathe-
`matics with serious implications for data analysis (4). MT
`instructs that measurements (i.e., the data) and the attributes
`being measured (i.e., the reality represented like absorption
`rate) are not one and the same; to draw valid conclusions about
`an attribute one must take into account the nature of the corre-
`
`spondence between the attribute and its measurement. In par—
`ticular, MT says if statistical inferences made from measure-
`ments are to apply to reality, then we must pay attention also to
`other key MT tenets such as the ‘level of measurement’ and
`
`0724—874 1/98/0200-027631 5.00/0 © I998 Plenum Publishing Corporation
`
`276
`
`Aurobindo v. Andrx
`
`Andrx 2004
`
`|PR2017-01648
`
`Andrx 2004
`Aurobindo v. Andrx
`IPR2017-01648
`
`

`

`277
`
`guidelines was applied to logarithmic transformations of three
`variables: Cmax, AUC0_, and AUCOM respectively.
`
`RESULTS
`
`Comparison of Analysis Conclusions for Absorption Rate
`
`Conventional BEES for the three studies appears in Table
`I. In all three studies AUC declares formulations to be BE in the
`extent of absorption. As is so often the case in BE, if there is a
`‘bad actor’ it will be Cm“. However, in all three examples, Cmam
`passes the widened (.70 to 1.43) BE bounds advocated for Cmx
`by Canadian and EEC authorities, good evidence here that none
`of these studies really have a bioinequivalence problem.
`In study 1 two additional variables, Tmax and half—life,
`were analyzed by questionable continuous variable signifi-
`cance tests. The tests all agreed that the new formulations and
`the marketed product were BE. When Tmax means are very
`close, as in this example, they are unlikely to be found statisti—
`cally different in absorption rate, no matter what assessment
`
`Table I. 90% Confidence Limits on Separation of Least Squares
`Mean (Log transformed Data)
`
`Least Squares Mean
`
`90%
`Ratio of
`Confidence
`Contrastsa
`Test
`Reference means”
`IntervalC Outcome
`
`
`
`Study l-Antibiotic #1
`
`17.25
`29.55
`29.84
`
`17.57
`29.37
`29.64
`
`A vs, C
`C...“
`AUC“
`AUCo...
`B vs. C
`Pass
`.93 to 1.21
`1.06
`17.57
`18.72
`Crm
`AUCo,t
`29.36
`29.37
`1.00
`.95 to 1.06
`Pass
`
` AUC0_,., 29.63 29.64 1.00 .95 to 1.06 Pass
`
`
`
`
`
`
`.97
`1.00
`1.00
`
`.86 to 1.11
`.94 to 1.06
`.94 to 1.06
`
`Pass
`Pass
`Pass
`
`Study 2-Antibiotic #2
`
`max
`AUC.“
`AUC0_,,,
`B vs. C
`Fail
`0.70 to 0.97
`0.82
`14.94
`12.65
`C...“
`AUC“.t
`13.53
`13.30
`1.01
`0.95 to 1.07
`Pass
`
`AUC“...
`13.78
`13.54
`1.01
`0.96 to 1.07
`Pass
`
`13.97
`13.18
`13.43
`
`14.94
`13.30
`13.54
`
`0.95
`0.99
`0.99
`
`0.82 to 1.12
`0.93 to 1.04
`0.94 to 1.04
`
`Pass
`Pass
`Pass
`
`M C
`
`
`Study 3-Antiviral
`A vs. B
`Cmax
`AUC“
`AUG)...
`
`321.3
`1488.3
`1657.5
`
`362.9
`1531.3
`1637.3
`
`.89
`0.97
`1.01
`
`0.75 to 1.05
`0.85 to 1.10
`0.93 to 1.10
`
`Fail
`Pass
`Pass
`
`3 Units for parameters: Cm“, ng/mL; AUC(H and AUC0_., ng-hr/mL.
`b Analyses of Cmax and AUC parameters are based on log-transformed
`data. Antilogs of transformed scale fed minus fasted differences and
`their 90% confidence limits supply a tesUreference ratio estimate and
`corresponding 90% confidence interval. The point estimate of the ratio
`of equivalent means is 1.0.
`9 BE range is 0.80 to 1.25.
`
`Why Rate of Absorption Inferences are Often Inappropriate
`
`‘permissible transformations’. For example, because integer
`counts reflect an absolute level of measurement, Tmax data that
`arise for subjects from a crossover study need to be analyzed
`appropriately. Measurement theorists warn the price usually
`paid for inattention to these matters is ‘meaningless state-
`ments’. Uncritical analysis of Cmax and Tmax data for subjects in
`a BEE, is a practical example of such inattention.
`
`Statistical Methodology
`
`An analysis of Tmax count data for subjects from a cross-
`over study and which meets these MT constraints has been
`published (2). Performing the computations for counts that arise
`within the context of a generalized linear model is an innovation
`largely due to McCullagh and Nelder (5). Software that can per-
`form the necessary computations is available from SAS Insti—
`tute Inc.
`(6). Software to perform exact nonparametric
`inference for count data is available from Cytel Software Corp.
`(7). Using the appropriate variance—covariance matrix of the
`estimates to calculate confidence limits for estimates, and their
`differences, the analysis given in (2) can be extended. This
`report illustrates this for three BE studies.
`Continuous data for subjects that arise from a crossover
`study, like Cmax and AUC, have long been analyzed by general
`linear model procedures. Westlake (8) first suggested the log
`transforms of Cmax and AUC be analyzed, and a confidence
`interval method similar to that given by Schuirman (9) is used
`to crimpare values between two formulations. A comprehensive
`approach to performing these computations is described in SAS
`Institute Inc. (10,11). Schultz and Steinijans (12) have advo-
`cated widening the bioequivalence range for Cmax from
`08—125 to 0.7—1 .43, and this has been embraced by Canadian
`and BBC authorities. Nonparametric bounds for Tm, which are
`similar to those we present, have been published (12).
`Alternative approaches are usually based on Cm”. While
`traditional, the practice of analyzing Cmax data instead of Tmax
`for absorption rate simply is not logical (2). Widening the BE
`bounds for Cmax‘ but not for AUC, is a empirical solution, and
`preferable to doing nothing. It seems not to be generally per—
`ceived that multiple testing is involved. For example, if AUC0_I
`is chosen as the primary extent variable‘then it follows that
`AUC0_.,., is a secondary extent Cmax is a tertiary extent variable.
`If all these extent variables are to be analyzed in a BE
`study, then some form of adjustment for multiple testing is
`mandatory if we are to maintain the size of the test at the
`desired 0t level (1 3); otherwise a narrower bioequivalence win-
`dow than was intended is used.
`
`Three Ordinary BE Studies
`
`Single dose crossover studies (two antibiotic, one antivi—
`ral) were conducted by Lilly Research Laboratories to assess
`BE of test and reference formulations. Periods of blood collec—
`tion lasted at least eight hours, after a single dose, and treatment
`periods were separated by a washout period of not less than
`three days between doses. Twenty four healthy male subjects
`enrolled in and completed both study 1 and study 3. Sixteen
`healthy male subjects enrolled in study 2; selected pharmacoki-
`netic data appeared in (2).
`Analyses performed in accordance with standard BB
`
`

`

`278
`
`method we use, and this study illustrates the fact that Cmax can
`find the correct answer by sheer luck.
`In study 2 the Cmax result appears due to three subjects in
`particular. On formulation B all three had unexpectedly law
`Cmax readings, 7.3 ug/ml. 718 ug/ml and 7.1 ug/ml, respec—
`tively, and correspondingly long Tmax values, 1.25 hr, 1.75 hr
`and 1.25 hr, respectively, for a drug that usually is absorbed in
`1 hr or less (2). A plausible explanation for this anomaly is that
`the fasting state was compromised.
`Analysis of Tmax regarded as a continuous variable in this
`study actually contradicts Cmax and found no statistically signif—
`icant differences (p = 0.13) beyond random fluctuation between
`the B and C formulations. However, this indication would usu—
`ally be overruled, and the study would be repeated.
`In study 3 the Cmax result is caused by subject 10 whose
`low concentration time profile on formulation A was noticeably
`aberrant. Corresponding Tmax values for subject 10 were not
`affected, so Tmax treated as a continuous variable is robust to
`this influential subject (p-value : 0.61). No matter. this study
`also, would be repeated.
`The discrete Tmax count data for the three studies is given
`in Table II; an appropriate analysis for this absolute variable
`appears in Table III.
`In studies 1 and 2, which both used a sample collection
`interval of 15 minutes, absorption rate means have an estimated
`standard deviation of 18 minutes and 19 minutes, respectively.
`The mean formulation absorption rates in study 3 have a stan—
`dard deviation of 27 minutes. This too is slightly greater than
`the sampling density interval (1/3 hour, or 20 minutes) used to
`collect the data.
`
`The reciprocal of the constant absorption phase sampling
`
`Basson, Ghosh, Cerimele, DeSante, and Howey
`
`rate seems to roughly define a standard set of confidence
`bounds for absorption rate estimates. When estimates differ by
`less than this basic indeterminacy interval they are statistically
`indistinguishable from each other. Analysis of me is necessar-
`ily oblivious to this fundamental limitation imposed by the
`study design. So in contrast to the conventional analysis, in all
`three cases, Poisson regression analysis of Tmax fails to declare
`any of the formulation: to have different absorption rates. This
`more robust analysis happens to agree with the ‘widened
`bounds’ approach, in these three examples.
`
`DISCUSSION
`
`These three BE examples are not extraordinary. They
`illustrate that tightly regulated BB is not a fair game of chance.
`In the first example me is barely well-behaved enough to not
`disrupt an otherwise uneventful study. In study 2 a more com-
`mon BE dilemma occurs. A few subjects who were supposed to
`observe a 14 hr fast exhibit signs consistent with having con—
`sumed food. The rate surrogate me admirably detects data
`outliers, but, if used inappropriately, will declare that formula--
`lions B and C are not BE. Current regulatory guides are inflex-
`ible and intolerant regarding biological variation or individual
`outliers so that all an unfortunate sponsor can do is bury the
`study, and repeat the work hoping for better luck. Analyses
`which deal more realistically with individual subject variabil-
`ity, declare B and C formulations BE in both rate and extent of
`absorption! In the second and third studies even naive analysis
`of Tmax actually does contradict an errant Cm“; apparently how-
`ever that signifies nothing.
`There are latent unintended consequences to the BE
`
`Table II. Number of Fractional Hours to Reach Tmax
`
`Study l-Antibiotic #1
`
`Frequency of me value by sampling time (quarter hr.)
`1
`2
`3
`4
`5
`6
`7
`Formulation
`8
`Total
`
`
`24
`0
`l
`9
`5
`8
`1
`0
`A
`24
`2
`2
`4
`4
`10
`2
`0
`B
`24
`0
`4
`5
`6
`9
`0
`0
`C
`Total
`0
`3
`27
`5
`18
`7
`2
`72
`
`
`
`Study 2-Antibiotic #2
`
`Frequency of Tmax value by sampling time (quarter hr)
`Formulation
`l
`2
`3
`4
`5
`6
`7
`8
`Total
`
`
`15
`0
`O
`0
`O
`0
`4
`9
`2
`A
`15
`O
`1
`0
`2
`O
`4
`6
`2
`B
`15
`O
`O
`0
`O
`1
`3
`8
`3
`C
`Total
`7
`23
`11
`1
`2
`0
`l
`0
`45
`
`
`
`Study 3-Antiviral
`
`Frequency of Tmax value by sampling time (third hr)
`
`Formulation
`1
`2
`3
`4
`5
`6
`8
`9
`Total
`
`A
`B
`Total
`
`O
`0
`0
`
`2
`1
`3
`
`5
`6
`11
`
`4
`4
`8
`
`6
`6
`12
`
`3
`5
`8
`
`2
`3
`5
`
`1
`0
`1
`
`24
`24
`48
`
`

`

`Why Rate of Absorption Inferences are Often Inappropriate
`
`279
`
`Table III. Histograms Means and Confidence Intervals (Poisson Regression)
`————-———
`90%
`Mean
`Difference
`Confidence
`Significance
`Contrastsa
`Test
`Reference
`in means
`Interval
`p-value
`
`
`_——__—.___—_
`Study l-Antibiotic #1
`
`A_VS_-.C
`Tm“
`B vs. C
`Tm,
`
`60
`
`61
`
`62
`
`62
`
`—2
`
`—1
`
`717 to 13
`
`—16 to 13
`
`0.83
`
`0.89
`
`
`Study 2-Antibiotic #2
`
`32
`
`43
`
`32
`
`32
`
`0.0
`
`11
`
`714 to 14
`
`4 to 26
`
`1.0
`
`0.20
`
`A vs. C
`T"m
`
`m T
`
`m,
`
`
`Study 3-Antiviral
`
`A vs. B
`Tmax
`
`1.54
`
`1.63
`
`$.08
`
`—0.44 to 0.27
`
`0.69
`
`" Units for parameters: Tm“, min. for studies 1 and 2, hr for study 3.
`b The Test minus reference difference is given. The point estimate of the difference
`in equivalent means 0.0.
`
`dilemma. To control the rogue Cmax variable, sponsors run ever
`larger, costlier, studies. Subjecting two dozen or more subjects
`to invaSive experimentation has become routine in BEE. Naive
`analysis of Tm,“ particularly in a large study, generates its own
`problems.
`
`CONCLUSIONS
`
`Efficient BEE grounded in good science will facilitate fair
`competition on a flat playing field and is a worthy goal.
`We have illustrated a way to improve the overall effi—
`ciency of the BEE process. The first step consists in using
`a refined but simple sampling scheme to empower Tmax
`to function as the metric for absorption rate. The second
`step requires no more than respect for the tenets of measure-
`ment theory: analyze the absorption rate attribute, Tm“, (a
`count variable), with an appropriately restricted statistical
`analysis.
`Alternative approaches are more convoluted. If AUC is
`the primary extent measure, then admit Cm, is a secondary
`extent Variable. To analyze Cm, and control the on level of the
`test, make an adjustment for the multiple testing that
`this action implies (13). Widening of the BE bounds arbi-
`trarily for Cmaxybut not for AUC, is an alternative approach
`that has already been embraced by Canadian and EEC
`authorities.
`
`This will lower the incidence of inappropriate inferences
`in BE studies, reduce the need to redo many of them, save that
`development cost, and reduce the number of subjects studied in
`each BEE.
`
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`
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