When planning bioavailability analysis, it is very important to choose the right sample size as this affects the power of the study (Wang and Bakhai, 2006). The sample size, according to bioequivalence studies, is the total number of subjects involved in the study. This number, as stated by Hauschke et al. (2007), is determined by the amount of variability in the PK characteristic, the power of the test, the level of significance and the expected deviation of the T from the R formulation. A larger sample size has a better power and has the ability to detect any treatment effect while a small sample size has less power and could necessarily not be able to accurately detect a treatment effect. That is, by taking larger samples, the ability to find a difference in means of the two formulations, if they do exist, is improved. Also, the power of the test decreases as the population variance reduces and as the difference in the means increases, the power also increases.
The power of the test, according to Chow and Liu (2008) and Hauschke et al. (2007), is defined as the likelihood of rejecting the null hypothesis of bioinequivalence between an R and a T drug, while the alternative hypoth- esis of bioequivalence is true.
H0 : bioinequivalence
H1 : bioequivalence.
This implies that the power of a test is the likelihood of concluding correct- ly that a drug is effective and bioequivalent when it is. According to Owen (1965), power in BE studies is the likelihood of demonstrating that two drugs are bioequivalent correctly when the two drug formulations are indeed bioe- quivalent.
power = 1 − β,
= P (reject H0 when H0 is f alse),
where β = P (type II error).
The power (1 − β) of the decision rule is the chance of correctly concluding bioequivalence.
There are two types of errors that depend on the sample size and the power of the test. The two types of errors are used when testing the null hypoth- esis against the alternative hypothesis for average bioequivalence. In ABE, there are chances of incorrectly establishing that two drug formulations are bioequivalent when they are not. This phenomenom is referred to as making a Type I error. A Type I error is perpetrated whenever the null hypothesis (bioinequivalent) is rejected whilst it is indeed true and a Type II error occurs when the null hypothesis is false but it is not rejected. The two types of errors are shown in Table 2.2 (Chow and Liu, 2008).
Table 2.2: Type I and Type II errors for a hypothesis test. The null hypothesis is
True False Fail to reject
null hypothesis
Correct decision Type II error β Reject null
hypothesis
Type I error α Correct decision
Usually the sample size used in bioequivalence studies, as stated by Chow and Liu (2008), is chosen based on a power function which tests the null hypothesis
of bioequivalence between the two formulations (µT = µR). In every BE study
it is important to choose the sample size while considering the Type I error rate as well as the equivalence criteria, the power (normally 90%) and the intra- subject variation (Patterson, 2003). Whenever the intra-subject coefficient of variation (CV) increases beyond 30%, the sample size required for BE increases as shown in Table 2.3 (Patterson, 2003).
Table 2.3: Sample sizes producing 90% power in BE for Two period crossover design(COD).
CVw% Two period COD∗ Two period COD
30 40 50 54 60 112 124 45 84 90 112 120 230 244 60 140 146 184 194 384 404 75 200 206 264 276 554 574
Two period COD∗ assumes subject-by-formulation interaction is negligible. Two period COD assumes subject-by-formulation interaction is non-negligible.
Patterson (2003) indicated that the number of samples needed for BE studies reduces by half when using replicate designs with high intra-subject variabil- ity. However, when the variability is low, a non-replicate two period COD is preferred as the replicate design does not improve precision drastically.
In order to test for bioequivalence between an R and a T drug, two types of hypothesis approaches are used, namely direct and indirect bioequivalence testing (Hauschke et al., 2007). The indirect bioequivalence testing uses the hypothesis in Equation 2.26,
H0 : bioequivalence
H1 : bioinequivalence.
(2.26) The major shortcoming of this indirect approach, according to Hauschke et al. (2007), is the fact that the chances of judging bioinequivalence mistakenly is regulated and therefore is not accepted by the regulatory authorities.
Table 2.4: Type I and Type II errors for indirect bioequivalence testing. The null hypothesis of bioequivalence is
True False Fail to reject
null hypothesis of bioequivalence
Correct decision Consumer risk β Reject null hypothesis of
bioequivalence
Producer risk α Correct decision
The ultimate regulatory concern for regulatory bodies is to control consumer risks, thus limiting the chances of concluding incorrectly bioequivalence (Hauschke et al., 2007). Due to this, the direct approach is the approved method by the regulatory bodies as in Equation 2.25.
The producer and consumer risks for the direct method of BE assessment are illustrated in Table 2.5.
Table 2.5: Type I and Type II errors for direct bioequivalence testing. The null hypothesis of bioinequivalence is
True False Fail to reject
null hypothesis of bioinequivalence
Correct decision Producer risk β Reject null hypothesis of
bioinequivalence
Consumer risk α Correct decision
In ABE, Type I error is defined as the likelihood of deciding that two drug formulations are bioequivalent. This probability is also known as alpha, con- fidence or regulatory risk.
The relationship between a Type I and a Type II error for a bioequivalence study, as illustrated by Chow and Liu (2008), is shown in Table 2.6. The power is determined based on a hypothesis and the outcome. There are four possible outcomes with hypothesis testing, two of which are correct decisions while the other two are incorrect, as shown in Table 2.6. The inferences which are incorrect are the errors. The two types of errors, Type I and Type II, in some cases, are referred to as consumer’s risk and producer’s risk, respectively, as explained in Table 2.6 (Patterson, 2003).
Table 2.6: Type I and Type II errors. True State H0
Bioinequivalent Bioequivalent Bioinequivalent Right decision Type II error Bioequivalent Type I error Right decision
The power of the test is not the main issue of this study but rather the com- parison of the formulation means and shall not be investigated further.