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5 Population bioequivalence As noted in Section 7.1, population bioequivalence (PBE) is concerned with assessing whether a patient who has not yet been treated with R or T can be prescribed either formulation. It can be assessed using the following aggregate metric (FDA Guidance, 1997). (µ (7.8) max(0.04,σ ) where σ and σ . As long as an appropriate mixed model is fitted to the data, this metric can be calculated using data from a 2×2 design or from a replicate design. Using data from Sections 7.2 and 7.4, we will illustrate the calculation of the metric in each of the two designs. 7.5.1 PBE using a 2× 2 design As in the previous section we will test for equivalence using a linearized version of the metric and test the null hypotheses: H : ν = δ +σ − (1 + c when σ > 0.04 or H : ν = δ +σ −σ (0.04) ≥ 0, (7.10) when σ > 0.04, where σ and σ are the between-subject variances of T and R, re-spectively. Let ω denote the between-subject covariance of T and R and σ denote the variance of δˆ = µˆ . The REML estimates of σ , o btained from using the SAS code in Appendix B, are asymptoti-cally normally distributed with expecta tion vector σ l lT×ω σ and variance-covariance matrix l lT×ω l lω Then νˆ = δˆ + σˆ − (1 + c )σˆ (7.11) is an estimate for the reference-scaled PBE metric in accordance with FDA Guidance (2001) when σˆ > 0.04 and using a REML UN model. This estimate is asymptotically normally distributed and unbiased (Pat-terson, 2003; Patterson and Jones, 2002b) with E[νˆ ] = δ +σ
DOI link for 5 Population bioequivalence As noted in Section 7.1, population bioequivalence (PBE) is concerned with assessing whether a patient who has not yet been treated with R or T can be prescribed either formulation. It can be assessed using the following aggregate metric (FDA Guidance, 1997). (µ (7.8) max(0.04,σ ) where σ and σ . As long as an appropriate mixed model is fitted to the data, this metric can be calculated using data from a 2×2 design or from a replicate design. Using data from Sections 7.2 and 7.4, we will illustrate the calculation of the metric in each of the two designs. 7.5.1 PBE using a 2× 2 design As in the previous section we will test for equivalence using a linearized version of the metric and test the null hypotheses: H : ν = δ +σ − (1 + c when σ > 0.04 or H : ν = δ +σ −σ (0.04) ≥ 0, (7.10) when σ > 0.04, where σ and σ are the between-subject variances of T and R, re-spectively. Let ω denote the between-subject covariance of T and R and σ denote the variance of δˆ = µˆ . The REML estimates of σ , o btained from using the SAS code in Appendix B, are asymptoti-cally normally distributed with expecta tion vector σ l lT×ω σ and variance-covariance matrix l lT×ω l lω Then νˆ = δˆ + σˆ − (1 + c )σˆ (7.11) is an estimate for the reference-scaled PBE metric in accordance with FDA Guidance (2001) when σˆ > 0.04 and using a REML UN model. This estimate is asymptotically normally distributed and unbiased (Pat-terson, 2003; Patterson and Jones, 2002b) with E[νˆ ] = δ +σ
5 Population bioequivalence As noted in Section 7.1, population bioequivalence (PBE) is concerned with assessing whether a patient who has not yet been treated with R or T can be prescribed either formulation. It can be assessed using the following aggregate metric (FDA Guidance, 1997). (µ (7.8) max(0.04,σ ) where σ and σ . As long as an appropriate mixed model is fitted to the data, this metric can be calculated using data from a 2×2 design or from a replicate design. Using data from Sections 7.2 and 7.4, we will illustrate the calculation of the metric in each of the two designs. 7.5.1 PBE using a 2× 2 design As in the previous section we will test for equivalence using a linearized version of the metric and test the null hypotheses: H : ν = δ +σ − (1 + c when σ > 0.04 or H : ν = δ +σ −σ (0.04) ≥ 0, (7.10) when σ > 0.04, where σ and σ are the between-subject variances of T and R, re-spectively. Let ω denote the between-subject covariance of T and R and σ denote the variance of δˆ = µˆ . The REML estimates of σ , o btained from using the SAS code in Appendix B, are asymptoti-cally normally distributed with expecta tion vector σ l lT×ω σ and variance-covariance matrix l lT×ω l lω Then νˆ = δˆ + σˆ − (1 + c )σˆ (7.11) is an estimate for the reference-scaled PBE metric in accordance with FDA Guidance (2001) when σˆ > 0.04 and using a REML UN model. This estimate is asymptotically normally distributed and unbiased (Pat-terson, 2003; Patterson and Jones, 2002b) with E[νˆ ] = δ +σ
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