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USING TWO 1-SIDED TOLERANCE INTERVAL APPROACH TO SET QUALITY SPECIFICATION AND SAMPLING ACCEPTANCE PLAN OF DELIVERY DOSE

2009 NCB Conference at Boston, MA. 2. OUTLINES. TWO 1-SIDED APPROACHESi.TWO 1-SIDED TESTS (TOST)ii.TWO 1-SIDED TOLERANCE INTERVALS (TOSTI) BACKGROUND OF DDU TESTS DEVELOPMENTFDA 2005 TOSTI APPROACHPROPERTIES OF TOSTI APPROACH DISCUSSION

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USING TWO 1-SIDED TOLERANCE INTERVAL APPROACH TO SET QUALITY SPECIFICATION AND SAMPLING ACCEPTANCE PLAN OF DELIVERY DOSE

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    1. 2009 NCB Conference at Boston, MA 1 USING TWO 1-SIDED TOLERANCE INTERVAL APPROACH TO SET QUALITY SPECIFICATION AND SAMPLING ACCEPTANCE PLAN OF DELIVERY DOSE CONTENT UNIFORMITY Yi Tsong, Meiyu Shen & Richard Lostritto Office of Biostatistics, CDER, FDA

    2. 2009 NCB Conference at Boston, MA 2 OUTLINES TWO 1-SIDED APPROACHES i. TWO 1-SIDED TESTS (TOST) ii. TWO 1-SIDED TOLERANCE INTERVALS (TOSTI) BACKGROUND OF DDU TESTS DEVELOPMENT FDA 2005 TOSTI APPROACH PROPERTIES OF TOSTI APPROACH DISCUSSION & SUMMARY

    3. 2009 NCB Conference at Boston, MA 3 I. TWO 1-SIDED APPROACHES Let Y be a drug attribute of interest and L and U as the lower and upper limit of the specification of Y. In quality assessment of the product using a sample of size N, FDA chemists want the quality specification of Y be described as “< QL% of the batch (lot) should be below L and < QU% of the batch (lot) should be above U” Instead of “= (1 - QL% - QU% ) of the batch (lot) should be between L and U”.

    4. 2009 NCB Conference at Boston, MA 4 TWO 1-SIDED TESTS (TOST) The acceptance sampling test can be represented as hypothesis testing (Tsong & Shen, JBS 2003) with H0L: Pr(Y ? L ) ? QL% vs HaL: Pr(Y ? L ) < QL% and H0U: Pr(Y ? U ) ? QU% vs HaU: Pr(Y ? U ) < QU% (1)

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    6. 2009 NCB Conference at Boston, MA 6 TWO 1-SIDED TOLERANCE INTERVALS (TOSTI) The estimate of the intervals (-8, and with a 1- a confidence level are called tolerance intervals. The procedure of testing hypotheses (1) is called two one-sided tests (Schuirman, JPB 1987; Tsong & Shen, JBS 2007.1). The corresponding testing procedure of (2) is called two one-sided tolerance intervals procedure (Tsong, Shen & Shah, JBS 2002; Tsong & Shen, JBS 2007.2).

    7. 2009 NCB Conference at Boston, MA 7 PARAMETRIC APPROACHES OF TOST AND TOSTI When Y follows a normal distribution N(µ, s2), Null hypotheses (1) can be re-written as H0L: Pr[(Y – ?)/? ? (L - ?)/?)] ? QL% and H0U: Pr[(Y – ?)/? ? (U - ?)/?)] = QU% Null hypotheses (1) become H0L: ? - L + ? ? 0 and H0U: ? - U + ? ? 0 (1’)

    8. 2009 NCB Conference at Boston, MA 8 With unknown ?, tL(N) =[?y - L + s(N)Z QL%]/[s(N)/?N] =[(?y - L+?Z QL% -?Z QL%)+s(N)Z QL%]/[s(N)/?N] =[(?y - ?)?N/? + ?N Z QL%]/[s(N)/ ?] -?N Z QL% where s(N) is the estimate of ?. Under H0L, [(?y -?)?N/?+?NZ QL%]/[s(N)/?]?t(N-1, ?N Z QL%). Reject H0L if tL(N) + ?N Z QL% > t(N-1, ?N ZQL%, (1-?)). Similarly, let tU(N) =[?y - U + s(N)Z 1-QU%]/[s(N)/?N] Reject H0U if tU(N) + ?N Z 1-QU% < t(N-1, ?N Z1-QU%, (1-?)).

    9. 2009 NCB Conference at Boston, MA 9 For TOSTI, with normality assumption, the tolerance intervals are (- ?, ?y + KLs) and (?y - KUs, ?), where KL = t(N-1, ?N ZQL%, 1 - a)/?N, KU = t (N-1, ?N ZQU%, 1 - a)/?N Reject H0L if ?y - KLs > L Reject H0U if ?y + KUs < U ?y - KLs is the lower confidence limit of the QL-th %-tile, ?y + KUs is the upper confidence limit of the (1- QU)-th %-tile

    10. 2009 NCB Conference at Boston, MA 10 STATISTICAL PROPERTIES OF TOST & TOSTI TOST is an intersection-union test (IUT), it is also the likelihood ratio test (LRT) for testing this type of hypotheses (1) (Berger et al 1989) TOST controls type I error rate for testing hypotheses (1) TOST is the uniformly most powerful test among all monotone, a-level tests for linear hypothesis (1) as shown by Berger (1989). A monotone test has a desirable property in interpretation such that for testing hypotheses (1), p(?) = p(?*) if ??*(tk) = (??(tk)) for all tk for any ? and ?* (= (??*(t1), …, ??*(tK)) in the parameter space T.

    11. 2009 NCB Conference at Boston, MA 11 Berger (1989) also pointed out that this is not an unbiased test because the power p(?) < p(?0), ? = ((??(t1), …, ??(tK)), ?0 = ((??’(t1), …, ??’(tK)), are in the parameter subspaces Ta of Ha and ?0 is in the parameter subspace T0 of H0 respectively. TOSTI has exactly solution and is easy to calculate TOSTI are determined by given specification limits, L and U, QL (the % below L), QU (the % above U) and a. In quality acceptance plan, we specify L and U, then determine QL and QU for the desirable quality

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    18. 2009 NCB Conference at Boston, MA 18 IV. PROPERTIES OF TOSTI APPROACH Novick et al (2008) Part 1 to 3

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    20. 2009 NCB Conference at Boston, MA 20 Novick et al (2008a): Because of performing two 1-sided tests, the coverage (between 80-120%) of 5% acceptance probability of on-target products is actually 91.5% instead of 87.5% (1-12.5%).

    21. 2009 NCB Conference at Boston, MA 21 Novick et al (2008b): With Q = 12.5%, µ = 100, when N increases, the probability of acceptance remains at 5% if the coverage is 91.5%. But the probability of acceptance increases to near 100% when the coverage > 91.5%. Should we reduce Q when N increases?

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    23. 2009 NCB Conference at Boston, MA 23 Generates a much steeper OC curve than the 1998/2003 FDA draft guidance More power in discriminating the bad and good product generates a distinct gap of OC curves between a lot with on-target mean and a lot with off-target mean. Q can be modified for products with large variability Q needs to be adjusted for sample size N

    24. 2009 NCB Conference at Boston, MA 24 References FDA/CDER. Draft Guidance for Industry “Metered Dose Inhaler (MDI) and Dry Powder Inhaler (DPI) Drug Products Chemistry, Manufacturing, and Controls Documentation”. October 1998. Available at http://www.fda.gov/cder/guidance/2180dft.pdf. Accessed September 11, 2008. FDA/CDER. Guidance for Industry “Nasal Spray and Inhalation Solution, Suspension, and Spray Drug Products Chemistry, Manufacturing, and Controls Documentation”. Draft: May 1999, Available at http://www.fda.gov/ohrms/dockets/ac/00/backgrd/3609b1k.pdf. Accessed September 11, 2008. Final: July 2002. Available at http://www.fda.gov/cder/guidance/4234fnl.pdf. Accessed September 11, 2008. Nasr MM. (2005). Parametric Tolerance Interval Test for Delivered Dose Uniformity (DDU). Presentation to Advisory Committee for Pharmaceutical Science on 25 October 2005. Lostritto R, (2005) Transcripts of the Advisory Committee for Pharmaceutical Science Meeting on 25 October 2005, page 361. Tsong Y, Shen M, Lostritto RT, Poochikian GK (2008). Parametric two-tier sequential quality assurance test of delivery dose uniformity of multiple-dose inhaler and dry powder inhaler drug products. J of Biopharm. Statist, 18:5, 976-984.

    25. 2009 NCB Conference at Boston, MA 25 6) IPAC-RS. A parametric tolerance interval test for improved control of delivered dose uniformity of orally inhaled and nasal drug products. 2001. Novick S, Christopher D, Dey M, Lyapustina S, Golden M, Leiner S, Wyka B, Delzeit H-J, Novak C, Larner G (2008a) A Two One-Sided Parametric 1 Tolerance Interval Test For Control of Delivered Dose Uniformity – Part 1 – Characterization of FDA Proposed Test. Pharmaceutical Research. Novick S, Christopher D, Dey M, Lyapustina S, Golden M, Leiner S, Wyka B, Delzeit H-J, Novak C, Larner G (2008b) A Two One-Sided Parametric 1 Tolerance Interval Test For Control of Delivered Dose Uniformity – Part 2 – Effect of Changing Parameters. Pharmaceutical Research. Novick S, Christopher D, Dey M, Lyapustina S, Golden M, Leiner S, Wyka B, Delzeit H-J, Novak C, Larner G (2008c) A Two One-Sided Parametric 1 Tolerance Interval Test For Control of Delivered Dose Uniformity – Part 3 – Investigation of Robustness to Deviations from Normality. Pharmaceutical Research.

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