Statistical Methods for CMC Applications

  • Richard K. Burdick
  • David J. LeBlond
  • Lori B. Pfahler
  • Jorge Quiroz
  • Leslie Sidor
  • Kimberly Vukovinsky
  • Lanju Zhang
Part of the Statistics for Biology and Health book series (SBH)


In this chapter, we provide statistical methods that are useful in CMC applications. Our goal is to provide a description of these methods without delving deeply into the theoretical aspects. References are provided for the reader who desires a more in depth understanding of the material.


Analysis of variance Bayesian analysis Confidence intervals Data reporting Data rounding Data transformations Dependent measures Equivalence testing Hypothesis testing Interaction effects LOQ values Mixed models Multiple regression Nonlinear models Non-normal data Prediction intervals Quadratic effects Regression analysis Residual analysis Statistical consulting Statistical intervals Tolerance intervals Visualization of data 


  1. ASTM E29 (2013) Standard practice for using significant digits in test data to determine conformance with specifications. ASTM International, West ConshohockenGoogle Scholar
  2. Berger RL, Hsu JC (1996) Bioequivalence trials, intersection-union tests and equivalence confidence sets. Stat Sci 11(4):283–302MathSciNetCrossRefzbMATHGoogle Scholar
  3. Berry SM, Carlin BP, Lee JJ, Muller P (2010) Bayesian adaptive methods for clinical trials. CRC Press, Taylor & Francis Group, Boca RatonCrossRefzbMATHGoogle Scholar
  4. Bolstad WM (2007) Introduction to Bayesian statistics, 2nd edn. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  5. Borman PJ, Chatfield MJ (2015) Avoid the perils of using rounded data. J Pharm Biomed Anal 115:502–508CrossRefGoogle Scholar
  6. Boylan GL, Cho RR (2012) The normal probability plot as a tool for understanding data: a shape analysis from the perspective of skewness, kurtosis, and variability. Qual Reliab Eng Int 28:249–264CrossRefGoogle Scholar
  7. Brown H, Prescott R (2006) Applied mixed models in medicine, 2nd edn. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  8. Burdick RK, Graybill FA (1992) Confidence intervals on variance components. Marcel Dekker, New YorkzbMATHGoogle Scholar
  9. Burdick RK, Borror CM, Montgomery DC (2005) Design and analysis of gauge R&R experiments: making decisions with confidence intervals in random and mixed ANOVA models. ASA-SIAM Series on Statistics and Applied Probability. SIAM, PhiladelphiaCrossRefzbMATHGoogle Scholar
  10. Burgess C (2013) Rounding results for comparison with specification. Pharm Technol 37(4):122–124Google Scholar
  11. Casella G, George EI (1992) Explaining the Gibbs sampler. Am Stat 46:167–174MathSciNetGoogle Scholar
  12. Cleveland WS (1985) The elements of graphing data. Wadsworth Advanced Books and Software, MontereyGoogle Scholar
  13. Dong X, Tsong Y, Shen M, Zhong J (2015) Using tolerance intervals for assessment of pharmaceutical quality. J Biopharm Stat 25(2):317–327MathSciNetCrossRefGoogle Scholar
  14. Eberhardt KR, Mee RW, Reeve CP (1989) Computing factors for exact two-sided tolerance limits for a normal distribution. Commun Stat Simul Comput 18(1):397–413CrossRefzbMATHGoogle Scholar
  15. Gelman A, Hill J (2007) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, New YorkGoogle Scholar
  16. Gitlow H, Awad H (2013) Intro students need both confidence and tolerance intervals. Am Stat 67(4):229–234MathSciNetCrossRefGoogle Scholar
  17. Graybill FA, Wang C-M (1980) Confidence intervals on nonnegative linear combinations of variances. J Am Stat Assoc 75(372):869–873MathSciNetCrossRefGoogle Scholar
  18. Hahn GJ, Meeker WQ (1991) Statistical intervals: a guide for practitioners. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  19. Hannig J, Iyer H, Patterson P (2006) Fiducial generalized confidence intervals. J Am Stat Assoc 101(473):254–269MathSciNetCrossRefzbMATHGoogle Scholar
  20. Hoffman D, Kringle R (2005) Two-sided tolerance intervals for balanced and unbalanced random effects models. J Biopharm Stat 15:283–293MathSciNetCrossRefGoogle Scholar
  21. Howe WG (1969) Two-sided tolerance limits for normal populations--some improvements. J Am Stat Assoc 64:610–620zbMATHGoogle Scholar
  22. International Conference on Harmonization (2004) Q5E Comparability of biotechnological/biological products subject to changes in their manufacturing processGoogle Scholar
  23. Joseph L, Gyorkos TW, Coupal L (1995) Bayesian estimation of disease prevalence and the parameters of diagnostic tests in the absence of a gold standard. Am J Epidemiol 141(3):263–272CrossRefGoogle Scholar
  24. Kelley K (2007) Confidence intervals for standardized effect sizes: theory, application, and implementation. J Stat Softw 20(8):1–24.
  25. Krishnamoorthy K, Mathew T (2009) Statistical tolerance regions: theory, applications, and computation. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  26. Krishnamoorthy K, Xia Y, Xie F (2011) A simple approximate procedure for constructing binomial and Poisson tolerance intervals. Commun Stat Theory Methods 40(12):2243–2258MathSciNetCrossRefzbMATHGoogle Scholar
  27. Kruschke JK (2015) Doing Bayesian data analysis, 2nd edn. Academic Press, Burlington, MAGoogle Scholar
  28. Limentani GB, Ringo MC, Ye F, Bergquist ML, McSorley EO (2005) Beyond the t-test: statistical equivalence testing. Anal Chem 77(11):221–226Google Scholar
  29. Littell RC, Milliken GA, Stroup WW, Wolfinger RD, Schabenberger O (2006) SAS for mixed models, 2nd edn. SAS Institute Inc, CaryGoogle Scholar
  30. Mee RW (1984) β-expectation and β-content tolerance limits for balanced one-way ANOVA random model. Technometrics 26(3):251–254Google Scholar
  31. Mee RW (1988) Estimation of the percentage of a normal distribution lying outside a specified interval. Commun Stat Theory Methods 17(5):1465–1479CrossRefGoogle Scholar
  32. Myers RH, Montgomery DC, Vining GG (2002) Generalized linear models with applications in engineering and the sciences. Wiley, New YorkzbMATHGoogle Scholar
  33. Nijhuis MB, Van den Heuvel ER (2007) Closed-form confidence intervals on measures of precision for an inter-laboratory study. J Biopharm Stat 17:123–142CrossRefGoogle Scholar
  34. NIST/SEMATECH e-handbook of statistical methods. Accessed 6 Jan 2016
  35. Office of Regulatory Affairs (ORA) Laboratory Manual. Accessed 6 Jan 2016
  36. Persson T, Rootzen H (1977) Simple and highly efficient estimators for a type I censored normal sample. Biometrika 64:123–128CrossRefzbMATHGoogle Scholar
  37. Quiroz J, Strong J, Zhang Z (2016) Risk management for moisture related effects in dry manufacturing processes: a statistical approach. Pharm Dev Technol 21:147–151CrossRefGoogle Scholar
  38. Suess EA, Fraser C, Trumbo BE (2000) Elementary uses of the Gibbs sampler: applications to medical screening tests. STATS Winter 27:3–10Google Scholar
  39. Thomas JD, Hultquist RA (1978) Interval estimation for the unbalanced case of the one-way random effects model. Ann Stat 6:582–587MathSciNetCrossRefzbMATHGoogle Scholar
  40. Torbeck LD (2010) %RSD: friend or foe? Pharm Technol 34(1):37–38Google Scholar
  41. Tufte ER (1983) The visual display of quantitative information. Graphics Press, CheshireGoogle Scholar
  42. USP 39-NF 34 (2016a) General Chapter <1010> Analytical data—interpretation and treatment. US Pharmacopeial Convention, RockvilleGoogle Scholar
  43. USP 39-NF 34 (2016b) General Notices 7.20: Rounding Rules. US Pharmacopeial Convention, RockvilleGoogle Scholar
  44. Vangel MG (1996) Confidence intervals for a normal coefficient of variation. Am Stat 15(1):21–26MathSciNetGoogle Scholar
  45. Vining G (2010) Technical advice: quantile plots to check assumptions. Qual Eng 22(4):364–367MathSciNetCrossRefGoogle Scholar
  46. Vining G (2011) Technical advice: residual plots to check assumptions. Qual Eng 23(1):105–110CrossRefGoogle Scholar
  47. Vukovinsky KE, Pfahler LB (2014) The role of the normal data distribution in pharmaceutical development and manufacturing. Pharm Technol 38(10)Google Scholar
  48. Yu Q-L, Burdick RK (1995) Confidence intervals on variance components in regression models with balanced (Q-1)-fold nested error structure. Commun Stat Theory Methods 24:1151–1167MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Richard K. Burdick
    • 1
  • David J. LeBlond
    • 2
  • Lori B. Pfahler
    • 3
  • Jorge Quiroz
    • 4
  • Leslie Sidor
    • 5
  • Kimberly Vukovinsky
    • 6
  • Lanju Zhang
    • 7
  1. 1.Elion LabsLouisvilleUSA
  2. 2.CMC StatisticsWadsworthUSA
  3. 3.Merck & Co., Inc.TelfordUSA
  4. 4.Merck & Co., Inc.KenilworthUSA
  5. 5.BiogenCambridgeUSA
  6. 6.PfizerOld SaybrookUSA
  7. 7.Nonclinical Statistics, Abbvie Inc.North ChicagoUSA

Personalised recommendations