364
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

Survey and Recommendations on the Use of P-Values Driving Decisions in Nonclinical Pharmaceutical Applications

, , , , , , , , , , , , , , , , , , , , & show all
Pages 343-358 | Received 20 Jun 2021, Accepted 21 Jan 2022, Published online: 21 Mar 2022

References

  • Altan, S., Geys, H., Kuhn, M., LeBlond, D., and Peterson, J. (2018), Nonclinical Statistics. Hoboken, NJ: Wiley StatsRef: Statistics Reference Online, available at DOI: 10.1002/9781118445112.stat08058.
  • Altan, S., Kolassa, J., and Novick, S. (2021), “Report on the Non-Clinical Biostatistics Scientific Working Group on P-Values,” Biopharm Report, 28, 10–12.
  • Amaratunga, D. (n.d.), “Practical Matters Regarding p-Values and the Generalizability of Results,” Unpublished Manuscript.
  • Benjamin, D., and Berger, J. (2019), “Three Recommendations for Improving the Use of p-Values,” The American Statistician, 73, 186–191. DOI: 10.1080/00031305.2018.1543135.
  • Billheimer, D. (2019), “Predictive Inference and Scientific Reproducibility,” The American Statistician, 73(S1), 291–295. DOI: 10.1080/00031305.2018.1518270.
  • Blume, J., Greevy, R., Welty, V., Smith, J., and Dupont, W. (2019), “An Introduction to Second-Generation p-Values,” The American Statistician, 73(S1), 157–167. DOI: 10.1080/00031305.2018.1537893.
  • Boos, D. D., and Stefanski, L. A. (2011), “P-Value Precision and Reproducibility,” The American Statistician, 65, 213–221. DOI: 10.1198/tas.2011.10129.
  • Carroll, A. (2016), “Undue Influence: The P Value in Scientific Publishing and Health Policy,” JAMA Health Forum, DOI: 10.1001/jamahealthforum.2016.0026.
  • Editorial in Nature. (2019), “It’s Time to Talk About Ditching Statistical Significance,” Nature, 567, 283.
  • FDA. (2001), Draft Guidance for Industry: Statistical Aspects of the Design, Analysis, and Interpretation of Chronic Rodent Carcinogenicity Studies of the Pharmaceuticals. MD: Center for Drug Evaluation and Research (CDER).
  • Gadbury, G. L., and Allison, D. B. (2012), “Inappropriate Fiddling with Statistical Analyses to Obtain a Desirable P-Value: Tests to Detect Its Presence in Published Literature,” PLOS One, 7, e46363. DOI: 10.1371/journal.pone.0046363.
  • Gibson, E. W. (2021), “The Role of p-Values in Judging the Strength of Evidence and Realistic Replication Expectations. Special Section on Roles of Hypothesis Testing, p-Values, and Decision-Making in Biopharmaceutical Research,” Statistics in Biopharmaceutical Research, 13, 6–18. DOI: 10.1080/19466315.2020.1724560.
  • Goodman, S. N. (1992), “A Comment on Replication, p-Values and Evidence,” Statistics in Medicine, 11, 875–879. DOI: 10.1002/sim.4780110705.
  • Hamasaki, T., Bretz, F., LaVange, L. M., Müller, P., Pennello, G., and Pinheiro, J. C. (2021), “Editorial: Roles of Hypothesis Testing, p-Values and Decision Making in Biopharmaceutical Research. Special Section on Roles of Hypothesis Testing, p-Values, and Decision-Making in Biopharmaceutical Research,” Statistics in Biopharmaceutical Research, 13, 1–5. DOI: 10.1080/19466315.2021.1874803.
  • Harrington, D., D’Agostino, R. B., Gatsonis, C., Hogan, J. W., Hunter, D. J., Normand, S.-L. T., Drazen, J. M., and Hamel, M. B. (2019), “New Guidelines for Statistical Reporting in the Journal,” The New England Journal of Medicine, 381, 285–286. DOI: 10.1056/NEJMe1906559.
  • Jeffreys, H. (1961), Theory of Probability, Oxford: Oxford University Press.
  • Kraemer, H. C. (2019), “Is It Time to Ban the P Value,” JAMA Psychiatry, 76, 1219–1220. DOI: 10.1001/jamapsychiatry.2019.1965.
  • McShane, B., Gal, D., Gelman, A., Robert, C., and Tackett, J. (2019), “Abandon Statistical Significance,” The American Statistician, 73, 235–245. DOI: 10.1080/00031305.2018.1527253.
  • National Academies of Sciences, Engineering, and Medicine. (2019), Reproducibility and Replicability in Science. Washington, DC: The National Academies Press, available at DOI: 10.17226/25303.
  • Pearson, K. (1900), “On the Criterion that a Given System of Deviations from the Probable in the Case of a Correlated System of Variables is such that it can be Reasonably Supposed to Have Arisen from Random Sampling,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science?, 50, 157–175. DOI: 10.1080/14786440009463897.
  • Wasserstein, R. L., and Lazar, N. A. (2016), “The ASA Statement on p-Values: Context, Process, and Purpose,” The American Statistician, 70, 129–133. DOI: 10.1080/00031305.2016.1154108.
  • Wasserstein, R. L., Schirm, A. L., and Lazar, N. A. (2019), “Moving to a World Beyond,” The American Statistician, 73(S1), 1–1. p < 0.05,”
  • Trafimow, D., and Marks, M. (2015), “Editorial,” Basic and Applied Social Psychology, 37, 1–2. DOI: 10.1080/01973533.2015.1012991.

References for Drug Discovery/-omics section

  • Aban, I., and George, B. (2015), “Statistical Considerations for Preclinical Studies,” Experimental Neurology, 270, 82–87. DOI: 10.1016/j.expneurol.2015.02.024.
  • Akaike, H. (1974), “A New Look at the Statistical Model Identification,” IEEE Transactions on Automatic Control, 19, 716–723. DOI: 10.1109/TAC.1974.1100705.
  • Begley, C., and Ellis, L. (2012), “Drug Development: Raise Standards for Preclinical Cancer Research,” Nature, 483, 531–533. DOI: 10.1038/483531a.
  • Benjamini, Y., and Hochberg, Y. (1995), “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing,” Journal of the Royal Statistical Society, Series B, 57, 289–300. http://www.jstor.org/stable/2346101 DOI: 10.1111/j.2517-6161.1995.tb02031.x.
  • Benjamini, Y. (2016), “It’s Not the p-values’ Fault,” Supplemental material to Wasserstein and Lazar (2016).
  • Border, R., Johnson, E. C., Evans, L. M., Smolen, A., Berley, N., Sullivan, P. F., and Keller, M. C. (2019), “No Support for Historical Candidate Gene or Candidate Gene-by-Interaction Hypotheses for Major Depression Across Multiple Large Samples,” The American Journal of Psychiatry, 176, 376–387. DOI: 10.1176/appi.ajp.2018.18070881.
  • Checkley, S., MacCallum, L., Yates, J., Jasper, P., Luo, H., Tolsma, J., and Bendtsen, C. (2015), “Bridging the Gap Between in Vitro and in Vivo: Dose and Schedule Predictions for the ATR Inhibitor AZD6738,” Scientific Reports, 5, 13545 DOI: 10.1038/srep13545.
  • Edwards, D., and Berry, J. J. (1987), “The Efficiency of Simulation-Based Multiple Comparisons,” Biometrics, 43, 913–928. DOI: 10.2307/2531545.
  • Goodman, S. (2008), “A Dirty Dozen: Twelve p-Value Misconceptions,” Seminars in Hematology, 45, 135–140. DOI: 10.1053/j.seminhematol.2008.04.003.
  • Greenland, S. (2019), “Valid P-Values Behave Exactly as They Should: Some Misleading Criticisms of P-Values and Their Resolution With S-Values,” The American Statistician, 73, 106–114. DOI: 10.1080/00031305.2018.1529625.
  • Hwang, T., Carpenter, D., Lauffenburger, J., Wang, B., Franklin, J. M., and Kesselheim, A. (2016), “Failure of Investigational Drugs in Late-Stage Clinical Development and Publication of Trial Results,” JAMA Internal Medicine, 176, 1826–1833. DOI: 10.1001/jamainternmed.2016.6008.
  • Kraljevic, S., Stambrook, P., and Pavelic, K. (2004), “Accelerating Drug Discovery,” EMBO Reports, 5, 837–842. DOI: 10.1038/sj.embor.7400236.
  • Lendrem, D. (2002), “Statistical Support to Non-Clinical,” Pharmaceutical Statistics, 1, 71–73. DOI: 10.1002/pst.29.
  • Polak, S. (2013), “In Vitro to Human in Vivo Translation—Pharmacokinetics and Pharmacodynamics of Quinidine,” Altex, 30, 309–318. DOI: 10.14573/altex.2013.3.309.
  • Prinz, F., Schlange, T., and Asadullah, K. (2011), “Believe It or Not: How Much Can We Rely on Published Data on Potential Drug Targets?,” Nature Reviews. Drug Discovery, 10, 712. DOI: 10.1038/nrd3439-c1.
  • Quintana, D., and Williams, D. (2018), “Bayesian Alternatives for Common Null-Hypothesis Significance Tests in Psychiatry: A Non-Technical Guide Using JASP,” BMC Psychiatry, 18, 178. DOI: 10.1186/s12888-018-1761-4.
  • Storey, J. D., and Tibshirani, R. (2003), “Statistical Significance for Genomewide Studies,” Proceedings of the National Academy of Sciences of the United States of America, 100, 9440–9445. DOI: 10.1073/pnas.1530509100.
  • Tukey, J. (1962), “The Future of Data Analysis,” The Annals of Mathematical Statistics, 33, 1–67. DOI: 10.1214/aoms/1177704711.
  • Tukey, J. (1980), “We Need Both Exploratory and Confirmatory,” The American Statistician, 34, 23–25.
  • Vamathevan, J., Clark, D., Czodrowski, P., Dunham, I., Ferran, E., Lee, G., Li, B., Madabhushi, A., Shah, P., Spitzer, M., and Zhao, S. (2019), “Applications of Machine Learning in Drug Discovery and Development,” Nat Rev Drug Discov, 18, 463–477. DOI: 10.1038/s41573-019-0024-5.
  • Wiklund, S. (2019), “A Modelling Framework for Improved Design and Decision-Making in Drug Development,” PLos One, 14, e0220812. DOI: 10.1371/journal.pone.0220812.

References to Preclinical Safety/Toxicology Section

  • Altman, D. G., and Bland, J. M. (1995), “Statistics Notes: Absence of Evidence is Not Evidence of Absence,” BMJ, 311, 485–485. DOI: 10.1136/bmj.311.7003.485.
  • Bailer, A., and Portier, C. (1988), “Effects of Treatment-Induced Mortality and Tumor-Induced Mortality on Tests for Carcinogenicity in Small Samples,” Biometrics, 44, 417–431. DOI: 10.2307/2531856.
  • Benjamini, Y., and Hochberg, Y. (1995), “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing,” Journal of the Royal Statistical Society, Series B, 1, 289–300. DOI: 10.1111/j.2517-6161.1995.tb02031.x.
  • Bieler, G., and Williams, R. (1993), “Ratio Estimates, the Delta Method, and Quantal Response Tests for Increased Carcinogenicity,” Biometrics, 49, 793–801. DOI: 10.2307/2532200.
  • DaSilva, J., Cobbina, E., Tyszkiewicz, C., Li, D., and Goody, S. (2019), “Quantitative Association Analyses of CNS Safety Pharmacology Parameters to Clinical Observations in Toxicology Studies,” Journal of Pharmacological and Toxicological Methods, 9, 106595. DOI: 10.1016/j.vascn.2019.05.002.
  • Gregg, D. (1994), “A Comparison of Tumour Incidence Analyses Applicable in Single-Sacrifice Animal Experiments,” Statistics in Medicine, 3, 689–708.
  • Dunnett, C. (1955), “A Multiple Comparison Procedure for Comparing Several Treatments with a Control,” Journal of the American Statistical Association, 12, 1096–1121. DOI: 10.1080/01621459.1955.10501294.
  • EFSA (2019), Technical Report, Outcome of the Pesticides Peer Review Meeting on General Recurring Issues in Ecotoxicology.
  • EPA (2010), “National Pollutant Discharge Elimination System Test of Significant Toxicity Implementation Document,” Environmental Protection Agency Office of Wastewater Management, 6, 5–7.
  • EPA (2012), Benchmark Dose Technical Guidance, EPA/100/R-12/001
  • Guy, R. C. (2014), Ames Test, Editor(s): Philip Wexler Encyclopedia of Toxicology (3rd ed., pp. 187–188), Waltham, MA: Academic Press.
  • Hothorn, L. (2014), “Statistical Evaluation of Toxicological Bioassays – A Review,” Toxicology Research, 3, 418–432. DOI: 10.1039/C4TX00047A.
  • Hothorn, L., and Hasler, M. (2008), “Proof of Hazard and Proof of Safety in Toxicological Studies Using Simultaneous Confidence Intervals for Differences and Ratios to Control,” Journal of Biopharmaceutical Statistics, 18, 915–933. DOI: 10.1080/10543400802287511.
  • Kluxen, F., and Hothorn, L. (2020), “Alternatives to Statistical Decision Trees in Regulatory (Eco-)Toxicological Bioassays,” Archives of Toxicology, 3, 19. DOI: 10.1007/s00204-020-02690-w.
  • Lazic, S., Semenova, E., and Williams, D. (2020), “Determining Organ Weight Toxicity with Bayesian Causal Models: Improving on the Analysis of Relative Organ Weights,” Scientific Reports, 6625. DOI: 10.1038/s41598-020-63465-y.
  • Lazic, S., Edmunds, N., and Pollard, C. (2018), “Predicting Drug Safety and Communicating Risk: Benefits of a Bayesian Approach,” Toxicological Sciences: An Official Journal of the Society of Toxicology, 162, 89–98. DOI: 10.1093/toxsci/kfx236.
  • MacGregor, J., Frötschl, R., White, P., Crump, K., Eastmond, D., Fukushima, S., Guérard, M., Fukushima, S., Guérard, M., Hayashi, M., Soeteman-Hernández, L., Kasamatsu, T., Levy, D., Morital, M., Müller, L., Schoeny, R., Schuler, M., Thybaud, V., and Johnson, G. (2015), “IWGT Report on Quantitative Approaches to Genotoxicity Risk Assessment I. Methods and Metrics for Defining Exposure-Response Relationships and Points of Departure (PoD),” Mutation Research. Genetic Toxicology and Environmental Mutagenesis, 783, 55–65. DOI: 10.1016/j.mrgentox.2014.09.011.
  • Nüesch, P. (1991), Order Restricted Statistical Inference, T. Robertson, F. T. Wright, R. L. Dykstra Wiley Series in Probability and Mathematical Statistics, Wiley, Chichester, 1988. pp. 488. J. Appl. Econ.,
  • Portier, C. J., and Bailer, A. J. (1989), “Testing for Increased Carcinogenicity Using a Survival-adjusted Quantal Response Test,” Fundamental and Applied Toxicology: Official Journal of the Society of Toxicology, 12, 731–737. DOI: 10.1016/0272-0590(89)90004-3.
  • Schaarschmidt, F., Sill, M., and Hothorn, L. (2008), “Approximate Simultaneous Confidence Intervals for Multiple Contrasts of Binomial Proportions,” Biometrical Journal, 10, 782–792. DOI: 10.1002/bimj.200710465.
  • Tarone, R. (1982), “The Use of Historical Control Information in Testing for a Trend in Poisson Means,” Biometrics, 38, 457–462. DOI: 10.2307/2530459.
  • Williams, D., Lazic, S., Foster, A., Semenova, E., and Morgan, P. (2020), “Predicting Drug-Induced Liver Injury with Bayesian Machine Learning,” Chemical Research in Toxicology, 239–248. DOI: 10.1021/acs.chemrestox.9b00264.

References for CMC Section

A. Parameter Criticality Identification

  • Atkinson, A., and Donev, A. (1992), Optimum Experimental Designs. Clarendon Press: Oxford
  • Box, G., Hunter, W. G., and Hunter, J. S. (2005), Statistics for Experimenters: Design, Innovation, and Discovery (2nd ed.), Hoboken, NJ: Wiley.
  • Burdick, R. K., Pfahler, L. B., Zhang, L., Quiroz, J., Vukovinsky, K., Leblond, D., and Sidor, L. (2017), Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry, Cham, Switzerland: Springer International Publishing.
  • Cochran, W. G., and Cox, G. M. (1957), Experimental Designs, New York: Wiley.
  • Fang, K.-T., Li, R., and Sudjianto, A. (2006), Design and Modeling for Computer Experiments, Boca Raton, FL: Chapman and Hall/CRC, Boca Raton.
  • Gramacy, R. B. (2020), Surrogates: Gaussian Process Modeling, Design, and Optimization for the Applied Sciences, Boca Raton, FL: Chapman and Hall/CRC.
  • Hakemeyer, C., McKnight, N., St. John, R., Meier, S., Trexler-Schmidt, M., Kelley, B., Zettl, F., Puskeiler, R., Kleinjans, A., Lim, F., and Wurth, C. (2016), “Process Characterization and Design Space Definition,” Biologicals: Journal of the International Association of Biological Standardization, 44, 306–318. DOI: 10.1016/j.biologicals.2016.06.004.
  • John, J. A., and Quenouille, M. H. (1977), Experiments: Design and Analysis. New York: Macmillan Publishing Co.
  • Lee, B. W., Peterson, J. J., Yin, K., Stockdale, G. S., Liu, Y. C., and O’Brien, A. (2020), “System Model Development and Computer Experiments for Continuous API Manufacturing,” Chemical Engineering Research and Design, 156, 495–506. DOI: 10.1016/j.cherd.2020.02.003.
  • Li, F., Evans, B., Liu, F., Zhang, J., Wang, K., and Cheng, A. (2018), “Removing Subjectivity from the Assessment of Critical Process Parameters and Their Impact,” Pharmaceutical Technology, 42, 46–54.
  • Otava, M., and Mylona, K. (2020), “Communicating Statistical Conclusions of Experiments to Scientists,” Quality and Reliability Engineering International, 36, 2688–2698. DOI: 10.1002/qre.2697.
  • Perry, L. A., Montgomery, D. C., and Fowler, J. W. (2001), “Partition Experimental Designs for Sequential Processes: Part I—First-Order Models,” Quality and Reliability Engineering International, 17, 429–443.
  • Plackett, R. L., and Burman, J. P. (1946), “The Design of Optimum Multifactorial Experiments,” Biometrika, 33, 305–325. DOI: 10.1093/biomet/33.4.305.
  • Santer, T. J., Williams, B. J., and Notz, W. I. (2003), The Design and Analysis of Computer Experiments, New York: Springer.
  • Wang, K., Ide, N. D., Dirat, O., Subashi, A. K., Thomson, N. K., Vukovinsky, K. E., and Watson, T. J. (2016), “Statistical Tools to Aid the Assessment of Critical Process Parameters,” Pharmaceutical Technology, 40, 36–44.

B. Quality by Design

  • Dispas, A., Avohou, H. T., Lebrun, P., Hubert, P., and Hubert, C. (2018), “‘Quality by Design’ Approach for the Analysis of Impurities in Pharmaceutical Drug Products and Drug Substances, TrAC Trends in Analytical Chemistry, 101, 24–33. DOI: 10.1016/j.trac.2017.10.028.
  • LeBrun, P., Boulanger, B., Debrus, B., Lambert, P., and Hubert, P. (2013), “A Bayesian Design Space for Analytical Methods Based on Multivariate Models and Predictions,” Journal of Biopharmaceutical Statistics, 23, 1330–1351. DOI: 10.1080/10543406.2013.834922.
  • Peterson, J. J. (2007), A Review of Bayesian Reliability Approaches to Multiple Response Surface Optimization. Chapter 10 in Bayesian Process Monitoring, Control, and Optimization, Colosimo, B. M. and Del Castillo, E., eds., New York: Chapman and Hall/CRC.
  • Peterson, J. J. (2008), “A Bayesian Approach to the ICH Q8 Definition of Design Space,” Journal of Biopharmaceutical Statistics, 18, 959–975.
  • Peterson, J. J., and Yahyah, M. (2009), “A Bayesian Design Space Approach to Robustness and System Suitability for Pharmaceutical Assays and Other Processes,” Statistics in Biopharmaceutical Research, 1, 441–449. DOI: 10.1198/sbr.2009.0037.
  • Peterson, J. J., and Lief, K. (2010), “The ICH Q8 Definition of Design Space: A Comparison of the Overlapping Means and the Bayesian Predictive Approaches,” Statistics in Biopharmaceutical Research, 2, 249–259. DOI: 10.1198/sbr.2009.08065.
  • Peterson, J. J. (2020), Process Development and Validation, Chapter 19 in Bayesian Methods in Pharmaceutical Research. Lasaffre, W., Baio, G., Boulanger, B., eds., New York: CRC Press.
  • Scherder, T., and Giacoletti, K. (2020), Bayesian Statistics for Manufacturing, Chapter 24 in Bayesian Methods in Pharmaceutical Research (1st ed.). Lesaffre, E., Baio, G., & Boulanger, B., eds., New York: CRC Press.
  • Berger, R., and Hsu, J. (1996), “Bioequivalence Trials, Intersection-Union Tests and Equivalence Confidence Intervals,” Statistical Science, 11, 283–319. DOI: 10.1214/ss/1032280304.
  • European Pharmacopoeia 6.0, General Chapter 5.3. Statistical Analysis of Results of Biological Assays and Tests, 01/2008:50300.
  • Faya, P., Rauk, A. P., Griffiths, K. L., and Parekh, B. (2020), “A Curve Similarity Approach to Parallelism Testing in Bioassay,” Journal of Biopharmaceutical Statistics, 30, 721–733. DOI: 10.1080/10543406.2020.1730875.
  • Hauk, W. W., Capen, R. C., Callahan, J. D., De Muth, J. E., Hsu, H., Lansky, D., Sajjadi, N. C., Seaver, S. S., Singer, R. R., and Weisman, D. (2005), “Assessing Parallelism Prior to Determining Relative Potency,” PDA J. Pharmaceutical Science & Technology, 59, 127–137.
  • Schofield, T. L. (2015), Nonclinical for Pharmaceutical and Biotechnology Industries, Chapter 17 in Lifecycle Approach to Bioassays. Zhang, L., Altan, S., eds., Springer, Cham: CRC Press.
  • Schuirmann, D. (1987), “A Comparison of the Two One-Sided Tests Procedure and the Power Approach for Assessing the Equivalence of Average Bioavailability,” Journal of Pharmacokinetics and Biopharmaceutics, 15, 657–680. DOI: 10.1007/BF01068419.
  • USP General Chapter <1032 > Design and Development of Biological Assays.
  • Yang, H. (2020), Emerging Non-Clinical Biostatistics in Biopharmaceutical Development and Manufacturing, New York: Chapman and Hall/CRC Press.

D. Stability

  • Altan, S., Manola, A., Shoung, J., and Shen, Y. (2013), “Perspectives on Pooling as Described in the ICH Q1E Guidance,” In JSM Proceedings, Biopharm Section. (pp. 1490–1496), Alexandria, VA: American Statistical Association.
  • Avohou, T. H., Lebrun, P., Rozet, E., and Boulanger, B. (2020), Bayesian Methods for the Design and Analysis of Stability Studies, Chapter 21 in Bayesian Methods in Pharmaceutical Research Lasaffre, w, Baio, G, Boulanger, B, eds. (2020), New York: CRC Press.
  • Bancroft, T. A. (1964), “Analysis and Inference for Incompletely Specified Models Including the Use of Preliminary Tests of Significance,” Biometrics, 20, 427–442. DOI: 10.2307/2528486.
  • Burdick, R., LeBlond, D., Pfahler, L., Quiroz, J., Sidor, L., Vukovinsky, K., and Zhang, L. (2017), Stability Chapter 8 in Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry.
  • Carlin, B. P., and Louis, T. A. (2009), Bayesian Methods for Data Analysis. Boca Raton, FL: CRC Press.
  • Chen, J. J., Hwang, J. S., and Tsong, Y. (1995), “Estimation of the Shelf-Life of Drugs with Mixed Effects Models,” Journal of Biopharmaceutical Statistics, 5, 131–140. DOI: 10.1080/10543409508835102.
  • Chow, S. C., and Shao, J. (1991), “Estimating Drug Shelf-Life with Random Batches,” Biometrics, 47, 1071–1079. DOI: 10.2307/2532659.
  • International Conference on Harmonization (2003), Evaluation for Stability Data Q1E, available at http://www.ich.org/fileadmin/Public_Web_Site/CH_Products/Guidelines/Quality/Q1E/Step4/Q1E_Guideline.pdf
  • Stroup, W. W., and Quinlan, M. (2016), “Statistical Considerations for Stability and the Estimation of Shelf Life,” Chapter 22 in Nonclinical Statistics for Pharmaceutical and Biotechnology Industries, Zhang, L., Kuhn, M., Peers, I. and Altan, S., eds., New York: Springer.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.