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Recent Research Projects by the FDA’s Pharmacology and Toxicology Statistics Team

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Nonclinical Statistics for Pharmaceutical and Biotechnology Industries

Part of the book series: Statistics for Biology and Health ((SBH))

Abstract

In addition to regular review work, the Pharmacology and Toxicology Statistics Team in CDER/FDA is actively engaged in a number of research projects. In this chapter we summarize some of our recent investigations and findings.

We have conducted a simulation study (discussed in Sect. 12.2) to evaluate the increase in Type 2 error attributable to the adoption by some non-statistical scientists within the agency of more stringent decision criteria than those we have recommended for the determination of statistically significant carcinogenicity findings in long term rodent bioassays. In many cases, the probability of a Type 2 error is inflated by a factor of 1. 5 or more.

A second simulation study (Sect. 12.3) has found that both the Type 1 and Type 2 error rates are highly sensitive to experimental design. In particular, designs using a dual vehicle control group are more powerful than designs using the same number of animals but a single vehicle control group, but this increase in power comes at the expense of a greatly inflated Type 1 error rate.

Since the column totals of the tables of permutations of animals to treatment groups cannot be presumed to be fixed, the exact methods used in the Cochran-Armitage test are not applicable to the poly-k test for trend. Section 12.4 presents simple examples showing all possible permutations of animals, and procedures for computing the probabilities of the individual permutations to obtain the exact p-values. Section 12.5 builds on this by proposing an exact ratio poly-k test method using samples of possible permutations of animals. The proposed ratio poly-k test does not assume fixed column sums and uses the procedure in Bieler and Williams (Biometrics 49(3):793–801, 1993) to obtain the null variance estimate of the adjusted quantal tumor response estimate. Results of simulations show that the modified exact poly-3 method has similar sizes and levels of power compared to the method proposed in Mancuso et al. (Biometrics 58:403–412, 2002) that also uses samples of permutations but uses the binomial null variance estimate of the adjusted response rates and is based on the assumption of fixed column sums.

Bayesians attempt to model not only the statistical data generating process as in the frequentist statistics, but also to model knowledge about the parameters governing that process. Section 12.6 includes a short review of possible reasons for adopting a Bayesian approach, and examples of survival and carcinogenicity analyses.

The article reflects the views of the authors and should not be construed to represent FDA’s views or policies.

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Notes

  1. 1.

    Although this tendency is not absolute. See the discussion in footnote 8 on page 37.

  2. 2.

    The NTP partition divides the 104 week study into the following subintervals: 0–52 weeks, 53–78 weeks, 79–92 weeks, 93–104 weeks, and terminal sacrifice.

  3. 3.

    It becomes more complicated in the evaluation of conservativeness or anti-conservativeness of the joint test (simultaneous combination of the trend test and the pairwise comparison test) under the agency practice. This is so because the two tests are not independent since the pairwise comparison tests used a subset (a half) of the data used in the trend test. Theoretically, if the trend test and the pairwise comparison test are actually independent and are tested at 0.005 and 0.01 levels of significance, respectively for the effect of a common tumor type, then the nominal level of significance of the joint tests should be 0. 005 × 0. 010 = 0. 00005. Some of the levels of attained Type I error of the joint tests are larger than 0. 00005 due to the dependence of the two tests that were applied simultaneously. To evaluate this nominal rate directly would require estimation of the association between the two tests. Results of the simulation study, as expected, show that the attained levels of type I error (1-retention probability under the simulation conditions in which there is no drug effect on tumor prevalence) are smaller than those of the trend test alone.

  4. 4.

    See, for instance, the discussion of osteosarcomas and osteomas in female mice in Center for Drug Evaluation and Research (2103).

  5. 5.

    This calculation assumes that all endpoints are independent. This assumption is not strictly true, especially when considering combinations of endpoints. However, it is reasonable to assume that the endpoints are close enough to being independent that the resulting estimate of the GFPR is accurate enough for our purposes.

  6. 6.

    In fact, if four independent experiments are to have a combined study-wise false positive rate of 10 %, then it suffices for them individually to have GFPRs of \(1 - (1 - 0.1)^{1/4} = 0.026\). However, since it is not practical to calibrate the GFPR so precisely, there is no practical distinction between target GFPRs of 0. 025 and 0. 026.

  7. 7.

    More sophisticated models might treat \(\mathcal{T}\) as higher dimensional. For example, in the simulation study in Sect. 12.2, the parameter space \(\mathcal{T}\) is two dimensional, with the two dimensions representing the background prevalence rate and the tumor onset time. (Although Eq. (12.1) has three independent parameters (not counting the dose response parameter D), the parameters A and B are not varied independently—see Table 12.3.)

  8. 8.

    It is a familiar result for asymptotic tests that simply increasing the sample size improves power while maintaining the Type 1 error rate at the nominal level. (This principle also applies to rare event data except that exact tests are frequently over-conservative, meaning that increases in the sample size can actually increase the Type 1 error rate even while keeping the rate below the nominal level, and that power can sometimes decrease as the sample size increases—see Chernick and Liu 2002). However, the inclusion of large numbers of extra animals is an inelegant (and expensive) way to shift the ROC curve; we are interested in modifications to the experimental design that leave the overall number of animals unchanged.

  9. 9.

    The observation that the trend tests is strongly over-conservative for rare tumors is not at odds with the finding in Dinse (1985) that the trend test is not over-conservative for tumors with a background prevalence rate of 5 or 20 %. As the expected number of tumors increases, one expects exact tests to converge to the asymptotic tests, and the LFPRs to converge to the nominal value of α.

  10. 10.

    For this reason, the converse effect is of much less concern; misclassification of rare tumors as common is positively associated with large p-values so the cases where misclassification occurs are unlikely to be significant at even the rare tumor thresholds.

  11. 11.

    The actual nominal value of the joint test is hard to evaluate. See footnote 3 on page 27.

  12. 12.

    Although it is to be hoped that in the longer term the use of the SEND data standard (Clinical Data Interchange Standards Consortium (CDISC) 2011) will enable the more efficient construction of large historical control databases.

  13. 13.

    For computational reasons, these calculations use the lifetime tumor incidence rate rather than the background prevalence rate used elsewhere in this chapter.

  14. 14.

    Insofar as we know what is typical. These spectra should only be taken to represent a range of plausible scenarios, and not assumed to be in any way definitive.

  15. 15.

    Portier et al. (1986) recommends k = 3, although other values have been investigated (Gebregziabher and Hoel 2009; Moon et al. 2003). However, as noted in Gebregziabher and Hoel (2009), it appears that the tests are largely insensitive to the choice of k.

  16. 16.

    For this reason it is often called a semiparametric model.

  17. 17.

    It is interesting to note that this model implies that the odds of tumorigenesis are proportional to \(t_{j}^{\gamma _{i}}\), which (when the probability of tumorigenesis is low) is essentially equivalent to the poly-k assumption discussed elsewhere in this chapter.

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Acknowledgements

The authors would like to acknowledge the support of Yi Tsong, the director of Division of Biometrics 6, in FDA/CDER/OTS/OB, while researching the work contained in this chapter.

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Authors and Affiliations

  1. Office of Translational Sciences, Office of Biostatistics, Division of Biometrics 6, US Food and Drug Administration, Center for Drug Evaluation and Research, Silver Spring, MD, USA

    Karl K. Lin, Min Min, Mohammad Atiar Rahman & Steven F. Thomson

  2. Formerly of FDA/CDER/OTS/OB/DB6, Silver Spring, MD, USA

    Matthew T. Jackson

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  1. Karl K. Lin
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Correspondence to Karl K. Lin .

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  1. Nonclinical Statistics, Abbvie Inc, North Chicago, Illinois, USA

    Lanju Zhang

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Lin, K.K., Jackson, M.T., Min, M., Rahman, M.A., Thomson, S.F. (2016). Recent Research Projects by the FDA’s Pharmacology and Toxicology Statistics Team. In: Zhang, L. (eds) Nonclinical Statistics for Pharmaceutical and Biotechnology Industries. Statistics for Biology and Health. Springer, Cham. https://doi.org/10.1007/978-3-319-23558-5_12

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