Shyamal D. Peddada Biostatistics Branch National Inst. Environmental

1. Incorporating Historical Control Data when Comparing Tumor Incidence Rates in Rodent Cancer Bioassay Shyamal D. PeddadaBiostatistics Branch National Inst. Environmental Health Sciences (NIH)Research Triangle Park, NC

2. Outline of the talk • The National Toxicology Program (NTP). • NTP’s 2-year rodent cancer bioassay. • Study design. • A motivating example. • Questions of interest. • Brief review of some existing methods and the current practice. • Proposed methodology. • Illustration. • Concluding remarks.

3. The National Toxicology Program (NTP) • Established in 1978 (became permanent in 1981) • One of the responsibilities of NTP is to provide information about potentially toxic chemicals. • Humans are exposed to a large collection of chemicals some of which can cause cancer. • So far NTP has evaluated nearly 550 chemicals.

4. Study design (NTP) • Species: Rats and Mice • Sex: Males and Females • Number of dose groups for a given chemical: • Control, Low, Medium and High • Number of animals per dose group: 50 • Duration of study: 2 years • Variable of interest: Tumor incidence in various organs

5. 2-Butoxyethanol (TR-484): Male Mice. Hepatocellular Carcinoma Route of exposure to the chemical: Inhalation.

6. 2-Butoxyethanol (TR-484): Male Mice. Hepatocellular Carcinoma The P-value using NTP’s trend test: 0.002. Question: Does this suggest a dose-related trend in the incidence of hepetaocellular carcinoma? Question: Is the chemical potentially carcinogenic?

7. NTP’s decision • NTP not only relies on the p-value from the current data, but also uses other information in making decisions. • E.g. • Any pre-cursors to the given tumor? • Tumor incidence in the other sex and species? • Mechanism/mode of action? • Historically how often was the specific tumor seen? • Other tumors? Etc.

8. Historical control data • NTP maintains a database of control animals from each study by sex and species.

9. (Statistical) problem • How to incorporate historical control (HC) data in evaluating the current experimental data for a given tumor? • Should HC be used at all? If so, what are the conditions/circumstances? • How to use the information?

10. Historical control data – heterogeneity among control groups • Potential genetic drift over time. • Differences among pathologists over time. • Differences between sexes and species. • Route of exposure to a chemical • Inhalation • Feed • Water • Subcutaneous • Dermal • Diet used (NIH-07, NTP 2000) • Etc.

11. NTP’s general strategy • Select suitable controls from the HC database. Match the HC data with the current data by • sex and species • route of chemical exposure (i.e. feed study or inhalation study etc.) • study period (most recent to the current study – 5 year sliding window). • Obtain the range of tumor incidence in the selected control groups. • This range is used by the NTP for making decisions.

12. 2-Butoxyethanol (TR-484): Male Mice. Hepatocellular Carcinoma Observed relative frequency of tumors: 10/50, 11/50, 16/50, 21/50 NTP’s trend test: P = 0.002 Historical range: 11% to 48% (mean = 25.7%, sd = 10.4%) The current data are within the historical range ! - Therefore NTP classified this neoplasm under “uncertain finding”.

13. 2-Butoxyethanol (TR-484): Forestomach squamous cell papillomas (Male mice) • Tumor rates: 1/50, 1/50, 2/50, 2/50 • P-value > 0.05 - Not significant. • Historical range: 0% to 2% (mean = 0.5%, sd = 0.9%) • Female mice: 0/50, 1/50, 2/50, 5/50 • P –value for trend = 0.008.

14. 2-Butoxyethanol (TR-484): (0, 62.5, 125, 250 ppm) Notes: • This is a rare tumor according to the HC database. • Although it is rare, 5/150 dosed male mice had this tumor. • A significant trend is seen in female mice. NTP classified this tumor as an “uncertain finding”.

15. Question Can a formal statistical procedure be developed to incorporate historical control data when analyzing “current data”?

16. Tarone (1982)Beta-binomial model Data from “current” study Number of animals per dose group = The subscript c stands for “current” study.

17. Tarone (1982) • = Number of historical control groups • = Number of tumors in the j-th historical control group • are assumed to be binomial random variables with binomial probability • are assumed to i.i.d. beta distributed. This is in attempt allow for extra binomial variation between studies.

18. The hypotheses versus Here denotes the tumor “rate” in dose group i in the current study (denoted by c).

19. An important feature of the data • Not all animals survive until the end of the study. • Consequently, the binomial parameter is not a suitable parameter to study. • This parameter represents life time risk of developing tumors and not tumor incidence!

20. An example • Control : All n = 50 survive until the end of the study (i.e. 2 years) and Y = 5 develop tumors. • High dose: 30 animals die within the first 6 months. Of the remaining 20, Y = 2 develop tumors. • Should we compare 5/50 vs 2/50 Or is it 5/50 vs 2/20?

21. Other methods • The following take a more direct approach by studying tumor incidence rather than life-time risk of developing tumors: • Ibrahim and Ryan (1996). Applicable if a tumor is known to be instantly lethal. • Ibrahim et al (1998). Applicable if a tumor is known to be non-lethal. • Dinse and Dunson (2001). A general Bayesian approach. Not very convenient to apply in practice.

22. NTP Board of Scientific Councilors recommendation (2005) • None of the existing methods are endorsed by the NTP and in the 2005 meeting of the NTP Board of Scientific Councilors they recommended the development of a formal statistical procedure to incorporate historical control data. • http://ntp.niehs.nih.gov/files/TRRSMins0905.pdf (page 10)

23. Some notations and background: Analysis of “current” data

24. Poly-3 methodology(Bailer and Portier, 1988) • Estimation of tumor incidence requires more data, e.g. interim animal sacrifice, or more assumptions. • Interim sacrifices are expensive. • NTP developed tests based on hypothesis regarding life time tumor rates but adjust estimates to account for animal survival. • The resulting test procedure seems to perform well even for testing hypothesis on the tumor incidence.

25. Notations Bailer and Portier (1988, Biometrics): • : Length of the study (current study) • : Number of days the j-th animal survived. • if the j-th animal in the i-th dose in the current study has a tumor. It is 0 otherwise.

26. Sample size correction for survival data • if tumor present before death or . otherwise: • Then effective sample size for the i-th group is:

27. NTP’s Poly-3 test • Poly-3 survival adjust tumor rate for the i-th dose group in the current study is given by: Using these estimates the NTP constructed the well-known Cochran-Armitage trend test. This is the Poly-3 test.

28. New test for trend (in “current” data): Basic idea • The classical Cochran-Armitage (CA) trend test is ideal for linear trend in dose-response. • The order-restricted inference based procedures work well for monotone responses that are not necessarily linear. • The trend test proposed in Peddada et al. (2005, 2006) is the maximum of tests 1 and 2. Thus this procedure works well for linear as well as non-linear, but monotonic responses.

29. Notations • Let

30. Modified Cochran-Armitage trend test for NTP data

31. Williams’ type test for NTP data • Let

32. Test for trend in the current data • Peddada, et al. (2005, 2006) • As good as Cochran-Armitage trend test for linear response. • Maintains good power for non-linear but monotone response.

33. Analysis of “current” data making use of historical control data

34. Data • Number of historical controls = k • Number of animals in the m-th historical control group: • Tumor status of the j-th animal in the control group:

35. Data • Number of animals with tumors in the control group: • Total number of animals with tumor among all historical controls

36. Basic ideas • The current and all historical controls are random realizations from a population of control animals. • If no animals die before the end of the study then we assume:

37. Basic ideas • The proposed test statistic has two components: • As in Peddada et al. (2005, 2006) compare the dose groups from the current study with the current control group by computing: • Similarly, compare the dose groups from the current study with the historical control group by computing:

38. Basic ideas • The two terms are analogous to respectively, except that they account for the “between controls” variability term, i.e.,

39. Proposed test • Thus the proposed test statistic is then given by: • Approximate null distribution of the above statistic can be derived very easily as follows:

40. Null distribution • Let • Similarly are isotonized values of

41. Null distribution • Then the null distribution of the proposed test is approximated by the distribution of

42. Back to the NTP examples

43. 2-Butoxyethanol (TR-484): Male Mice. Hepatocellular Carcinoma Observed relative frequency of tumors: 10/50, 11/50, 16/50, 21/50 NTP’s trend test: P = 0.002 Historical range: 11% to 48% (mean = 25.7%, sd = 10.4%) The current data are within the historical range ! - Therefore NTP classified this neoplasm under “uncertain finding”.

44. 2-Butoxyethanol (TR-484): Forestomach squamous cell papillomas (Male mice) • Tumor rates: 1/50, 1/50, 2/50, 2/50 • P-value > 0.05 - Not significant. • Historical range: 0% to 2% (mean = 0.5%, sd = 0.9%) • Female mice: 0/50, 1/50, 2/50, 5/50 • P –value for trend = 0.008.

45. 2-Butoxyethanol (TR-484): (0, 62.5, 125, 250 ppm) Hepatocellular Carcinoma P-value based on the new historical control test: 0.0024 Forestomach squamous cell papillomas P-value based on the new historical control test: 0.003

46. 2-Butoxyethanol (TR-484): (0, 62.5, 125, 250 ppm) NTP: “There was some evidence of carcinogenic activity of 2-Butoxyethanol in male B6C3F1 mice… based on Hemangiosarcoma of liver … A marginal increase in the forestomach squamous cell papilloma and an increase in the incidence of hepatocellular carcinoma may have been exposure related.”

47. Simulation study

48. Simulation experiment • As usually done, we generated independent Weibull random variables for (a) Tumor incidence and (b) Mortality. • Weibull parameters were chosen so that the data “resemble” some of the commonly seen patterns in NTP studies. • Dose effect on mortality: None, Moderate. • Background tumor rate: .001 (rare tumor), .01, .05, .15, .30 (common tumor) • Heterogeneity of historical control groups: Low, Medium and High. • Tumor incidence shape parameter: 1.5, 3 and 6 • Tumor incidence ratio patterns: 5 different non-null patterns and 1 null pattern. • Total number of non-null patterns = 450. • Total number of null patterns = 90. • Each simulation was based on 10000 samples.