1. How to compute CI’s – standard approach vs floating absolute risk GCRC Breakfast Workshop Series January 16, 2004 Patrick G. Arbogast Dept. of Biostatistics

2. Motivation Recently, collaborators from Million Women Study published investigation of HRT & breast cancer risk (Lancet, 2003). HR’s of incident & fatal breast cancer by HRT use were estimated from Cox regression models.

3. Motivation – cont’d When HRT use was expressed as 3+ groups (eg, never, past, current users), CI’s were computed using “floating absolute risks” (FAR’s). According to article, FAR method does not alter estimated HR’s but produces SE’s and CI’s allowing valid comparisons between any two HRT groups, even if neither is baseline group.

4. Floating absolute risk Originally proposed by Easton et al. for survival and case-control analyses (Stat Med, 1991). Width of CI’s from FAR method for HR’s & OR’s were consistently narrower than standard approach. Peto (letter) stated that floating CI’s should be used in place of standard CI’s (Lancet, 1997).

5. Controversy Greenland et al. (commentary) stated that FAR method does not yield valid CI’s for HR’s (Am J Epi, 1999). Claimed it can be proven mathematically that 95% CI from FAR method will not cover any parameter with 95% frequency. Also, does not make sense for fixed reference HR of 1.0 to have a CI. In addition, standard CI’s are asymptotically efficient & any intervals that are consistently narrower are invalid.

6. Rebuttal Easton et al. claimed that FAR CI’s are not directly CI’s for HR’s (Am J Epi, 2000). However, this is how FAR method has been applied in several studies, including recent HRT study. Easton et al. stated that point of FAR method is to allow computation of CI’s for HR’s for any pair of categories.

7. Proposal Clearly, there is controversy regarding FAR method. However, there has been no direct comparison of FAR method to standard approach. OBJECTIVE: Conduct simulation study comparing FAR method to standard approach.

8. Simulation study – part 1 Mimick study Easton et al. used to illustrate FAR method. Prognostic factors in 333 small-cell lung cancer patients. Relate performance status, WHO 5-pt scale, to time-of-death via Cox regression.

9. Simulation details Generated 1000 samples of 300 persons. Performance status & time-to-death simulated to mimic frequency & HR’s reported by Easton et al. For each sample, Cox model fit, HR and 95% CI’s computed using standard approach and FAR method.

10. Evaluation Mean SE of log(HR)’s computed for each method (avg SE from 1000 sim samples). Mean SE’s compared to SE estimate (SEE) (SE of 1000 log(HR)’s). Mean SE should approximate SEE. Coverage probabilities, proportion of 95% CI’s including true HR, computed for each method.

11. Simulation – lung cancer StandardFAR PSFreqHRSEEMean SE CPMean SE CP 013%1.0 151%1.930.240.2295%0.1059% 222%4.150.270.2694%0.1469% 311%5.310.310.3093%0.2180% 43%5.060.540.4994%0.4388% PS=performance status, CP=coverage probability.

12. Simulation study – part 2 Mimic HRT and breast cancer study. HRT use & time-to-breast cancer generated according to frequency & HR’s reported in article. HRT study included >800,000 patients. Due to computational considerations, samples of 1000 patients were generated.

13. Simulation – HRT & invasive breast cancer StandardFAR HRT use FreqHRSEEMean SE CPMean SE CP Never49%1.0 Cur36%1.660.08 93%0.0684% Last <5 yrs 10%1.040.13 95%0.1292% Last 5- 9 yrs 4%1.010.19 95%0.1994% Last 10+yrs 2%0.900.430.4093%0.3993%

14. Simulation – HRT & fatal breast cancer StandardFAR HRT use FreqHRSEEMean SE CPMean SE CP Never47%1.0 Cur34%1.220.08 94%0.0686% Past18%1.050.10 95%0.0891%

15. Conclusions FAR CI’s for HR’s can substantially underestimate the width of CI’s. Standard analyses provide correct CI’s for HR’s even when comparing two categories in which neither is reference group. Detailed manuscript submitted to Stat Med.

16. References Easton D, Peto J. Re: “Presenting statistical uncertainty in trends in dose-response relations”. Am J Epidemiol 2000; 152(4): 393-394. Easton EF, Peto J, Babiker AGAG. Floating absolute risk: an alternative to relative risk in survival and case-control analysis avoiding an arbitrary reference group. Stat Med 1991; 10: 1025-1035. Million Women Study Collaborators. Breast cancer and hormone-replacement therapy in the Million Women Study. Lancet 2003; 362: 419-427. Greenland S, Michels KB, Robins JM, Poole C, Willett WC. Presenting statistical uncertainty in trends and dose-response relations. Am J Epidemiol 1999; 149(12): 1077-1086.. Peto R. Birthweight as risk factor for breast cancer. Lancet 1997; 349: 501. Vincent MD, Ashley SE, Smith IE. Prognostic factors in small cell lung cancer: a simple prognostic index is better than conventional staging. Europ J Cancer & Clin Oncology 1987; 23: 1598-1599.