RE: "ESTIMATING THE RELATIVE RISK IN COHORT STUDIES AND CLINICAL TRIALS OF COMMON OUTCOMES"

Peter Cummings

Department of Epidemiology, School of Public Health and Community Medicine, University of Washington, Seattle, WA 98195

McNutt et al. (1) recently pointed out that Poisson regression can be used to estimate adjusted risk ratios from cumulative incidence cohort data. Although other investigators have made the same point (25), this use of Poisson regression is not widely known. In addition, McNutt et al. provided a useful comparison of several methods and gave valuable information about confidence intervals (1).

In cohort studies, researchers sometimes match exposed and unexposed subjects on certain characteristics that may be potential confounders—studies of twins (6), for example. Data from such studies are sometimes analyzed using conditional logistic regression. With this method, investigators can estimate odds ratios using information only from matched sets with a subject who had the study outcome. However, if the outcome is common, the resulting odds ratios may not closely approximate risk ratios (7).

Adjusted risk ratios, rather than odds ratios, can be estimated in matched cohort data using commercially available software. Information is needed only from the matched sets in which one or more members had the study outcome. One method is conditional Poisson regression (5, 810), which is implemented in Stata software (11). For matched-pair data, the Cox proportional hazards model can be used if follow-up time is the same for all subjects, the regression analysis is stratified on the pairs, and the Breslow or Efron method is used to account for the tied survival times; the likelihood is the same as the conditional Poisson likelihood (12, 13). (Breaking the tied survival times with the exact marginal or exact partial likelihoods will permit estimation of the odds ratio; the likelihood is the same as the conditional logistic likelihood.) My colleagues and I have reported that the 95 percent confidence intervals estimated with these methods cover approximately 98 percent of simulated risk ratio estimates (12), which is similar to the findings of McNutt et al. for unmatched data. Bootstrap methods can be used if more accurate confidence intervals are desired. These methods have been used in studies of traffic crashes, since persons involved in such crashes can be thought of as matched when they are in the same vehicle (1416).

REFERENCES

  1. McNutt LA, Wu C, Xue X, et al. Estimating the relative risk in cohort studies and clinical trials of common outcomes. Am J Epidemiol 2003;157:940–3.[Abstract/Free Full Text]
  2. Gourieroux C, Monfort A, Tognon C. Pseudo-maximum likelihood methods: theory. Econometrica 1984;52:681–700.[ISI]
  3. Gourieroux C, Monfort A, Tognon C. Pseudo-maximum likelihood methods: applications to Poisson models. Econometrica 1984;52:701–20.[ISI]
  4. Lloyd CJ. Statistical analysis of categorical data. New York, NY: John Wiley and Sons, Inc, 1999:84–7.
  5. Wooldridge JM. Econometric analysis of cross section and panel data. Cambridge, MA: The MIT Press, 2002:646–9, 674–6.
  6. Lynskey MT, Heath AC, Bucholz KK, et al. Escalation of drug use in early-onset cannabis users vs co-twin controls. JAMA 2003;289:427–33.[Abstract/Free Full Text]
  7. Cummings P. Early exposure to marijuana and risk of later drug use. (Letter). JAMA 2003;290:329.[Free Full Text]
  8. Hausman JA, Hall BH, Griliches Z. Econometric models for count data with an application to the patents-R&D relationship. Econometrica 1984;52:909–38.[ISI]
  9. Farrington CP. Relative incidence estimation from case series for vaccine safety evaluation. Biometrics 1995;51:228–35.[ISI][Medline]
  10. Cameron AC, Trivedi PK. Regression analysis of count data. New York, NY: Cambridge University Press, 1998:282–3.
  11. Stata Corporation. Stata statistical software, release 8.0. College Station, TX: Stata Corporation, 2003.
  12. Cummings P, McKnight B, Weiss NS. Matched-pair cohort methods in traffic crash research. Accid Anal Prev 2003;35:131–41.[CrossRef][ISI][Medline]
  13. Cummings P, McKnight B, Greenland S. Matched cohort methods in injury research. Epidemiol Rev 2003;25:43–50.[Free Full Text]
  14. Cummings P, McKnight B, Rivara FP, et al. Association of driver air bags with driver fatality: a matched cohort study. BMJ 2002;324:1119–22.[Abstract/Free Full Text]
  15. Norvell DC, Cummings P. Association of helmet use with death in motorcycle crashes: a matched-pair cohort study. Am J Epidemiol 2002;156:483–7.[Abstract/Free Full Text]
  16. Cummings P, Wells JD, Rivara FP. Estimating seat belt effectiveness using matched-pair cohort methods. Accid Anal Prev 2003;35:143–9.[CrossRef][ISI][Medline]




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