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Induction and latency (J-F Boivin, March 2006)

Induction and latency (J-F Boivin, March 2006). Introduction Rothman’s model of induction Analysis: largest estimate methods Modelling approaches Thomas 1983 Rachet et al. 2003. Version: 22 February 2006.

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Induction and latency (J-F Boivin, March 2006)

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  1. Induction and latency(J-F Boivin, March 2006) • Introduction • Rothman’s model of induction • Analysis: largest estimate methods • Modelling approaches • Thomas 1983 • Rachet et al. 2003 Version: 22 February 2006

  2. 19-year-old woman developed nausea, vomiting, salivation, and sweating soon after breakfast, and she was taken to a local hospital. She had a cardiorespiratory arrest but was successfully resuscitated. It was found that she had ingested the pesticide fonofos mistakenly used as flour in making the pancakes cooked for breakfast. Three other members of her family who ate the pancakes were also very sick and one died. At age 39, the woman developed a cancer of the liver and died.

  3. Causal inferences usually proceed without difficulty when cause and effect are close in time. When the interval between cause and effect is lengthy, however, the linkage between the two is more difficult to infer. (adapted from Rothman, 1981)

  4. Rothman KJ.Induction and latent periods. American Journal of Epidemiology 1981

  5. Point exposures • Atomic bombs • Food toxins • In utero exposures • Earthquake • Surgery • Vaccine

  6. Point exposure, fixed induction period Disease initiation Disease detection Exposure Induction period Diseases have several component causes, genetic and environmental: the complete induction period begins at conception of the fetus More useful to characterize induction periods in reference to specific component causes Induction period is not a fixed characteristic of the disease; varies according to component cause investigated

  7. Induction remaining component causes in the etiologic sequence contribute to the causal process Point exposure, fixed induction period Disease initiation Disease detection Exposure For any disease, at least one component cause, the last, will have a very short (zero) induction period

  8. Point exposure, fixed induction period Disease initiation Disease detection Exposure Latent period (= incubation) = Interval after disease initiation until disease is detected Could, in principle, be reduced to near zero with increasingly accurate means for detecting presymptomatic disease

  9. Point exposure, fixed induction period Disease initiation Disease detection Exposure Latent period Example: if cancer, once it reaches a certain critical point, is irreversible without therapy, it has a latent period that is distinct from the induction period Counter-example: if some infectious process can in principle be overcome by the host’s defenses until it becomes clinically manifest, there is no latent period

  10. Empirical induction period Point exposure, fixed induction period Disease initiation Disease detection Exposure Induction period Latent period In practice, induction and latent period can rarely be be separated

  11. Exposure Disease detection 17 yr 12 yr Empirical induction period (12 to 17 yr) Point exposure, variable induction period

  12. Excess incidence 0

  13. Exposed Incidence Unexposed Time

  14. Analysis Two simultaneous goals: • Estimate the mode of the distribution of empirical induction periods • Estimate the effect of the exposure on disease risk without bias due to inappropriate assumption about induction period

  15. Principle Measures of effect are reduced if an inappropriate assumption is used for the empirical induction period (nondifferential misclassification)

  16. 10–19 yr 1/10 000 1/10 000 1 20–29 yr 1 000/10 000 1/10 000 1000 all yr 1 002/30 000 3/30 000 334 In utero DES No exposure RR 0–9 yr 1/10 000 1/10 000 1

  17. Estimate the measure of association repeatedly with different assumptions about the induction period • The maximum point estimate of the measure of association corresponds to the most appropriate assumption about induction period and simultaneously offers an estimate of the maximum effect relatively unobscured by an inappropriate assumption

  18. Limitation of largest estimate methods(Rothman-Greenland 1998, pp. 298-299) • Tend to pick out induction periods whose estimate is large simply by virtue of large statistical variability • Exposure misclassification may vary over time, leading to distortions of patterns of effect estimates across time windows

  19. Example of inconsistent results using single time windows Richardson DB, Wing S. International Journal of Epidemiology 1999

  20. Limitation of largest estimate methods(Rothman-Greenland 1998, pp. 298-299)(several point exposures) • Some exposure effects may have long and variable induction times. Separate analyses of restricted time windows do not control for effects in other time windows. Such multiple effects would often lead to mutual confounding among the estimates using just one window at a time.

  21. Alternative approach Estimate the effects for each time window while adjusting for the exposures from other windows Sharpe et al. British Journal of Cancer 2002

  22. Multiple time-windows approach Problem: numbers

  23. Modelling Thomas 1983

  24. S (RE-R0) (T) = b T d(t) f (T-t) 0 excess risk up to time T

  25. S (RE-R0) (T) = b T d(t) f (T-t) 0 excess risk caused by unit dose

  26. S (RE-R0) (T) = b T d(t) f (T-t) 0 dose at time t “weight” of the dose at time t dose

  27. S (RE-R0) (T) = b T d(t) f (T-t) 0 excess risk per unit dose weighted dose excess risk =

  28. Some functional form is assumed: S (RE-R0) (T) = b T d(t) f (T-t) • Rothman’s approach (AJE 1981): 0 weight is 1 between times a and b 0 at other times DES example f = 1 between ages 20 and 29 f = 0 at other times a and b determined by trial and error

  29. E+ 10/10,000 55/10,000 100/10,000 E- 10/10,000 10/10,000 10/10,000 0 10 20 30 yr RE-R0 0 45/10,000 90/10,000

  30. 165/30,000 = 55/10,000 30/30,000 = 10/10,000 0 10 20 30 RE-R0 = 45/10,000 RE-R0 = (45/10,000) x 1

  31. RE-R0 = (67.5/10,000) x 0 + (67.5/10,000) x 1 10/10,000 155/20,000 = 77.5/10,000 10/10,000 20/20,000 = 10/10,000 RE-R0 = 0 67.5/10,000

  32. RE-R0 = (90/10,000) x 0 RE-R0 0 45/10,000 90/10,000 + (90/10,000) x 0.5 + (90/10,000) x 1 E+ 10/10,000 55/10,000 100/10,000 E- 10/10,000 10/10,000 10/10,000

  33. Lundin et al. (1979) Lung cancer in uranium miners f: assumed to be log normal (based on leukemia risk after single exposure to radiation and an incubation period for infectious diseases)  T d(t) f (T-t) dt ER (T) = b 0 Values of 5, 10, 15 yr for induction period are fitted Standard deviation of 0.17609 log t units is assumed

  34. Complexities of modelling • Relevant exposure may be a complex function of the intensity of the exposure and time (Rothman-Greenland, p. 83) • Influence of intensity • Influence of age at exposure • atomic bomb survivors

  35. Rachet et al. Statistics in Medicine 2003

  36. Limitation of Thomas’ approach Requires selecting a limited set of a priori parametric models for change in risks, such as the log-normal, piecewise constant, bilinear, etc. However, discriminating between alternative parametric models may be difficult.

  37. Rachet et al. • no strong a priori assumptions • however: dichotomous point exposure

  38. Rachet et al. Overall hazard ratio (HR) represents weighted average of • HR1 = 1 • HR2 > 1

  39. References Land CE, Tokunaja M. Induction period. In: Boice JD Jr, Faumeni JF Jr, eds. Radiation carcinogenesis. Epidemiology and biological significance. Progress in cancer research and therapy. Volume 26. New York: Raven Press. 1984. Pages 421-436. Lundin FE, et al. An exposure-time-response model for lung cancer mortality in uranium miners: Effects of radiation exposure, age, and cigarette smoking. In: Energy and health. Breslow NE, Whittermore AS, eds. Philadelphia: Society for industrial and applied mathematics. 1979. Rachet B, et al. Estimating the distribution of lag in the effect of short-term exposures and interventions: adaptation of a non-parametric regression spline model. Statistics in Medicine 2003; 22: 2335-2363. Richardson DB, Wing S. Greater sensitivity to ionizing radiation at older age: follow-up of workers at Oak Ridge National Laboratory through 1990. International Journal of Epidemiology 1999; 28: 428-436.

  40. Rothman KJ. Induction and latent periods. American Journal of Epidemiology 1981; 114:253-259. Rothman KJ, Greenland S. Modern epidemiology. Second edition. Pages 14, 15, 82-84, 297-300. Thomas DC. Statistical methods for analyzing effects of temporal patterns of exposure on cancer risks. Scandinavian Journal of Work and Environmental Health 1983; 9:353-366. Thomas DC. Models for exposure time-response relationships with applications to cancer epidemiology. Annual Reviews of Public Health 1988; 9:451-482. Sharpe CR, et al. The effects of tricyclic antidepressants on breast cancer risk. British Journal of Cancer 2002; 86: 92-97.

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