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: 28 February 2006 (abbreviated)

2. Point exposures

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

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

5. Excess
incidence

6. Incidence
Time
Exposed
Unexposed

7. 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

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

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

10. 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

11. Limitation of largest estimate methods (Rothman-Greenland 1998, pp

15. 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

18. Multiple time-windows approach
Problem:

19. Modelling
Thomas 1983

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

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

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

23. E+
10/10,000
55/10,000
100/10,000 E-
10/10,000
10/10,000
10/10,000 yr
RE-R0
45/10,000
90/10,000

24. E+ E-
165/30,000 = 55/10,000
30/30,000 = 10/10,000
RE-R = /10,000
RE-R = (45/10,000) x 1

25. E+ E-
10/10,000
155/20,000 = 77.5/10,000
10/10,000
20/20,000 = 10/10,000
RE-R = /10,000
RE-R = (67.5/10,000) x 0
+ (67.5/10,000) x 1

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

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

28. 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

30. Rachet et al.
Statistics in Medicine 2003

31. Limitation of Thomas’ approach

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

33. Rachet et al. Overall hazard ratio (HR) represents weighted average of