Transcript Induction and latency (J

Induction and latency
(J-F Boivin, March 2006)
1.
2.
3.
4.
Introduction
Rothman’s model of induction
Analysis: largest estimate methods
Modelling approaches
• Thomas 1983
• Rachet et al. 2003
Version: 22 February 2006
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.
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)
Rothman KJ.
Induction and latent periods.
American Journal of Epidemiology 1981
Point exposures
•
•
•
•
•
•
Atomic bombs
Food toxins
In utero exposures
Earthquake
Surgery
Vaccine
Point exposure, fixed induction period
Exposure
Disease
initiation
Disease
detection
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
Point exposure, fixed induction period
Exposure
Disease
initiation
Disease
detection
Induction
remaining component causes
in the etiologic sequence
contribute to the causal process
For any disease, at least one component cause, the last, will
have a very short (zero) induction period
Point exposure, fixed induction period
Exposure
Disease
initiation
Disease
detection
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
Point exposure, fixed induction period
Exposure
Disease
initiation
Disease
detection
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
Point exposure, fixed induction period
Exposure
Disease
initiation
Induction period
Disease
detection
Latent period
Empirical induction period
In practice, induction and latent period can rarely be
be separated
Point exposure, variable induction period
Exposure
Disease detection
12 yr
Empirical induction period (12 to 17 yr)
17 yr
Excess
incidence
0
Incidence
Exposed
Unexposed
Time
Analysis
Two simultaneous goals:
1. Estimate the mode of the distribution of
empirical induction periods
2. Estimate the effect of the exposure on
disease risk without bias due to
inappropriate assumption about induction
period
Principle
Measures of effect are reduced if an
inappropriate assumption is used for
the empirical induction period
(nondifferential misclassification)
In utero
DES
No
exposure
RR
1/10 000
1
0–9 yr
1/10 000
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
• 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
Limitation of largest estimate methods
(Rothman-Greenland 1998, pp. 298-299)
1.
Tend to pick out induction periods whose
estimate is large simply by virtue of large
statistical variability
2. Exposure misclassification may vary over
time, leading to distortions of patterns
of effect estimates across time windows
Example of inconsistent results
using single time windows
Richardson DB, Wing S.
International Journal of Epidemiology 1999
Limitation of largest estimate methods
(Rothman-Greenland 1998, pp. 298-299)
(several point exposures)
3. 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.
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
Multiple time-windows approach
Problem: numbers
Modelling
Thomas 1983
T
(RE-R0) (T) = b S 0d(t) f (T-t)
excess risk up to time T
T
(RE-R0) (T) = b S 0d(t) f (T-t)
excess risk caused by
unit dose
dose
T
(RE-R0) (T) = b S 0d(t) f (T-t)
dose at
time t
“weight” of the dose at time t
T
(RE-R0) (T) = b S 0d(t) f (T-t)
excess risk =
excess risk
per unit dose
weighted
dose
T
(RE-R0) (T) = b S 0d(t) f (T-t)
• Some functional form is assumed:
• Rothman’s approach (AJE 1981):
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
E+
10/10,000
55/10,000
100/10,000
E-
10/10,000
10/10,000
10/10,000
0
RE-R0
10
0
45/10,000
20
30 yr
90/10,000
E+
165/30,000 = 55/10,000
E-
30/30,000 = 10/10,000
0
RE-R0
=
RE-R0
=
10
20
45/10,000
(45/10,000) x 1
30
E+
10/10,000 155/20,000 = 77.5/10,000
E-
10/10,000
0
20/20,000 = 10/10,000
RE-R0
=
67.5/10,000
RE-R0
= (67.5/10,000) x 0
+ (67.5/10,000) x 1
E+
10/10,000
55/10,000
100/10,000
E-
10/10,000
10/10,000
10/10,000
RE-R0
RE-R0
0
45/10,000
= (90/10,000) x 0
+ (90/10,000) x 0.5
+ (90/10,000) x 1
90/10,000
Lundin et al. (1979)
Lung cancer in uranium miners
T
ER (T) = b  0 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 0.17609 log t units is assumed
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
Rachet et al.
Statistics in Medicine 2003
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.
Rachet et al.
• no strong a priori assumptions
• however: dichotomous point exposure
Rachet et al.
Overall hazard ratio (HR) represents
weighted average of
• HR1 = 1
• HR2 > 1
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 nonparametric 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.
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.