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

1. Introduction2. Rothman’s model of induction3. Analysis: largest estimate

methods4. 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

Diseaseinitiation

Diseasedetection

Induction period

Diseases have several component causes, genetic and environmental: the complete induction period begins at conception of the fetusMore 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

Diseaseinitiation

Diseasedetection

For any disease, at least one component cause, the last, will have a very short (zero) induction period

Induction

remaining component causesin the etiologic sequence contribute to the causal process

Point exposure, fixed induction period

Exposure

Diseaseinitiation

Diseasedetection

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

Diseaseinitiation

Diseasedetection

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

Diseaseinitiation

Diseasedetection

Latent period

In practice, induction and latent period can rarely bebe separated

Induction period

Empirical induction period

Exposure

Point exposure, variable induction period

Exposure Disease detection

12 yr 17 yr

Empirical induction period (12 to 17 yr)

Excessincidence

0

Incidence

Time

Exposed Unexposed

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)

RR No

exposureIn utero

DES

1 1/10 000 1/10 0000–9 yr

11/10 000 1/10 00010–19 yr

10001/10 0001 000/10 00020–29 yr

3343/30 0001 002/30 000all yr

• 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

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.

Limitation of largest estimate methods(Rothman-Greenland 1998, pp. 298-299)

(several point exposures)

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

(RE-R0) (T) = b T

0

d(t) f (T-t)

excess risk up to time T

excess risk caused byunit dose

(RE-R0) (T) = b T

0

d(t) f (T-t)

dose

dose at time t

“weight” of the dose at time t

(RE-R0) (T) = b T

0

d(t) f (T-t)

excess risk =excess risk per unit dose

weighteddose

(RE-R0) (T) = b T

0

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

0

DES example

f = 1 between ages 20 and 29

f = 0 at other times

a and b determined by trial and error

(RE-R0) (T) = b T

0

d(t) f (T-t)

E-

E+

0 10 20 30 yr

10/10,000

10/10,000

55/10,000

10/10,000

100/10,000

10/10,000

RE-R0 0 45/10,000 90/10,000

E+

E-

0 10 20 30

165/30,000 = 55/10,000

30/30,000 = 10/10,000

RE-R0 = 45/10,000RE-R0 = (45/10,000) x 1

E+

E-

10/10,000

10/10,000

RE-R0 = 0 67.5/10,000 RE-R0 = (67.5/10,000) x 0

+ (67.5/10,000) x 1

155/20,000 = 77.5/10,000

20/20,000 = 10/10,000

E-

E+ 10/10,000

10/10,000

55/10,000

10/10,000

100/10,000

10/10,000

RE-R0 0 45/10,000 90/10,000

RE-R0 = (90/10,000) x 0

+ (90/10,000) x 0.5

+ (90/10,000) x 1

Lundin et al. (1979)

Lung cancer in uranium miners

f: assumed to be log normal (based on leukemiarisk after single exposure to radiation and anincubation 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

ER (T) = bT

0

d(t) f (T-t) dt

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

ReferencesLand 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.

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.