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Archives of Environmental Health: An International Journal Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/vzeh20
Latency Analysis in Occupational Epidemiology a
b
c
Harvey Checkoway Ph.D. , Neil Pearce Ph.D. , John L.S. Hickey Ph.D. & John M. Dement Ph.D.
d
a
Department of Environmental Health , University of Washington, School of Public Health and Community Medicine , Seattle, Washington, USA b
Department of Community Health , Wellington School of Medicine, Wellington Hospital , Wellington, New Zealand c
Department of Environmental Sciences and Engineering , University of North Carolina, School of Public Health , Chapel Hill, North Carolina, USA d
Health and Safety Office , National Institute of Environmental Health Sciences, Research Triangle Park , North Carolina, USA Published online: 03 Aug 2010.
To cite this article: Harvey Checkoway Ph.D. , Neil Pearce Ph.D. , John L.S. Hickey Ph.D. & John M. Dement Ph.D. (1990) Latency Analysis in Occupational Epidemiology, Archives of Environmental Health: An International Journal, 45:2, 95-100, DOI: 10.1080/00039896.1990.9935932 To link to this article: http://dx.doi.org/10.1080/00039896.1990.9935932
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
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Latency Analysis in Occupational Epidemiology
HARVEY CHECKOWAY, Ph.D. Department of Environmental Health University of Washington School of Public Health and Community Medicine Seattle, Washington NEIL PEARCE, Ph.0. Department of Community Health Wellington School of Medicine Wellington Hospital Wellington, New Zealand JOHN L. S. HICKEY, Ph.D. Department of Environmental Sciences and Engineering University of North Carolina School of Public Health Chapel Hill, North Carolina JOHNM. DEMENT, Ph.D. Health and Safety Office National Institute of Environmental Health Sciences Research Triangle Park, North Carolina
ABSTRACT. Allowance for prolonged disease induction and latency times is an important consideration in occupational epidemiology studies of cancer and other delayed effects of exposure. Two useful approaches for assessing prolonged induction and latency periods are (1) exposure lagging and (2) considering exposures only within moving time windows. The exposure weighting scheme proposed by Jahr2 to assess exposure burdens is another method that accounts for induction and latency, although not explicitly. These three approaches, which are shown to be special cases of exposure weighting, are illustrated with an analysis of lung cancer mortality among a cohort of workers from an asbestos textile plant.
CANCER and other diseases that occur many years following initial exposure are often of principal interest in occupational cohort studies. Consequently, in an epidemiologic analysis focused on estimating exposure-response gradients, it is important to account for disease induction and latency periods to distinguish between etiologic and possibly unrelated exposures.’ The general approach used to accomplish this goal is usuMarchlApril 1990 [Vol. 45 (No. 211
ally referred to as “latency analysis.” Numerous methods of latency analysis have been described. The common feature of these methods is that each involves some form of exposure-weighting scheme, such that the assumed etiologically relevant exposures are weighted most heavily. In this paper, we describe several useful approaches to latency analysis. The underlying weighting schemes are described, and applica95
tions of the methods are illustrated with data from a cohort study of lung cancer mortality among asbestos textile plant workers. Each of the three latency analysis methods to be described-exposure lagging, exposure time windows, and an exposure burden model devised by Jahr'-involves specific assumptions about the relative durations of disease induction andlor latency periods. As will be shown, these assumptions are characterized by the exposure-weighting scheme used. These approaches to latency analysis were chosen for illustration because they are conceptually and computationally relatively straightforward and thus potentially have broad appl icabi I ity.
Downloaded by [University of Alberta] at 05:18 30 December 2014
Definition of terms Figure 1 depicts the time sequence of an exposure to a single agent that is sufficient to cause disease and the subsequent occurrence of disease. If exposure occurring between points A and B i s sufficient to induce disease, then the corresponding time interval is the disease induction period. Exposures received after point B are unrelated to disease induction (although for some diseases, e.g., silicosis, continued exposure may increase disease severity). The interval between B and D is the latency period because existing disease is "hidden" until time D. The interval from A to D has been called the empirical induction time3 and is what is often referred to simply as "latency." For a particular health endpoint, the relative lengths of the induction and latency periods will depend on the intensity and duration of exposure and its mechanism of action. In the extreme case of an acute exposure with an immediate effect, e g , a chemical burn, the time between points A and D would be effectively nil. More typically, however, induction and latency periods are uncertain. The temporal sequence of exposure, induction, and latency periods for diseases with multifactorial etiolo-
Unrelated
Induction period
gies is more complex than that depicted in Figure 1. To illustrate, consider a disease that has a sequential twostage induction process in which exposure to the factor that acts at the second stage is only effective when the effect of exposure to the first factor is complete. The time sequence of an induction process involving two overlapping exposures is illustrated in Figure 2. The etiologically relevant exposure period for factor 1 is the interval from A1 to B1. Exposure to factor 2 is not effective until B1, when the effect of factor 1 is complete. Thus, the relevant exposure period for factor 2 is the interval from B1 to B2. The disease latency interval is the time period 82 to D. From this example, it can be seen that each exposure factor has a specific etiologically relevant period that is determined by its mode of action in temporal relation to other exposures, whereas the latency period remains constant as the interval between completion of the effects of all necessary exposures and disease detection. According to Rothman's3 formulation, the induction period for factor 1 in Figure 2 would be the interval A1 to B2, whereas the induction period for factor 2 would be the interval B1 to B2. Ideally, one would want to separate exposures occurring before (causal) and after (etiologically irrelevant) point B2; however, the point in time at which disease is irreversibly initiated is seldom known. This objective is the motivation for latency analysis.
Methods of latency analysis For ease of illustration, the discussion will focus on the most straightforward case of an occupational cohort study in which disease risk is estimated in relation to cumulative exposure to a quantitatively measured exposure (e.g., mg/m3 of dust x y). Person-time of observation and cumulative exposure are treated as time-related factors, which is the appropriate manner to analyze such data.'.4 The approaches described here can also be applied to other dose surrogates, such as peak exposure or length of employment in an industry or job ~ a t e g o r y ,and ~ to other study designs, such as case-control studies nested within occupational cohorts.' Every method of treating cumulative exposure data involves some form of weighting of intensity. Consequently, a general expression for cumulative exposure (€1) at the end of the jth time interval ( Y j ) from exposures delivered during the previous i intervals (i = 1,2, ...,j 1 is:
Latency interval
A Exposure onset
B
Time
C D Exposure Disease term i natio n detected
-b
Fig. 1 . Temporal sequence of disease induction and latency for a single exposure that is a sufficient cause of disease.
96
where l i represents the exposure intensity value for the ith time interval, ti is the length of the ith interval, and Wi is the corresponding assigned weight. The form of latency analysis is therefore determined by the choice of weights. Exposure Lagging. If no latency interval is assumed, i.e., the entire period of exposure is regarded as potentially etiologic, then one would perform an analysis of disease rates in relation to cumulative exposure. All of the Wj in expression [l] would equal 1.0 when cumulative exposure is used as the exposure index. Archives of Environmental Health
Downloaded by [University of Alberta] at 05:18 30 December 2014
Exposure windows. An elaboration of the lagging method is to consider exposures only during specific time window^."^ According to this approach, only exposures received during some specified time interval prior to disease onset are treated as etiologically relevant; thus, the mast recent and the most far-removed exposures are ignored. (Relevant time windows for two exposures are illustrated in Fig. 2). To analyze time-related exposures appropriately, the exposure windows should be moving time intervals during the period of observation. As an example, one might classify persontime and case occurrences according to cumulative exposures received during the time window 5-19. This method is most suitable for situations where the disease latency can be estimated, and there is reason to believe that the effects of exposures received in the distant past are unrelated to the health outcome of interest, e.g., reversible toxicity. For example, if a 5-19 yr moving exposure time window is used, then the weights in expression [ l ] would be 0 for yr 0-4,l.O for yr 5-19, and 0 for yr 3 20. An extreme example would be an electrocution following high-voltage exposure, for which the time window of etiologic exposure would be well defined and exceedingly brief. Jahr’s mod-el. In 1974, Jahr‘ described an exposureweighting scheme to account for retention of substances in target tissues as a means of estimating the effect of exposure burden on subsequent disease risk. According to this method, each exposure received in a particular time interval (usually 1 yr) is weighted in direct proportion to the time since occurrence. Thus, the W i in expression [ l ] can be expressed as:
An alternative method is to lag cumulative exposure by the assumed latency period (1). Thus, each personyear of observation for a worker is classified according to the cumulative exposure level achieved 1 yr previously. Thus, in expression [ l ] the W i would be assigned a value of 1.0 for all yr before the assumed latency interval, and 0 thereafter. To illustrate, consider a worker in a nuclear family who had commenced work at age 30 yr in 1955, received a cumulative radiation dose of 4 rem by age 35 yr in 1960, and by age 45 yr in 1970 had attained a cumulative dose of 9 rern. Under a 10-yr latency assumption, the person-year of observation for age 35 yr in 1960 would be assigned a cumulative dose of 0, rather than 4 rem, and the person-year for age 45 yr in 1970 would be assigned a cumulative dose value of 4, rather than 9 rem. In contrast, under a 0-yr latency assumption (i.e., no lagging), the person-years at ages 35 yr and 45 yr would be assigned cumulative dose values of 4 and 9 rern, respectively. Exposure lagging can also be used for cruder dose indices, such as employment duration. As illustrated above, when lagging i s used, exposures occurring during the first L years of a worker’s employment are automatically set to zero, and the corresponding person-time is assigned to the person-time experience of an internal reference group. In some studies,’.’ investigators have attempted to incorporate latency into the analysis by deleting both the first L person-years of employment and any cases or deaths occurring during those years. This approach to latency analysis is less desirable than exposure lagging because information (person-time and associated cases or deaths) i s sacrificed. By contrast, exposure lagging uses all of the information available.
1
I
Unrelated exposure: Factor 2
I
Etiologically relevant exposure: Factor 2
Unrelated exposure: Factor 2
b4
4 Etiologically relevant exposure: Factor 1
wi = YJ - Y i + 0.5
4
Unrelated exposure: Factor 1
b
b4
4
Latency interval I
4 tL
tL
tL
A1 A2 B1 Exposure 1 Exposure 2 Action of onset Onset exposure 1 Eomplete
tL
IL
82
Action of exposure 2 complete (disease initiated) Time
c1
Termination of exposure 1
1
D
t c2
Termination of exposure 2
D Disease detected
,-e
Fig. 2. Temporal sequence of disease induction and latency for two exposures that act in sequence to cause disease. March/April1990 [Vol. 45 (No. Z)]
97
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where Yi is the year in which exposure occurred, and Y j is the year in which the effect of exposure is evaluated (Y, 2 Yi). The addition of 0.5 is made to allow for delivery of exposure throughout yr Yi, rather than all at once at the beginning of the year. As an example of the Jahr model, consider a worker exposed to a constant concentration of 10 mg/m3 of dust in 1970. From expressions [ l ] and [2], the worker‘s cumulative exposure at the beginning of 1971 is computed as 10 mg/m3 x yr; at the beginning of 1980, the cumulative exposure resulting from exposure received in 1970 would be 95 mg/m3 x yr. Similar calculations would be performed for 1971 and all subsequent years of exposure. The cumulative exposure received from all years is obtained by summation of the weighted (by time since occurrence) exposures received throughout the period of exposure. The Jahr model can be extended to allow for clearance of the substance. Under an assumption of an exponential clearance rate, the cumulative weighted exposure resulting from all years of exposure (Ej) can be estimated by:
E~
=
f /iti{l/k
bI
-
I / ~ V I - exp[-k])
131
(exp[-k(Yj - Y i l l ) } where k is the clearance rate, which is equal to ln2/T,,,, with T, representing the half-life (in yr) of the substance in the target organ. Non-linear (e.g., geometric) or inverse weighting schemes can be used with Jahr‘s model, depending on assumptions of etiologic mechanisms. However, weighting schemes more complex than a simple linear weighting by time since occurrence may be difficult to justify for many chronic environmentally induced diseases, especially when clearance rates are uncertain.’ lo Jahr’s method of exposure weighting differs from exposure lagging or the time window approach in that Jahr’s model requires no explicit estimate of the width of the latency interval, although the time-sinceexposure weighting scheme approximately specifies the induction period (i.e., the earliest years of exposure). In fact, the Jahr model could be modified easily to a direct latency analysis approach by assigning weights of zero to exposures that occurred during the assumed latency period.
findings presented here and the original report” arise primarily because the original study restricted the analysis to workers who were followed for at least 15 yr from first employment, whereas no such restriction was imposed in our reanalysis. Trends of lung cancer mortality in relation to cumulative asbestos exposure were examined for each of the following exposure indices: (1) simple cumulative exposure (i.e., 0-yr lag); (2) cumulative exposure lagged by 10 yr; (3) cumulative exposure attained during the moving time window 10-25 yr previously; (4) the Jahr model with weights assigned in direct proportion to time since occurrence; and (5) the Jahr model allowing for fiber clearance, assuming a 10-yr half-life in the lungs. In these analyses, the cohort was divided into seven exposure strata, with each stratum containing five lung cancer deaths. Therefore, the stratum-specific results are not directly comparable between exposure models because the stratum boundaries vary. Relative risks for lung cancer mortality were estimated by means of Poisson regression analysis using an iteratively reweighted least squares a1g0rithm.l~The relative risks were adjusted for age, calendar year, and duration of follow-up, each in 5-yr intervals. Person-years were stratified into the corresponding exposure and covariate categories using a specially devised computer prog r a m ~ . ’These ~ analyses were performed with the GLIM’’ statistical package. The results are summarized in Table 1. Consistent with the original analysis,12 the findings indicate a pronounced gradient of lung cancer mortality for each exposure-weighting scheme. The relative risks are largest in the highest two exposure categories under Model 3, the 10-25 yr time window, although the trend is somewhat dampened by the relatively high rate ratio (2.64) in the second exposure category. Table 2 shows comparative results for various lag intervals, 0, 5, and 15 yr. These data differ from those presented in Table 1 in that the exposure categories in Table 2 have fixed boundaries for each analysis, whereas in Table 1 the exposure strata were defined so that each contained a fixed number of lung cancer deaths. The exposure gradient is most pronounced under a 15-yr lag; however, the trend cannot be evaluated fully because there were no lung cancer cases who had achieved 100 000 f/cc x d 15 or more yr before death.
Example: Asbestos Textile Plant Worker Cohort Study The latency analysis methods described above are illustrated with a reanalysis of lung cancer mortality data from a study of asbestos textile plant workers. The study has been reported previously by Dement et al.’1,‘2 The cohort consisted of 1 261 white males who had achieved at least 1 mo of employment at the plant between January 1, 1940, and December 31, 1965. Follow-up was conducted for the interval January 1, 1940, through December 31, 1975, during which time 35 deaths from lung cancer occurred. Workers’ cumulative exposures to asbestos, expressed as fiberslcc x d (Wcc x d), were estimated from historical industrial hygiene monitoring data.’’ Discrepancies between the 98
Discussion This paper has reviewed some reasonably straightforward approaches for taking disease induction and latency into account in occupational epidemiology studies. More complex methods, such as those used in fitting multistage models of carcinogenesis,’“ are available but are more specialized than the procedures described in this paper. The choice of latency analysis method will depend on existing knowledge of disease etiology. For example, if past evidence indicates that exposures received within the proceeding 10 yr are unlikely to induce disease, then an exposure-response analysis in which Archives of Environmental Health
Table 1.-Relative Risks for Asbestos Exposure and Lung Cancer Mortality Using Various Latency Analysis Weighting Schemes Model
Stratum*
(1) Cumulative exposure 0-yr lag
(2) Cumulative exposure 10-yr lag
(3) Cumulative exposure in time window 10-25 yr
(4) Jahr model, no clearance
1.oo 2.08 1.46 3.35 4.28 5.70 11.17
1.oO 2.31 2.41 5.24 4.03 6.92 15.27
1.oo 2.64 1.97 3.33 5.94 9.84 16.96
1 1.53 2.26 6.34 3.46 5.72 13.33
It 2 3 4 5 6 7
.oo
(5) Jahr model T,,, = 10 yr 1.oo 1.92 1.96 4.32 3.76 6.68 13.57
I
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*Each stratum contains five lung cancer deaths; stratum boundaries vary between exposure models tReference category.
exposures are lagged by 10 yr would be justified. This seems to be the case for asbestos-induced lung cancer and mesothelioma.l’ However, for many occupational and environmental diseases, the probable lengths of the latency periods are subject to wide variations” and may therefore be difficult to estimate precisely, especially when variability is influenced by the timing and intensity of the causative expos~re.’~ Thus, an advisable strategy is to perform analyses using several assumed latency periods, including a 0-yr lag, to explore for consistency of trends. The time window approach may then be used as an embellishment of the lagging method to sharpen the analysis. Here again, trial and error estimation of the appropriate time window is re~ommended.~ The Jahr model, which was devised for estimating effects of exposure burden in target organs, does not involve explicit estimates of latency intervals, although it could be combined with exposure lagging or a time window approach. Jahr’s method is particularly useful for studying exposure-response relationships for agents that are retained in active forms in target tissues, such
Table 2.-Relative Risks for Asbestos Exposure and Lung Cancer Mortality Using Various Lag Intervals for Cumulative Exposure Cumulative exposure (1 OOO ficc x d) ~~~
0
Lag interval (yr) 5
15
~
Archives of Environmental Health: An International Journal Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/vzeh20
Latency Analysis in Occupational Epidemiology a
b
c
Harvey Checkoway Ph.D. , Neil Pearce Ph.D. , John L.S. Hickey Ph.D. & John M. Dement Ph.D.
d
a
Department of Environmental Health , University of Washington, School of Public Health and Community Medicine , Seattle, Washington, USA b
Department of Community Health , Wellington School of Medicine, Wellington Hospital , Wellington, New Zealand c
Department of Environmental Sciences and Engineering , University of North Carolina, School of Public Health , Chapel Hill, North Carolina, USA d
Health and Safety Office , National Institute of Environmental Health Sciences, Research Triangle Park , North Carolina, USA Published online: 03 Aug 2010.
To cite this article: Harvey Checkoway Ph.D. , Neil Pearce Ph.D. , John L.S. Hickey Ph.D. & John M. Dement Ph.D. (1990) Latency Analysis in Occupational Epidemiology, Archives of Environmental Health: An International Journal, 45:2, 95-100, DOI: 10.1080/00039896.1990.9935932 To link to this article: http://dx.doi.org/10.1080/00039896.1990.9935932
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
Downloaded by [University of Alberta] at 05:18 30 December 2014
Latency Analysis in Occupational Epidemiology
HARVEY CHECKOWAY, Ph.D. Department of Environmental Health University of Washington School of Public Health and Community Medicine Seattle, Washington NEIL PEARCE, Ph.0. Department of Community Health Wellington School of Medicine Wellington Hospital Wellington, New Zealand JOHN L. S. HICKEY, Ph.D. Department of Environmental Sciences and Engineering University of North Carolina School of Public Health Chapel Hill, North Carolina JOHNM. DEMENT, Ph.D. Health and Safety Office National Institute of Environmental Health Sciences Research Triangle Park, North Carolina
ABSTRACT. Allowance for prolonged disease induction and latency times is an important consideration in occupational epidemiology studies of cancer and other delayed effects of exposure. Two useful approaches for assessing prolonged induction and latency periods are (1) exposure lagging and (2) considering exposures only within moving time windows. The exposure weighting scheme proposed by Jahr2 to assess exposure burdens is another method that accounts for induction and latency, although not explicitly. These three approaches, which are shown to be special cases of exposure weighting, are illustrated with an analysis of lung cancer mortality among a cohort of workers from an asbestos textile plant.
CANCER and other diseases that occur many years following initial exposure are often of principal interest in occupational cohort studies. Consequently, in an epidemiologic analysis focused on estimating exposure-response gradients, it is important to account for disease induction and latency periods to distinguish between etiologic and possibly unrelated exposures.’ The general approach used to accomplish this goal is usuMarchlApril 1990 [Vol. 45 (No. 211
ally referred to as “latency analysis.” Numerous methods of latency analysis have been described. The common feature of these methods is that each involves some form of exposure-weighting scheme, such that the assumed etiologically relevant exposures are weighted most heavily. In this paper, we describe several useful approaches to latency analysis. The underlying weighting schemes are described, and applica95
tions of the methods are illustrated with data from a cohort study of lung cancer mortality among asbestos textile plant workers. Each of the three latency analysis methods to be described-exposure lagging, exposure time windows, and an exposure burden model devised by Jahr'-involves specific assumptions about the relative durations of disease induction andlor latency periods. As will be shown, these assumptions are characterized by the exposure-weighting scheme used. These approaches to latency analysis were chosen for illustration because they are conceptually and computationally relatively straightforward and thus potentially have broad appl icabi I ity.
Downloaded by [University of Alberta] at 05:18 30 December 2014
Definition of terms Figure 1 depicts the time sequence of an exposure to a single agent that is sufficient to cause disease and the subsequent occurrence of disease. If exposure occurring between points A and B i s sufficient to induce disease, then the corresponding time interval is the disease induction period. Exposures received after point B are unrelated to disease induction (although for some diseases, e.g., silicosis, continued exposure may increase disease severity). The interval between B and D is the latency period because existing disease is "hidden" until time D. The interval from A to D has been called the empirical induction time3 and is what is often referred to simply as "latency." For a particular health endpoint, the relative lengths of the induction and latency periods will depend on the intensity and duration of exposure and its mechanism of action. In the extreme case of an acute exposure with an immediate effect, e g , a chemical burn, the time between points A and D would be effectively nil. More typically, however, induction and latency periods are uncertain. The temporal sequence of exposure, induction, and latency periods for diseases with multifactorial etiolo-
Unrelated
Induction period
gies is more complex than that depicted in Figure 1. To illustrate, consider a disease that has a sequential twostage induction process in which exposure to the factor that acts at the second stage is only effective when the effect of exposure to the first factor is complete. The time sequence of an induction process involving two overlapping exposures is illustrated in Figure 2. The etiologically relevant exposure period for factor 1 is the interval from A1 to B1. Exposure to factor 2 is not effective until B1, when the effect of factor 1 is complete. Thus, the relevant exposure period for factor 2 is the interval from B1 to B2. The disease latency interval is the time period 82 to D. From this example, it can be seen that each exposure factor has a specific etiologically relevant period that is determined by its mode of action in temporal relation to other exposures, whereas the latency period remains constant as the interval between completion of the effects of all necessary exposures and disease detection. According to Rothman's3 formulation, the induction period for factor 1 in Figure 2 would be the interval A1 to B2, whereas the induction period for factor 2 would be the interval B1 to B2. Ideally, one would want to separate exposures occurring before (causal) and after (etiologically irrelevant) point B2; however, the point in time at which disease is irreversibly initiated is seldom known. This objective is the motivation for latency analysis.
Methods of latency analysis For ease of illustration, the discussion will focus on the most straightforward case of an occupational cohort study in which disease risk is estimated in relation to cumulative exposure to a quantitatively measured exposure (e.g., mg/m3 of dust x y). Person-time of observation and cumulative exposure are treated as time-related factors, which is the appropriate manner to analyze such data.'.4 The approaches described here can also be applied to other dose surrogates, such as peak exposure or length of employment in an industry or job ~ a t e g o r y ,and ~ to other study designs, such as case-control studies nested within occupational cohorts.' Every method of treating cumulative exposure data involves some form of weighting of intensity. Consequently, a general expression for cumulative exposure (€1) at the end of the jth time interval ( Y j ) from exposures delivered during the previous i intervals (i = 1,2, ...,j 1 is:
Latency interval
A Exposure onset
B
Time
C D Exposure Disease term i natio n detected
-b
Fig. 1 . Temporal sequence of disease induction and latency for a single exposure that is a sufficient cause of disease.
96
where l i represents the exposure intensity value for the ith time interval, ti is the length of the ith interval, and Wi is the corresponding assigned weight. The form of latency analysis is therefore determined by the choice of weights. Exposure Lagging. If no latency interval is assumed, i.e., the entire period of exposure is regarded as potentially etiologic, then one would perform an analysis of disease rates in relation to cumulative exposure. All of the Wj in expression [l] would equal 1.0 when cumulative exposure is used as the exposure index. Archives of Environmental Health
Downloaded by [University of Alberta] at 05:18 30 December 2014
Exposure windows. An elaboration of the lagging method is to consider exposures only during specific time window^."^ According to this approach, only exposures received during some specified time interval prior to disease onset are treated as etiologically relevant; thus, the mast recent and the most far-removed exposures are ignored. (Relevant time windows for two exposures are illustrated in Fig. 2). To analyze time-related exposures appropriately, the exposure windows should be moving time intervals during the period of observation. As an example, one might classify persontime and case occurrences according to cumulative exposures received during the time window 5-19. This method is most suitable for situations where the disease latency can be estimated, and there is reason to believe that the effects of exposures received in the distant past are unrelated to the health outcome of interest, e.g., reversible toxicity. For example, if a 5-19 yr moving exposure time window is used, then the weights in expression [ l ] would be 0 for yr 0-4,l.O for yr 5-19, and 0 for yr 3 20. An extreme example would be an electrocution following high-voltage exposure, for which the time window of etiologic exposure would be well defined and exceedingly brief. Jahr’s mod-el. In 1974, Jahr‘ described an exposureweighting scheme to account for retention of substances in target tissues as a means of estimating the effect of exposure burden on subsequent disease risk. According to this method, each exposure received in a particular time interval (usually 1 yr) is weighted in direct proportion to the time since occurrence. Thus, the W i in expression [ l ] can be expressed as:
An alternative method is to lag cumulative exposure by the assumed latency period (1). Thus, each personyear of observation for a worker is classified according to the cumulative exposure level achieved 1 yr previously. Thus, in expression [ l ] the W i would be assigned a value of 1.0 for all yr before the assumed latency interval, and 0 thereafter. To illustrate, consider a worker in a nuclear family who had commenced work at age 30 yr in 1955, received a cumulative radiation dose of 4 rem by age 35 yr in 1960, and by age 45 yr in 1970 had attained a cumulative dose of 9 rern. Under a 10-yr latency assumption, the person-year of observation for age 35 yr in 1960 would be assigned a cumulative dose of 0, rather than 4 rem, and the person-year for age 45 yr in 1970 would be assigned a cumulative dose value of 4, rather than 9 rem. In contrast, under a 0-yr latency assumption (i.e., no lagging), the person-years at ages 35 yr and 45 yr would be assigned cumulative dose values of 4 and 9 rern, respectively. Exposure lagging can also be used for cruder dose indices, such as employment duration. As illustrated above, when lagging i s used, exposures occurring during the first L years of a worker’s employment are automatically set to zero, and the corresponding person-time is assigned to the person-time experience of an internal reference group. In some studies,’.’ investigators have attempted to incorporate latency into the analysis by deleting both the first L person-years of employment and any cases or deaths occurring during those years. This approach to latency analysis is less desirable than exposure lagging because information (person-time and associated cases or deaths) i s sacrificed. By contrast, exposure lagging uses all of the information available.
1
I
Unrelated exposure: Factor 2
I
Etiologically relevant exposure: Factor 2
Unrelated exposure: Factor 2
b4
4 Etiologically relevant exposure: Factor 1
wi = YJ - Y i + 0.5
4
Unrelated exposure: Factor 1
b
b4
4
Latency interval I
4 tL
tL
tL
A1 A2 B1 Exposure 1 Exposure 2 Action of onset Onset exposure 1 Eomplete
tL
IL
82
Action of exposure 2 complete (disease initiated) Time
c1
Termination of exposure 1
1
D
t c2
Termination of exposure 2
D Disease detected
,-e
Fig. 2. Temporal sequence of disease induction and latency for two exposures that act in sequence to cause disease. March/April1990 [Vol. 45 (No. Z)]
97
Downloaded by [University of Alberta] at 05:18 30 December 2014
where Yi is the year in which exposure occurred, and Y j is the year in which the effect of exposure is evaluated (Y, 2 Yi). The addition of 0.5 is made to allow for delivery of exposure throughout yr Yi, rather than all at once at the beginning of the year. As an example of the Jahr model, consider a worker exposed to a constant concentration of 10 mg/m3 of dust in 1970. From expressions [ l ] and [2], the worker‘s cumulative exposure at the beginning of 1971 is computed as 10 mg/m3 x yr; at the beginning of 1980, the cumulative exposure resulting from exposure received in 1970 would be 95 mg/m3 x yr. Similar calculations would be performed for 1971 and all subsequent years of exposure. The cumulative exposure received from all years is obtained by summation of the weighted (by time since occurrence) exposures received throughout the period of exposure. The Jahr model can be extended to allow for clearance of the substance. Under an assumption of an exponential clearance rate, the cumulative weighted exposure resulting from all years of exposure (Ej) can be estimated by:
E~
=
f /iti{l/k
bI
-
I / ~ V I - exp[-k])
131
(exp[-k(Yj - Y i l l ) } where k is the clearance rate, which is equal to ln2/T,,,, with T, representing the half-life (in yr) of the substance in the target organ. Non-linear (e.g., geometric) or inverse weighting schemes can be used with Jahr‘s model, depending on assumptions of etiologic mechanisms. However, weighting schemes more complex than a simple linear weighting by time since occurrence may be difficult to justify for many chronic environmentally induced diseases, especially when clearance rates are uncertain.’ lo Jahr’s method of exposure weighting differs from exposure lagging or the time window approach in that Jahr’s model requires no explicit estimate of the width of the latency interval, although the time-sinceexposure weighting scheme approximately specifies the induction period (i.e., the earliest years of exposure). In fact, the Jahr model could be modified easily to a direct latency analysis approach by assigning weights of zero to exposures that occurred during the assumed latency period.
findings presented here and the original report” arise primarily because the original study restricted the analysis to workers who were followed for at least 15 yr from first employment, whereas no such restriction was imposed in our reanalysis. Trends of lung cancer mortality in relation to cumulative asbestos exposure were examined for each of the following exposure indices: (1) simple cumulative exposure (i.e., 0-yr lag); (2) cumulative exposure lagged by 10 yr; (3) cumulative exposure attained during the moving time window 10-25 yr previously; (4) the Jahr model with weights assigned in direct proportion to time since occurrence; and (5) the Jahr model allowing for fiber clearance, assuming a 10-yr half-life in the lungs. In these analyses, the cohort was divided into seven exposure strata, with each stratum containing five lung cancer deaths. Therefore, the stratum-specific results are not directly comparable between exposure models because the stratum boundaries vary. Relative risks for lung cancer mortality were estimated by means of Poisson regression analysis using an iteratively reweighted least squares a1g0rithm.l~The relative risks were adjusted for age, calendar year, and duration of follow-up, each in 5-yr intervals. Person-years were stratified into the corresponding exposure and covariate categories using a specially devised computer prog r a m ~ . ’These ~ analyses were performed with the GLIM’’ statistical package. The results are summarized in Table 1. Consistent with the original analysis,12 the findings indicate a pronounced gradient of lung cancer mortality for each exposure-weighting scheme. The relative risks are largest in the highest two exposure categories under Model 3, the 10-25 yr time window, although the trend is somewhat dampened by the relatively high rate ratio (2.64) in the second exposure category. Table 2 shows comparative results for various lag intervals, 0, 5, and 15 yr. These data differ from those presented in Table 1 in that the exposure categories in Table 2 have fixed boundaries for each analysis, whereas in Table 1 the exposure strata were defined so that each contained a fixed number of lung cancer deaths. The exposure gradient is most pronounced under a 15-yr lag; however, the trend cannot be evaluated fully because there were no lung cancer cases who had achieved 100 000 f/cc x d 15 or more yr before death.
Example: Asbestos Textile Plant Worker Cohort Study The latency analysis methods described above are illustrated with a reanalysis of lung cancer mortality data from a study of asbestos textile plant workers. The study has been reported previously by Dement et al.’1,‘2 The cohort consisted of 1 261 white males who had achieved at least 1 mo of employment at the plant between January 1, 1940, and December 31, 1965. Follow-up was conducted for the interval January 1, 1940, through December 31, 1975, during which time 35 deaths from lung cancer occurred. Workers’ cumulative exposures to asbestos, expressed as fiberslcc x d (Wcc x d), were estimated from historical industrial hygiene monitoring data.’’ Discrepancies between the 98
Discussion This paper has reviewed some reasonably straightforward approaches for taking disease induction and latency into account in occupational epidemiology studies. More complex methods, such as those used in fitting multistage models of carcinogenesis,’“ are available but are more specialized than the procedures described in this paper. The choice of latency analysis method will depend on existing knowledge of disease etiology. For example, if past evidence indicates that exposures received within the proceeding 10 yr are unlikely to induce disease, then an exposure-response analysis in which Archives of Environmental Health
Table 1.-Relative Risks for Asbestos Exposure and Lung Cancer Mortality Using Various Latency Analysis Weighting Schemes Model
Stratum*
(1) Cumulative exposure 0-yr lag
(2) Cumulative exposure 10-yr lag
(3) Cumulative exposure in time window 10-25 yr
(4) Jahr model, no clearance
1.oo 2.08 1.46 3.35 4.28 5.70 11.17
1.oO 2.31 2.41 5.24 4.03 6.92 15.27
1.oo 2.64 1.97 3.33 5.94 9.84 16.96
1 1.53 2.26 6.34 3.46 5.72 13.33
It 2 3 4 5 6 7
.oo
(5) Jahr model T,,, = 10 yr 1.oo 1.92 1.96 4.32 3.76 6.68 13.57
I
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*Each stratum contains five lung cancer deaths; stratum boundaries vary between exposure models tReference category.
exposures are lagged by 10 yr would be justified. This seems to be the case for asbestos-induced lung cancer and mesothelioma.l’ However, for many occupational and environmental diseases, the probable lengths of the latency periods are subject to wide variations” and may therefore be difficult to estimate precisely, especially when variability is influenced by the timing and intensity of the causative expos~re.’~ Thus, an advisable strategy is to perform analyses using several assumed latency periods, including a 0-yr lag, to explore for consistency of trends. The time window approach may then be used as an embellishment of the lagging method to sharpen the analysis. Here again, trial and error estimation of the appropriate time window is re~ommended.~ The Jahr model, which was devised for estimating effects of exposure burden in target organs, does not involve explicit estimates of latency intervals, although it could be combined with exposure lagging or a time window approach. Jahr’s method is particularly useful for studying exposure-response relationships for agents that are retained in active forms in target tissues, such
Table 2.-Relative Risks for Asbestos Exposure and Lung Cancer Mortality Using Various Lag Intervals for Cumulative Exposure Cumulative exposure (1 OOO ficc x d) ~~~
0
Lag interval (yr) 5
15
~
