Most recent studies report more than one relative risk (RR) for a given medical end-point, and a few studies report these RRs in more than one table, even though only one independent population cohort was investigated. Therefore, we have to come up with a systematic way of picking the RR most representative of a given independent study out of the total.
Because there is a clear distinction between the methodologies used in the occupational and the residential studies, the selections or recalculations of the RR were done differently for these two groups of studies.(I) Occupational Studies
The occupational studies were often performed as a part of a wider study with many different job classifications or titles. If a study reported a RR for more than one group of workers with a job title indicating exposure to electromagnetic fields, we picked the RR value that we believed best reflects a summary of all the job groups that are so exposed. In the case where such a summarized RR is not available, we performed a mini fixed-effect model meta-analysis (see infra) to combine all the relevant RR. For the more recent studies which have several different levels of electromagnetic field exposure (or surrogate for such exposure) included in their tables, we recalculated the RR using a dichotomous model with the highest dose category as the benchmark.(II) Residential Studies
We have identified four main estimators and surrogates for electromagnetic field exposure that appeared most frequently in the literature, as many recent studies used alternative exposure estimators as a reference for the calculation of relative risk. While no one is certain which estimator should best describe the potential carcinogenicity of EMF, it is already clear from the data, that the exposure estimators do not correlate linearly with each other and in some cases they present contradictory results, even though the data were sampled from the same population.
Most residential studies were case-control studies. These studies uses the exposure estimators to ascertain the relative risk of a medical end-point. Since the risk quoted is relative and since the whole population under study had some level of electromagnetic field exposure, the epidemiologist needs to come up with a way of sorting the data in two groups of high exposure and low exposure to enable him or her to calculate the relative risk. While old studies often divided the cases into two dose groups, i.e. a dichotomous model, more recent studies often had a few groups with different levels of exposure. Here, the relative risk is often calculated by comparing with a reference level called the non-exposed group( which in reality usually means the lowest level of exposure). It is indeed a good exercise for the investigators in the various papers to present many different facet of the data by trying out different configuration of binning or grouping of the data, for we are, at this moment, still uncertain about what level of EMF exposure will lead to cancer. However, for our purpose of presenting a meaningful and consistent summary, the results quoted from these papers cannot be extracted directly because there appeared to be no standard way of binning or separating cases of the different exposure levels among authors. We recalculated all the RR according to a dichotomous model, using the cutoff values found most commonly among all studies. We are aware that locating the cutoff at different values from those in the paper may give a different result. Therefore, before any analysis was done, we chose the most common cutoff value found among the various papers to minimize the effect, if any, of our prejudice on the results.1) The first residential study done by Wertheimer and Leeper (1979)77 used a "wire code configuration" as a surrogate for electromagnetic field exposure. This describe the configuration of the power lines outside the residence and were coded based on size, type of electrical equipment and proximity to the residence.
In addition to these, some more recent residential studies also included a cumulative dose-response category. We included the RR for such end-points in our summary but did not perform any analysis on them due to their small number.
Much controversy regarding the validity of epidemiological studies arises from the inconsistency of the results reported by independent studies. For example, Amstrong et al.(1994)70 found no correlation between electromagnetic field and leukemia while London et al.(1991)88 found a significant correlation between EMF and acute non-lymphpcytic leukemia. In addition, different exposure estimators from a given independent studies sometimes also presents contradictory results [Feyching (1993)95, Savitz (1993)99]. In most studies, details given in the paper were insufficient to determine how the electromagnetic fields were actually measured and how the authors accounted for the fluctuation in the field strengths. For occupational studies, most studies used jobs titles as a surrogate for actual electromagnetic field exposure. As mentioned above, residential studies used wire codes, distance or calculated fields as surrogates for electromagnetic field exposure. The "Spot" measurement exposure estimator that was used in some recent studies in fact attempted to use actual average field measurements to account for the exposure. However, since most studies are retrospective in nature and cancer has a latency period, the measured field strength is very often different from the field that might have been involved in the development of cancer.
If a Standardized Mortality Ratio was given and not a Risk Ratio, we interpret it as a Risk Ratio with the equation:
RR = SMR/100
Each study or independent observation was assigned a reference number, increasing with the date of the study This is used in the reference list, in table 1, and in the abscissa of figures 1 and 2. Table 1 and these figures plotted all occupational studies in figure 1 and all residential studies in figure 2. These figures give an overview of all available epidemiological data and its results, and serve as a visual summary of the risk ratios with their associated upper and lower 95th percentile confidence limits.
For some independent studies listed in table 1 more then one risk ratio and associated 95% confidence limits were quoted. However, only one value was selected for presentation graphically in figure 1 or figure 2. For example, the childhood residential study of Feychting (1993)95 found risk ratio values for three exposure estimators, namely calculated fields, distance and spot measurement. There are enough data in Table 1 for any reader of this paper to change the presented points in figure 2 by switching from using data of calculated fields to spot measurement and obtain a different graphic summary in figure 2. This gives the reader the flexibility of choosing between different exposure estimators. (This mainly apply to residential studies though more recent occupational studies did include the use of field strengths as estimators rather than the usual electrical-related job titles as surrogates for exposure to electromagnetic field).
i) Generalized Mantel-Hanzel method:
Two different methods of meta analysis were used. The first assumed a "fixed effect" model, using the generalized Mantel-Hanzel inverse variance method109. This is equivalent to assuming that all the numbers came from the same statistical sample, and combines them assuming that only the random sampling errors are of importance. It would be exact if indeed each separate study were a part of a larger study with only the different sampling numbers distinguishing them.
Assuming all studies are independent and each is representative of a larger population, each RR is weighted according to the inverse squared width of the 95% CI. From the quoted upper (RRi,u) and lower (RRi,l) bounds of the risk ratios quoted in the i-th study, we derive s i which is defined as the standard error of the i-th study:
s =[ln(RRu)-ln(RRl)]/2(1.96)Then the weight of the i-th study becomes:
wi = 1/s i2
The weighted relative risk averaged over all studies (RRmh) is then given by:
RRmh = Sigma (wiRRi)/ ?wi summed over all n studies, i=1...n.
The standard error of the sum of the studies is given by:s 2mh = 1/wmh = 1/Sigma wi
It was crucial for us to declare our cutoff values before we actually perform the any analysis, in particular, meta-analysis of any sort, for by placing the value differently, the outcome of the analysis might be drastically different. Precisely because of the uncertainty in the cutoff, the validity of the pooled relative risk is again put into question, presenting yet another limitation of meta-analysis.
The general results of the meta-analysis, both fixed-effect and random effect model, of the two groups of studies, namely occupational and residential, are presented in table 1 and figures 1 and 2 in entries 76 and 105.
The results of more detailed analysis of dividing the occupational group and residential group into various subgroups are presented in Table 2. Occupational studies are reanalyzed by dividing into three sub-groups in accordance to the design of study .(Table 2a) Residential studies are regrouped to present summaries of relative risk from i)Adult studies and ii)Childhood studies. In a different analysis, they are divided into four sub-groups by the four most common exposure estimators. Another separate analysis is done for the two most common design of study: case-control and retrospective cohort studies.(Table 2b)
B) Uncertainty Modeling
In this section we discuss the distribution of quoted uncertainties using a procedure outlined by Shlyakhter111. The aim is to estimate the extent of unquoted errors (often called "systematic errors"). This model, originally developed to study over confidence in the evolution of the physical measurements such as elementary particle data and physical constants, could help us understand the systematic errors that are inevitably present but often unaccounted for at the time the measurement was taken. Our analysis of epidemiological studies using this model can then be compared with the results of similar analysis done on physical measurements111.
We define a dimensionless constant called the normalized deviation of ln(RR) from the true value [ln(Â)]:
Xi = [ln(RRi) - ln(Â)] / ln(GSDi)
where Â is the assumed true relative risk and GSD is the geometric standard deviation of the RR given by
ln(GSD) = [ln(RR) - ln(RRl)]/1.96 if RR > Â
or ln(GSD) = [ln(RRu)-ln(RR)]/1.96 if RR < Â<for a given 95% CI of RR in the form of (RRl-RRu).
The fundamental difference in methodology between occupational studies and residential studies suggest to us the it is sensible to divide our analysis into these two groups. Within each group, various subgroups of interest were analyzed to investigate the unreported systematic errors.
We then calculated the complementary-cumulative probability distribution of X of the following subgroups:
1) By Design of Study
comparing Case-control studies, Proportional studies and Retrospective Cohort studies. (Figure 3a)
2) By Disease:
A restriction to studies that reported both Total Leukemia and AML end-points. (Figure 3b)
3) By Study Size:
A restriction to Case-control residential studies; comparing studies with number of cases (n) less than the median, versus studies with n larger than median. (not presented)The results of the analysis are inherently dependent on the number of data points or independent studies we have. Too few studies would give results that are far to jagged to be interpreted meaningfully.
In each plot for the various subgroups, the cumulative probability distribution of a Gaussian for Â = 1 is plotted along side as a comparison. [ This is the plot of the assumed relative risk with statistical sampling errors as the only uncertainties.]
I) Tabulation and Visual Summary of Relative Risk
We first make some general observations about the results in Table 1 and figures 1 and 2. As epidemiological studies of a process proceed, one expects for them to improve, the heterogeneity to be reduced, and the later value to be more representative of the true value than earlier ones.
We first look at the occupational studies. It is still unclear whether an elevated risk, if found, is due to a certain type of job within the electrical industry. Even if the risk is found to be causally related to the occupation, it is not possible to ascertain whether the elevated risk is due to exposure to electromagnetic fields or some other factors to which the workers are exposed. This might be resolved by a careful dose response study. The most recent occupational study of Savitz and Loomis (1995)74 shows no leukemogenic effect, and puzzling results for brain cancer. On the one hand the SMR is below 100, suggesting no effect, and on the other there is a significant dose-response trend, although a careful look at the paper shows that it is a peculiar one. In contrast, Floderus(1993)62 found an elevated Risk Ratio with a dose response for Chronic Lymphocytic Leukemia (CLL). This is puzzling whereas ionizing radiation is known to cause three types of leukemia, namely ALL, CML, and AML, it does not seem to cause CLL. Nor is any other agent known to cause CLL. Moreover there is the slow rate of increase of blood cell counts in CLL patients suggests that a first doubling occurred many years before (perhaps even in vitro) suggesting that the latency period for CLL is so long that the effects of occupational exposure would not be seen if that exposure were the initiator of a leukemia 114. More recent studies among our set of literature did confirmed the non-correlation between CLL and EMF exposure.[Amstrong et al.(1994)70, London et al.(1994)71 and Theriault et al.(1994)72] Having a good understanding of the characteristic of CLL enable us to use the discussion of the results regarding CLL and EMF to highlight the unpredictability and contingent nature of epidemiological studies.
The residential studies, presented in figure 2, are more sparse and the relative risk is less accurate statistically. In addition, these studies probably involve smaller elactromagnetic fields than the occupational studies.
The results from both the fixed-effect and random effect model are listed next to each other in table 2, with the latter in italicized font. As was mentioned briefly in the abstract, the purpose of our analysis is not obtain an effective risk ratios for the different cancer subtypes and try to ascertain the absolute risk of EMF on the various cancers. Rather, the analysis serves as a preliminary study to our investigations of the contradictory results presented by different studies. Results from meta-analysis alone, if accepted without supporting and other comparative analysis, would certainly lead to misleading conclusions.
Combining results in the "ordinary" way using the Mantel-Hanzel method assumed that the studies are homogenous, i.e. the differences between studies are purely random (statistical) errors. Despite our many efforts to regroup the studies and to recalculate the relative risk, in many instances, this method is still insufficient because the data points under analysis are seldom homogenous. The DerSimonian-Laird method is designed to take care of any heterogeneity between studies. This means that it accounts for non-random errors, if present, and if they differ from study to study. It cannot take account of unsuspected non-random errors that are present in all studies. The results using the DerSimonian-Laird method are usually slightly higher than or same as the Mantel-Hanzel method with a larger error bound.
The analysis of childhood residential studies is shown to have a higher RR compared to adult residential studies.(Table 2b) Further, the results from the analysis of residential studies divided by different exposure estimators shows the well known feature that there is a stronger association with some surrogate for magnetic fields based upon proximity to power lines (namely the wire code configuration and calculated fields) than to contemporaneously measured magnetic fields(spot measurements). Exposure estimated by distance also gives a smaller result. It has been suggested that in some of these studies there may be a reporting bias or an alternate cause (confounder) related to power lines but not directly to fields. A full discussion is outside the chosen scope of this paper.
III) Uncertainty Analysis
The distributions in the normalized deviation X are similar for occupational and residential studies. Both resemble the Gaussian curve but are shifted to the right. This is consistent with the true Risk Ratio being slightly elevated.
Table 2 and figure 3 top, for occupational studies only, show that the curve of retrospective cohort studies is the closest to the Gaussian distribution and very close to the plot representing errors in measurements of physical constants. Since retrospective cohort studies are generally considered to be the most reliable epidemiological studies, this may be indicative of no effect. Proportional studies, which are often regarded as the most inaccurate of the three, produce a plot which is both far away from the Gaussian curve and has a long extrapolated tail. As expected, the plot for case-control studies lies in between the two.
The cumulative probability density distribution curve (not shown) of X sorted by study size using only residential case-control studies shows a long, non-Gaussian tail for the large studies. This is consistent with the hypothesis that in these large studies, the statistical errors have become smaller than systematic errors which are presumably independent of study size. Thus, the result fits the expectation that systematic errors to dominate over statistical errors in large studies.
VI) Total Leukemia versus AML
Table 2, across all subgroups as well as the total summary, suggests that AML in general has a higher RR than that for Total Leukemia. However, this difference may be a result of selection of studies. In only some studies was types of leukemia differentiated. The recalculation of RR of AML and Total Leukemia restricted to studies that reported leukemia subtypes separated (Table 2: Total Leukemia and AML compared), resulted in a RR value that is similar in magnitude for AML and Total Leukemia. This suggests that the difference in the summary may be caused by a common defect in these studies rather than a real difference in risk ratio between leukemia type. The Cumulative Probability plots by disease when restricted occupational studies that reported both AML and Total Leukemia subgroups, showed little differences, suggesting that there is a systematic error which cancels when the same study is used.
Risk Ratios less than 2 have not usually been considered as evidence of causality in the absence of strong evidence from other scientific disciplines. Our meta-analysis results of the various sub-groups that recorded significant association results in combined risk ratio RR £ 2.Even if these meta-analysis results are taken at face value (without including any systematic errors), they do not give a clear indication of where either a postulated casual relation between cancer and exposure to electromagnetic fields or systematic errors might lie. Further, the analysis can only be considered as a upper bound of the relative risk and not the other way round because publication biases tend to shift the results to the positive end. Thus any future epidemiological studies can only follow general principles.
In addition to the inaccuracy and the possibility misclassifications of some of the data obtained from the literature aside, this analysis is also limited by the bias and subjective selection of the RR from the many tables presented in most of the studies.
The studies are sufficiently different from each other that simple mathematical meta-analyses as performed here, are obviously inadequate. We urge that any serious reader, therefore, primarily regard this paper as a guide to the literature. For the future we suggest that :
(i) An advisory group be formed to suggest one indicator, or a limited set of indicators of exposure against which to plot the data.
(ii) A large prospective-cohort study be performed with a specific limited set of end-points and measurements as of (i).
A copy of the spreadsheet which contains the full data set from which Table 1 was made, including the averaging programs, is available from the authors.
AcknowledgmentsThis work is partially supported by the Faculty Aide Program, Harvard University. Yeong Shang Loh was also given a grant from the Michelson fund to attend the 2nd Michelson Conference in August 1995 where these results were first presented.
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Studies of leukemia and brain cancer and occupational explosure to electromagnetic fields included in analysis.
|Total leukemia and AML compared.||
|By exposure estimator:|
REFERENCES (Alphabetical order)<> <>Aldrich TE and Easterly CE (1987): Electromagnetic fields and public health. Envir Health Persp 75: 159-71.