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Effects of geographic cancer incidence on risk estimates

Draper et al’s (1) observation that: “ Compared with those who lived
more than 600 m from a transmission line at birth, children who lived
within 200 m had a relative risk of leukaemia of 1.69 (95% confidence
interval 1.13 to 2.53); those born between 200 and 600 m had a relative
risk of 1.23 (1.02 to 1.49)” prompted a “rapid response” from Roman et al
(2) which concluded: “Their positive result over 100m may [therefore] be
explained not by an excess of cases but by a deficit of controls.”

Draper et al matched cases and controls within the registration
districts where the cases’ births were registered. There are some 400 of
them and they vary greatly in size, age standardised rates (ASR) for
childhood cancers and fractions of their populations exposed to
transmission line fields. The Committee on Medical Aspects of Radiation in
the Environment (COMARE) (3) produced a report on the geographic incidence
of childhood cancer over the years 1969 – 1993, which covers most of the
period of the Draper study and Jeffers (4) suggested that the geographic
volatility revealed by COMARE might explain why the relative risks which
were generated using the “leukaemia” controls disappeared when the “total
cancer” controls were used instead (1, 5).

It will be shown here how the volatilities in registration district
populations, incidence rates and exposed fractions can, in combination,
give rise to the underestimate of the exposed fraction of controls
suggested by Roman.

Total population =N

Population of j’th registration district = N(j)

Average age standardised incidence rate =R

Total number of cases / controls =NR

Average exposed fraction in population = A

ASR in j’th district, R(j) = R (1 + r(j))

Exposed fraction in j’th district, A(j) = A (1 + a(j))

Number of exposed controls = Sum N(j) R(j) A(j)

Giving an estimated exposed fraction

= Exposed controls / Total number of controls

= (A/N) Sum N(j) (1+r(j))(1+a(j))

=A + (A/N)Sum N(j) r(j) a(j)

= average exposed fraction (A) + offset

It should be noted that, if the ASR were constant over the districts,
the a(j), their range and the offset would all be zero, making the
estimated exposed fraction equal to the population average, A.

In England and Wales, the COMARE report shows an average ASR of 37.7
for leukaemia of and 113 (per million children per year) for total
cancers. The extremes of the two geographic ASR distributions are similar
to the extent that both diseases have their minima in West Glamorgan and
their maxima in Buckinghamshire. For leukaemia, the minimum is 29.1 and
the maximum is 48.3, giving a minimum “r” of -0.228, a maximum of 0.281
and a range (leukaemia) of 0.509. For the total cancers, the extremes are
132.2 and 94.1, resulting in a minimum value for “r” of -0.167, a maximum
of 0.170 and a range (total cancers) of 0.337. In districts which are not
crossed by transmission lines, A(j) = 0 and a(j) = -1, as a consequence
the range is very much larger than that for r. The values of “a” depend
on geography and are independent of the type of control but because new
houses would have been constructed during the course of the study, both A
and a(j) may change with time and the summations above apply to averages
over the duration of the study. The ASRs derived from the COMARE report
are averaged over the period 1969 – 1993.

Draper et al show 39 out of 9700 “leukaemia” controls within 200 m of
a transmission line, making the estimated exposed fraction 0.402%. For
total cancers, 151 out of 29081 were within a similar distance, making the
estimated exposed fraction 0.519%. One thus has two “estimated exposed
fraction,range” pairs: (0.402%, 0.509) for the leukaemia controls and
(0.519%, 0.337) for the total cancer controls. Extrapolating to zero
range gives a third pair (0.75%, 0). It was shown above that the estimated
exposed fraction is equal to the population average when the range is zero
and this estimate of 0.75% is larger than both Draper’s measured exposed
fraction of 64/9700 (= 0.66%) for the leukaemia cases and the 0.402%
estimated for the controls. An excess risk is no longer predicted.

When the calculation is repeated for all of the controls within 600
m, one obtains a value of 3.32% for population average exposed fraction
which is equal to that for the cases. An excess risk is, again, no longer
predicted.

Whilst recognising that the analysis here relies on drastic
simplifying assumptions and that Draper et al leave open the possibility
that the variations in estimated risk may be due to chance; the analysis
provides some support for Roman et al’s contention that the elevated risk
ratios reported by Draper et al are the consequence of underestimates of
the exposed fraction of controls rather than an excess of cases. It is
suggested that the effects of geographic volatility merit further
consideration.

References

1. Draper, G., Vincent, T., and Swanson, J.; Childhood cancer in
relation to distance from high voltage power lines in England and Wales:
a case control study, BMJ 2005; 330: 1290.

2. Roman, E, Day, N, Eden, T, McKinney, P and Simpson, J.; Childhood
Cancer and distance from high-voltage power lines – what do the data mean?
bmj.com, 5 Jul 2005

3. Committee on Medical Aspects of Radiation in the Environment; The
distribution of childhood cancers in Great Britain 1969 – 1993. (2006) http://www.comare.org.uk/comare_docs.htm

4. Jeffers, D; Geography and Controls, bmj.com, 19 March 2008.

5. Kheifets L, Feychting M and Schuz J; Control selection in the
Study of Childhood cancer in relation to distance from high voltage power
lines in England and Wales. bmj.com, 28 Jun 2005.

Draper et al’s (1) observation that: “ Compared with those who lived

more than 600 m from a transmission line at birth, children who lived

within 200 m had a relative risk of leukaemia of 1.69 (95% confidence

interval 1.13 to 2.53); those born between 200 and 600 m had a relative

risk of 1.23 (1.02 to 1.49)” prompted a “rapid response” from Roman et al

(2) which concluded: “Their positive result over 100m may [therefore] be

explained not by an excess of cases but by a deficit of controls.”

Draper et al matched cases and controls within the registration

districts where the cases’ births were registered. There are some 400 of

them and they vary greatly in size, age standardised rates (ASR) for

childhood cancers and fractions of their populations exposed to

transmission line fields. The Committee on Medical Aspects of Radiation in

the Environment (COMARE) (3) produced a report on the geographic incidence

of childhood cancer over the years 1969 – 1993, which covers most of the

period of the Draper study and Jeffers (4) suggested that the geographic

volatility revealed by COMARE might explain why the relative risks which

were generated using the “leukaemia” controls disappeared when the “total

cancer” controls were used instead (1, 5).

It will be shown here how the volatilities in registration district

populations, incidence rates and exposed fractions can, in combination,

give rise to the underestimate of the exposed fraction of controls

suggested by Roman.

Total population =N

Population of j’th registration district = N(j)

Average age standardised incidence rate =R

Total number of cases / controls =NR

Average exposed fraction in population = A

ASR in j’th district, R(j) = R (1 + r(j))

Exposed fraction in j’th district, A(j) = A (1 + a(j))

Number of exposed controls = Sum N(j) R(j) A(j)

Giving an estimated exposed fraction

= Exposed controls / Total number of controls

= (A/N) Sum N(j) (1+r(j))(1+a(j))

=A + (A/N)Sum N(j) r(j) a(j)

= average exposed fraction (A) + offset

It should be noted that, if the ASR were constant over the districts,

the a(j), their range and the offset would all be zero, making the

estimated exposed fraction equal to the population average, A.

In England and Wales, the COMARE report shows an average ASR of 37.7

for leukaemia of and 113 (per million children per year) for total

cancers. The extremes of the two geographic ASR distributions are similar

to the extent that both diseases have their minima in West Glamorgan and

their maxima in Buckinghamshire. For leukaemia, the minimum is 29.1 and

the maximum is 48.3, giving a minimum “r” of -0.228, a maximum of 0.281

and a range (leukaemia) of 0.509. For the total cancers, the extremes are

132.2 and 94.1, resulting in a minimum value for “r” of -0.167, a maximum

of 0.170 and a range (total cancers) of 0.337. In districts which are not

crossed by transmission lines, A(j) = 0 and a(j) = -1, as a consequence

the range is very much larger than that for r. The values of “a” depend

on geography and are independent of the type of control but because new

houses would have been constructed during the course of the study, both A

and a(j) may change with time and the summations above apply to averages

over the duration of the study. The ASRs derived from the COMARE report

are averaged over the period 1969 – 1993.

Draper et al show 39 out of 9700 “leukaemia” controls within 200 m of

a transmission line, making the estimated exposed fraction 0.402%. For

total cancers, 151 out of 29081 were within a similar distance, making the

estimated exposed fraction 0.519%. One thus has two “estimated exposed

fraction,range” pairs: (0.402%, 0.509) for the leukaemia controls and

(0.519%, 0.337) for the total cancer controls. Extrapolating to zero

range gives a third pair (0.75%, 0). It was shown above that the estimated

exposed fraction is equal to the population average when the range is zero

and this estimate of 0.75% is larger than both Draper’s measured exposed

fraction of 64/9700 (= 0.66%) for the leukaemia cases and the 0.402%

estimated for the controls. An excess risk is no longer predicted.

When the calculation is repeated for all of the controls within 600

m, one obtains a value of 3.32% for population average exposed fraction

which is equal to that for the cases. An excess risk is, again, no longer

predicted.

Whilst recognising that the analysis here relies on drastic

simplifying assumptions and that Draper et al leave open the possibility

that the variations in estimated risk may be due to chance; the analysis

provides some support for Roman et al’s contention that the elevated risk

ratios reported by Draper et al are the consequence of underestimates of

the exposed fraction of controls rather than an excess of cases. It is

suggested that the effects of geographic volatility merit further

consideration.

References

1. Draper, G., Vincent, T., and Swanson, J.; Childhood cancer in

relation to distance from high voltage power lines in England and Wales:

a case control study, BMJ 2005; 330: 1290.

2. Roman, E, Day, N, Eden, T, McKinney, P and Simpson, J.; Childhood

Cancer and distance from high-voltage power lines – what do the data mean?

bmj.com, 5 Jul 2005

3. Committee on Medical Aspects of Radiation in the Environment; The

distribution of childhood cancers in Great Britain 1969 – 1993. (2006)

http://www.comare.org.uk/comare_docs.htm

4. Jeffers, D; Geography and Controls, bmj.com, 19 March 2008.

5. Kheifets L, Feychting M and Schuz J; Control selection in the

Study of Childhood cancer in relation to distance from high voltage power

lines in England and Wales. bmj.com, 28 Jun 2005.

Competing interests:

None declared

Competing interests:No competing interests20 March 2009