### Exchange with Julian Peto

Not long before the Hammersmith confrontation between Burch and Richard Peto, the *British Journal of Cancer* published its review of *The Biology of Cancer*, or rather, as Burch acerbically noted, “one part of one chapter of a 12-chapter book”. That section is Burch’s calculation of lung cancer rates predicted by Doll’s model and data on smoking, rates far lower than those actually observed. The reviewer was Julian Peto, younger brother of Richard Peto, who worked on Doll’s studies of exposure to asbestos. He had no particular expertise on the subject of cancer (indeed he missed the association of asbestos with mesothelioma). The review consists mainly of rhetoric (“a bewildering array”, “enthusiastic extrapolation”, “Procrustean model”) obfuscating the burden of proof. A controversy by letter ensued, in which Burch responded to the review in the sarcastic tones it had initiated, barely pretending to treat Julian Peto as other than his brother’s mouthpiece. The review contains one quantitative argument, which looks like this:

1913 | 1923 | 1933 | 1943 | 1953 | 1963 | 1973 |
---|---|---|---|---|---|---|

1.7 | 2.5 | 4.7 | 6.4 | 8.9 | 5.6 | 3.3 |

The figures represent rates of lung cancer in men divided by rates in women at ten year intervals from 1913 to 1973: it will be seen that they rise and fall over the period. Peto explains this pattern by a factor which affected male rates of lung cancer from around 1920 and female rates from around 1950. That factor was, of course, the rise in male smoking from around 1890 and in women from around 1920 (Two time lags of 30 years are involved: women took up smoking 30 years after men, and lung cancer is held to have a 30-year incubation period.) He claimed that this refuted Burch’s idea that rising lung cancer rates were due to misdiagnosis.

The refutation only works if rates of misdiagnosis were the same in men and women, and Burch pointed this out in his reply. But were Peto’s male-female lung cancer ratios those actually predicted by Doll’s theory? In the book, Burch had shown that cigarette consumption combined with Doll’s dose-response relationship predicted that lung cancer rates for men and women in 1956 should have been 2.9 and 2.3 times the rates in 1903 (in fact they apparently rose 100 times). Given a male-female ratio of 1.2 in 1903, a simple calculation gave the predicted ratios in 1956:

1903 | 1956 |
---|---|

1.2 | 2.5 |

Burch asserted that “By no plausible stretch of the “conventional model” can cigarette smoking account for as much as 10% of the recorded increase in age-standardised rates in males.”

Peto, in rejoinder, proposed to account for the 100 fold increase in lung cancer rates by taking early 20th century levels, multiplying by a factor reflecting the real increase and again by a factor representing improved diagnosis. He obtained the first factor by amending Burch’s factor of 2.9 in males to about 10 and estimated the second from data on non-smoking generations of women. “The hundred-fold increase in recorded rates may thus be crudely summarized as the effect of a 10-fold increase due to smoking and a 10-fold increase due to diagnosis. (These 2 factors must of course be multiplied. Burch’s “best estimate from published data” is obtained by assuming that they are additive.)”

In a final exchange, Burch contrasts his “Procrustean” and therefore falsifiable hypothesis with Peto’s resort to “fudge factor”. As for the two factors of 10%, they are each 50% of Peto’s explanation of lung cancer rates.

A final letter from Peto addressed three points.

1. That rates of misdiagnosis are the same in both sexes is not a hidden assumption but part of the hypothesis being tested.

2. Burch’s simultaneous proportional changes in both sexes are entirely due to diagnostic change and therefore irrelevant to how much lung cancer is due to smoking.

3. Not 10% of the rise in lung cancer but 90% is caused by smoking. “By the same token, of course, 90% could be attributed to improved diagnosis.”

The structure of the arguments bears analysing. In his first letter, Peto seems to appeal to incremental effects of a single factor, smoking, to account for the changing male-female ratios:

1913 | 1923 | 1933 | 1943 | 1953 | 1963 | 1973 |
---|---|---|---|---|---|---|

1.7 | 2.5 | 4.7 | 6.4 | 8.9 | 5.6 | 3.3 |

m | m† | m†† | m††† | m†††† | m†††† | m†††† |

f | f | f | f | f | f † | f †† |

In his second, he invokes two such factors, one affecting men and women in the period to 1953, the second affecting men only:

1913 | 1923 | 1933 | 1943 | 1953 | 1963 | 1973 |
---|---|---|---|---|---|---|

1.7 | 2.5 | 4.7 | 6.4 | 8.9 | 5.6 | 3.3 |

m | (m†)* | (m††)** | (m†††)*** | (m††††)**** | (m††††)**** | (m††††)**** |

f | (f )* | (f )** | (f )*** | (f )**** | (f † )**** | (f †† )**** |

On Peto’s simplified model involving two consecutive periods of 30 years and two factors of equal strength, the claims he makes in his final letter are narrowly true. For instance the ratio of *(m†††)***** to *(m††††)***** is the same as the ratio of *f**** to *f*******; so that the changes in lung cancer rates in each sex would reflect diagnostic change only, the sex ratios would reflect the effect of smoking only, and Peto’s facts would refute Burch’s hypothesis. (However, there is no reason why real change and diagnostic change should both be of equal magnitude, as Peto’s explanation assumes.)