Sandler on passive smoking

Two papers on passive smoking by Sandler, Wilcox and Everson appeared at the end of 1985 and the start of 1986. Both relate to a study of 518 cancer patients at a hospital in North Carolina and an equal number of cancer-free controls matched for age, sex and race. The researchers elicited information on how many smokers the subjects had lived with in the course of their lives: this was held to be a measure of passive exposure to other people’s cigarette smoke. Passive smoking in adulthood only considered smoking rates (by level and duration) of spouses and its key finding was this extract from one of the tables.

Cases % Controls % Crude OR
[odds ratio]
[All] 55 43 1.6

That is to say, more of the cancer patients than controls had been exposed to passive smoking, and the difference was statistically significant. The pattern was still apparent if you made allowance for “confounding factors” such as age, sex, race, education, class and active smoking.

A correspondence followed. Gary Friedman contended that more confounding factors should have been considered. Nathan Mantel argued that active smokers and non-smokers should have been separated out at the first step and that age was not really a confounding factor. Burch said that Sandler had ignored workplace smoking and the tendency of smokers to marry other smokers and had admitted that a dose-response relationship was lacking. Once more he drew attention to Whitehall and MRFIT. Sandler and his colleagues replied that all these points were true but their conclusion was still tenable.

There were surprisingly few lung cancer patients in the sample because it had been deliberately drawn from younger age groups. The researchers wanted subjects who were young enough to be children of women smokers. Cumulative effects of lifetime passive smoking considered exposure from childhood on. In fact the researchers had originally hoped to investigate Everson’s 1980 hypothesis in Individuals transplacentally exposed to maternal smoking, but had chosen exposure to cigarette smoke instead because it was “common and measurable”. This time the crucial fact is supposed to arise from the following extract from one of the tables.

0 1 2 3
[All] 1 1.4 2.3 2.6
Smokers 1 1.4 2.2 2.4
Non-smokers 1 1.5 2.3 2.8

The columns represent the number of smokers the subject had lived with in a lifetime (parents, siblings, spouse etc), and the cells represent the ratio of cancer patients to cancer-free controls in each category. It appears that the risk of cancer rises continually to the right (more exposure to passive smoke) in both active smokers and in non-smokers.

A letter from Burch pointed out an amusing consequence of this. Sandler’s idea was that a background risk of cancer N was augmented by a factor P for each exposure:

0 1 2 3

But, he pointed out, active smokers are passively exposed to their own smoke, giving an extra P and a factor A for active smoking. In which case, the model for active smokers is

0 1 2 3
N+(A+P) N+(A+P)+P N+(A+P)+P+P N+(A+P)+P+P+P

and since the effect is the same in smokers and non-smokers, A+P must cancel out to give 0.

“I have to admit being partial to ‘A + P = 0’,” he wrote to Thornton.

Another letter, from Ian Higgins, questioned the matching of cases to controls. In reply, Sandler referred him to Passive smoking in adulthood.

To Burch he replied that P need not have a constant value: he had shown reason in both papers to think that it had a different value for childhood and adult exposure and supplied a table of new data to illustrate the point. On 22 June, Peter Lee joined in, pointing out that variable values for P would have to affect non-smokers more than smokers in adulthood and the other way round in childhood. Burch rejected a suggestion by Sandler that he thought passive smoking protected against cancer.

The correspondence ended there, but Burch followed up Lee’s point in passing in his next publication on the subject. Sandler’s new table, simplified, looks like this:

0 Childhood only Adulthood only
Smokers 1 1.9 1.2
Non-smokers 1 1.3 1.8

Assuming two different constants, PC and PA for exposure in childhood and exposure in adulthood, the model is

0 Childhood only Adulthood only
Smokers N N+ PC N+PA+A
Non-smokers N N+ PC N+ PA

And a few lines of algebra show that A must have the value of -07N, implying that active smoking in adulthood on top of passive smoking in childhood reduces the risk of cancer.


A Half-life of Burch