If someone makes a statement like below:
"Overall, nonsmokers exposed to environmental smoke had a relative risk of coronary heart disease of 1.25 (95 percent confidence interval, 1.17 to 1.32) as compared with nonsmokers not exposed to smoke."
What is the relative risk for the population as a whole? How many things are connected with coronary heart disease? Of the vast number of things that can be tested, very few actually are connected to coronary heart disease, so the chance that any particular thing chosen at random is connected is vanishingly small. Thus we can say that the relative risk for the population is 1. But the quoted interval does not contain the value 1. So either there actually is a connection between the two things, the probability of which is vanishingly small, or this is one of the 5% of intervals that do not contain the parameter. As the latter is far more likely than the former it is what we should assume. Therefore, the appropriate conclusion is that the data set was almost certainly atypical of the population, and thus no connection can be implied.
Of course, if there is some basis for assuming that more than 5% of things are linked to coronary heart disease then there might be some evidence in the statistic to support the suggestion that environmental smoke is one of them. Common sense suggests that this is unlikely.
What is the error in their reasoning (as all health organizations agree that there is significant literature regarding the damaging effects of second-hand smoking)? Is it because of their premise that "Of the vast number of things that can be tested, very few actually are connected to coronary heart disease"? This sentence may be true for any randomly chosen factor (ie. how many dogs a person owns with the risk of coronary artery disease) but the a priori probability is much higher for second hand smoking and coronary heart disease than just 'any random factor'.
Is this the correct reasoning? Or is there something else?