Melanie A Wakefield PhD et al.

Statistical comments

Statistician: Hazel Inskip

This is an interesting paper particularly given the concerns about teenage smoking. I do

however have a number of comments:

1. The statistical methods are rather complex and the methods were not familiar to me though I understood the gist of what was done. It seems similar to ordinal logistic regression but is a method that I have not come across before. I think it would be helpful if the authors would spell out exactly what the resulting odds ratios mean. My impression is that each odds ratio in Table 2 represents the odds ratio for being in the group given compared to the baseline group as a result of the restrictions/bans being in place. However, colleagues on the ‘Hanging Committee’ had not been able to work this out and I could well be wrong. I am particularly doubtful as I am not clear what is meant by the ‘non-proportional’ differences from the odds ratio at the first threshold. Presumably, below the first threshold the odds ratio is 1, since this is the baseline, and odds ratios indicate proportional reductions - so what does ‘non-proportional’ mean?

2. Also in Table 2, I do not understand why there are gaps in two of the rows. There is no explanation given for this.

3. I was not clear about the response rate. We are told that 73% of the schools selected as primary or reserve schools participated. But how many primary sample schools were chosen? How often was it necessary to choose a first reserve, second reserve etc?

4. The definition of number of cigarettes smoked per day confused me. If someone had smoked one cigarette in the last thirty days the definition given on page 9 implies that they are categorised exactly the same as someone who smoked one each day. Since these are people who may be experimenting with cigarettes and often obtaining them illegally then some respondents may have smoked a large number one day but not on any other day. This needs clarification because large differences in cigarette consumption appear to be being grouped together here.

5. I would suggest dropping Table 4 or alternatively converting the estimates into proportional

6. Reductions in numbers of cigarettes smoked if the ban/restrictions were in place. Most people will find it impossible to interpret a reduction of 0.02 in the logarithm of the number of cigarettes smoked. If the table is retained then confidence intervals should be given for the estimates of reduction. If the definition of number of cigarettes smoked is as it appears to me at the moment then this table is likely to add little to the paper (see comment above).

7. The pupils are asked individually about the existence of school bans and if in place whether they were strictly enforced or not. Was there agreement between the pupils within schools over these answers? I could imagine that in a school where there was a school ban, those who flout it may think that it is not well enforced, whereas those who do not smoke may think that it is more strict. Since the data are analysed at an individual level this could have an impact on the strength of the associations. Some comment on the concordance within schools would be helpful.