For Participant 4, a resumed quit attempt at month 9 led to 6 months of abstinence; hence, this participant would be counted as a success. Participant 5 ended follow-up abstinent, but because her quit attempt started after treatment finished, it cannot logically be due to the treatment. We would expect such participants example to be spread evenly across the treatment and control groups, but including them as successes leads to random error and will distort the true treatment effect, usually underestimating it. Whether such people should be counted as successes depends on the plausibility that the treatment induced and sustained abstinence after it was completed. We know of no evidence that pharmacotherapy for smoking cessation supports cessation after participants have ceased using it; thus, in our review, we did not count such participants as successes, even if follow-up had lasted 6 months or more after treatment stopped.

Participant 6 started her quit attempt during the 12th month of treatment and is potentially a success, but follow-up ceased in her 4th month of abstinence. It would be wrong to count her as a failure because she might have continued cessation for 6 months, but she also had not yet sustained abstinence for 6 months and so she was not considered a success. We propose dealing with this case by censoring. We would estimate the proportion of 4-month quit attempts that led to 6 months of abstinence and apply this correction factor to all similar participants who sustained 4 months of abstinence before they were censored. The formula for this process is as follows.

Let N6 represents the potential number of smokers who sustain abstinence for at least 6 months measured from any timepoint during the treatment period. N6 is calculated in two steps: (a) count the uncorrected number of smokers (N6u) who have sustained abstinence for at least 6 months within the study period (starting at any time within treatment period) and (b) calculate the censored number of smokers (N6c) who would have sustained abstinence for at least 6 months if the follow-up had been sufficiently extended. This censored estimate is the sum of the numbers of subjects abstinent for less than 6 months (j [<6] months [Nj]) but still abstinent at the end of the study, multiplied by the probability (Pj) they would have gone on to remain abstinent for at least 6 months.

Pj is obtained from the number of smokers who sustained abstinence for at least 6 months (N6u), divided by the total number of all quits made during the treatment period (excluding those censored [Nj]), that is, , where nj is calculated as the number of smokers who sustain at least j months of abstinence to the end of the follow-up period, excluding those who are AV-951 censored. Although the algorithm has been presented for estimating the rate of sustained abstinence for at least 6 months, it can be generalized to estimate the rate of sustained abstinence for at least T months.