Long-term benzodiazepine and Z-drugs: are we committing the denominator fallacy?

In a US population of patients co-prescribed benzodiazepines with antidepressants, only 12% went on to long-term use.¹ Yet, in this UK study, ‘35% of all users of BZD are taking these drugs long term’.² How can we reconcile these two findings? One possibility is that UK prescribing is more liberal than in the US. Another is that the UK study looked at BZDs (benzodiazepines and Z drugs), whereas the US study looked at benzodiazepines alone.

Another explanation is the difference between individual risk and prevalence. In a survey of 1 year’s BZD prescriptions, you are likely to include those patients who started in previous years and are still receiving a BZD prescription, but omit shorter-term users from previous years. This increases your numerator (longer-term users) but omits short-term users from the denominator (all users), inflating the percentage of longer-term users. In fact, it is not clear how they calculate ‘that 35% of all users of BZD are taking these drugs long term’. If, for example, the search strategy was ‘all patients prescribed BZD in 2014 or 2015’, then longer-term users who started in 2013 or earlier would be captured, but shorter-term users would not. It may therefore be valid to say that ‘over the time period studied, 35% of patients prescribed a BZD are taking these drugs long term’. This does not, however, equate to the risk to an individual of their BZD use becoming long term (which Bushnell et al estimate at 12%, albeit in a different population).¹

We are in danger of committing the prosecutor’s fallacy, assuming P(A|B) = P(B|A); that is, probability of A given B = probability of B given A. The ‘denominator fallacy’,³ failing to identify the denominator correctly, which has been previously described in medicine and beyond, is also relevant here. I would suggest that patients are more interested in individual risks than in population statistics. Doctors of course need to be aware of prevalence, not least when designing services. But with a patient in front of us, it’s important we don’t confuse the two.