Fact or fiction : the problem of bias in Government Statistical Service estimates of patient waiting times
The cumulative likelihood of admission estimated for any given 'time-since-enrolment' depends on how we define membership of the population 'at-risk' and on how we handle right and left censored waiting times. As a result, published statistics will be biased because they assume that the waiting list is both stationary and closed and exclude all those not yet or never to be admitted. The cumulative likelihood of admission within three months was estimated using the Government Statistical Service method and compared with estimates which relaxed the assumption of stationarity and reflected variation in the numbers recruited to, and admitted from, the waiting list each quarter. The difference between the two estimates ranged from +5.5 to -9.1 percentage points among 11 Orthopaedic waiting lists in South Thames Region. In the absence of information on 'times-to-admission', exact 'times-since-enrolment' were extracted from Hospital Episode Statistics and assumed to be similarly distributed. In the absence of information on 'times-to-competing-event', the number of competing events falling in each waiting time category was estimated by differencing. A period lifetable was constructed using these approximations, census counts, counts of the number of new recruits and estimates of the number 'reset-to-zero' each quarter. The results support the view that the method used by the Government Statistical Service overestimates the cumulative likelihood of elective admission among those listed. The Government Statistical Service calculates the cumulative likelihood of admission within three months (range: 0.62-0.27) conditional on the fact of admission. Multiplying by the unconditional likelihood of being admitted (range: 0.93-0.31) estimates the cumulative likelihood of admission within three months among those listed (range: 0.55-0.12) and gives a rather different ranking of waiting list performance among 34 Orthopaedic waiting lists in South Thames Region.