Unrepresentative, invalid and misleading: are waiting times for elective admission wrongly calculated?

The UK Government Statistical Service reports the percentage of elective 'admissions' that took place in England within 3 months of a patient being added to NHS waiting lists. This percentage is calculated from cross-sectional data using the total number of elective episodes within a specified calendar period as denominator and the number of these enrolled on the waiting list less than 3 months previously as numerator. This approach assumes that NHS waiting lists are closed and stationary populations, and has been widely used by government and non-government researchers in the UK and elsewhere.

Little attention has been given to the bias introduced when waiting lists are neither stationary nor closed. This paper identifies four groups of patients which are excluded from the denominator used by the Government Statistical Service and criticises the established method of ignoring left and right censored observations.

We describe two alternative formulae that would give the same results as the Government Statistical Service method if waiting lists were closed and stationary, but that also give unbiased results when waiting lists are open and non-stationary. They require a limited amount of additional cross-sectional data to produce upper and lower estimates of the cumulative likelihood of admission among those listed. We recommend the production of unbiased estimates by applying period life-table techniques to a complete and consistent set of 'times since enrolment'.