The ebb and flow of the NHS waiting list: how do recruitment and admission affect event-based measures of the length of 'time-to-admission'?

The likelihood of admission is reported in England as the percentage of elective episodes occurring within a certain time, for example, within three months of the date of enrollment on the waiting list. This event-based measure is calculated from cross-sectional data: the denominator is the number of elective episodes occurring in a specified calendar period, and the numerator is the number found to have enrolled on the waiting list less than three months previously. Now the number of elective episodes occurring within three months reflects the likelihood of admission and the numbers eligible to be admitted. If there is any increase in the likelihood of admission or in the number of people exposed to that likelihood then there will be an increase in the number of elective episodes found to have enrolled on the waiting list less than three months previously. Thus the numerator used by the Government Statistical Service accurately reflects conditions during the calendar period and within the enrollment cohorts of interest. The Government Statistical Service also needs a denominator so the episodes observed 0-2, 3-5, 6-8, 9-11 etc. months after enrollment are added as an indication of the number of people that could have been admitted within three months. This denominator implies that the number of people eligible for admission from the 3-5 month waiting time category is the same as the number surviving admission from the 0-2 month waiting time category but, during the period of interest, these two groups of people belong to cohorts that were recruited to the waiting list quite independently. As a result, this denominator will be too big if the number surviving to the end of one waiting time category is bigger than the number eligible for admission from the next and it will be too small if the number surviving to the end of one waiting time category is smaller than the number eligible for admission from the next. The event-based measure assumes that the waiting list is stationary and closed and only gives unbiased estimates under these conditions. This paper describes three alternative measures which recognize that the number of people recruited or admitted may vary from one quarter to the next. It uses Department of Health data to assess the size of the error if the event-based measure is used in these circumstances.