Exploratory data analysis

HES data for 2001/2002 and 2002/2003 covering the English NHS are analysed.

Due to the fact that we have the waiting times for all the admissions recorded in each year the data are complete with respect to date of admission; hence they are not right-censored. This analysis focuses on elective care; it excludes emergency and maternity cases, which are not counted as part of waiting lists.

14http://www.hesonline.nhs.uk/Ease/servlet/ContentServer?siteID=1937&categoryID=331

Data are included on all three principal routes to admission for elective surgery:

waiting lists, where there is no exact date of admission; booked admissions, where there is an exact date for admission; and planned, where there is an exact date of admission for a course of treatment over time or a second operation.

As shown in Table 2.2, waiting times for elective surgery are asymmetrical;

for both years, they are positively skewed with long right tails and have an average of at least 130 days for all methods of admission (waiting lists, booked and planned) and 155 days if admission takes place by waiting lists. Another feature of interest is the huge standard deviations observed for all the cases, revealing the extent of the variability of waits.

Table 2.2: Descriptive statistics of the variable waiting time.

2001/2002 2002/2003

elective waiting list elective waiting list Number of observations 1639007 1052279 1709155 1042757

Mean 130.29 155.67 134.39 161.43

Standard deviation 157.93 155.73 159.78 154.17

Median 70 101 75 112

Minimum 1 1 1 1

Maximum 4236 3691 7577 5102

Skewness 2.94 1.92 3.26 2.09

Kurtosis 21.95 11.32 29.58 16.74

Figure 2.3 illustrates the kernel densities of the patients’ waiting times ad-mitted from a waiting list. The kernel density estimation is a non-parametric way to estimate the probability density function (pdf) of a random variable. It is a data smoothing process in which the smoothing parameter (the bandwidth) has a strong influence on the derived estimate. The kernel densities of Figure 2.3 illustrate that overall waiting times distributions are skewed to the right with the bulk of the distribution lying way below 500 days of wait. However, as the rest of the chapter (and Chapter 3) will show, duration analysis is a much more informative estimation technique.

0.001.002.003.004Density

0 1000 2000 3000 4000

waiting time kernel = epanechnikov, bandwidth = 8.0003

0.001.002.003.004Density

0 1000 2000 3000 4000 5000

waiting time kernel = epanechnikov, bandwidth = 8.6823

Figure 2.3: Kernel densities of waiting times, 2001/2002 (top) and 2002/2003 (bottom).

The probability of remaining on the waiting list past a certain point in time (survival function) may be more interesting than expected waiting time, especially for policymaking. In particular, with regards to the impact of waiting time targets, which is a major focus of this chapter, the kernel density can only provide information on whether the bulk of the distribution lies around the set

targeted waiting time. However, the hazard function can lend more insight on the ‘failure’ mechanism, that is, the response of the admission mechanism to the set target. The hazard rate allows to approximate the probability of exiting the list within an incremental interval, conditional on having ‘survived’ up to that point. It thus approximates the conditional probability of leaving the list given the amount of time on test, rather than the unconditional probability (pdf), and as such is more meaningful.

As we will see, we can utilise the hazard rate to essentially establish whether there is increased probability (or not) of patients being treated ‘around’ the interval of the waiting time target. The duration analysis technique can help us with the question: given that the patients’ duration is approaching the waiting time target, what is the probability of exiting the list? The unconditional probability (pdf) does not take into account the time that has elapsed and the pre-announced waiting time target.

We obtained HES data on each episode, including specialty, diagnosis, op-eration, admitting hospital and type of admission, and on the characteristics of the patient whose episode it was, including age, sex, ethnicity, and residence.

The data were anonymous with respect to patients.

We evaluate data from three specialties: general surgery; trauma and or-thopaedics and ophthalmology. These were chosen because together they con-stitute more than 50% of the patients waiting for elective treatment. Initial analysis reveals some patients who appear to have waited an implausibly long time -some greater than ten years- which is most likely the result of coding prob-lems; consequently, the 0.1% of patients whose waits appeared to be longer than three years were excluded.

We analyse the data at three levels. The incentives associated with waiting times targets apply to the hospital, so it is appropriate to analyse overall hospi-tal waits. However, given the possibility of systematic differences in waiting list

management between specialties within any hospital, we examine the waiting times separately for the three specialties. Moreover, it is possible that waiting lists are managed differently for particular operations, so we also focus on the four most frequently performed procedures within each specialty, as described in Table 2.3.

Table2.3:Thefourmostcommonproceduresineachofthethreesurgicalspecialties. SurgicalspecialtiesandtheircommonproceduresPercentage Generalsurgery Excisionofgallbladder(totalcholecystectomy)26%ofallgeneralsurgery Ligationofvaricoseveinsofleg Excisionoflesionofskin Primaryrepairofinguinalhernia Trauma&Orthopaedics Releaseofentrapmentofperipheralnerveatwrist28%ofallorthopaedicsurgery Totalprostheticreplacementofhipjointusingcement Totalprostheticreplacementofkneejointusingcement Endoscopicoperationsonsemilunarcartilage Ophthalmology Extirpationoflesionofeyelid71%ofallophthalmologicsurgery; Incisionofcapsuleoflenslensprosthesisaccountsfor62% Prosthesisoflens Cauterisationoflesionofretina Source:HospitalEpisodeStatistics

2.4 Results

We start off by analysing the managing of waiting times according to clini-cal characteristics; that is specialty, operative procedure and admission source.

We then explore the overall waiting times of a selected set of NHS hospitals for both years. In all levels of analysis, the survival and hazard functions are estimated non-parametrically and the long-rank test for significance of differ-ences is performed. Also, note that the HES data are very rich and a fine level of disaggregation of the data is possible. This generates a very large set of possible analyses; here only a fraction of the results generated is reported. Key differences or similarities between the data that were selected for presentation, and those not shown, are identified.