Why does the number of people waiting for outpatient appointments reach its height in September? The answer, says Rodney Jones, can be found in the mismatch between supply and demand

There was much alarm this autumn in the NHS at the apparent rise in the number of outpatients waiting longer than 13 weeks for their first appointment. But in fact the alarm was not warranted since the total number of patients waiting (and hence those waiting longer than 13 weeks) always reaches a seasonal peak in September.

Figure 1 gives an example from one trust covering the past three years (the September 2000 figure is an actual number, whereas December 2000 and March 2001 figures are forecast from the underlying seasonal pattern, plus additional work to achieve waiting-time targets).

This seasonal behaviour is fundamental to the forecasting of the total number waiting for an appointment and thus the outpatient waiting time.

Any waiting list is simply the difference between demand (GP referrals) and supply (available consultant first appointments). If demand and supply follow different monthly patterns, then the number waiting will fluctuate accordingly. We need therefore to determine why these two processes should follow different patterns.

Let us turn first to demand - namely, the number of GP referrals made each month. All disease conditions are seasonal and hence it should be no surprise if a unique GP referral profile is required for each specialty.

1This referral profile will be the composite profile arising from the basket of disease conditions encountered in that specialty.

Figure 2 shows the profile for referrals to the varicose veins clinic, a sub-specialty within general surgery. Of interest is the fact that the seasonal profile (as referrals per workday) does not vary greatly from the pattern expected in a given year (as GP referrals per workday multiplied by the number of workdays in the month - ie the total number of referrals per month).

This indicates that holiday periods of summer and Christmas have little impact on attendance at a GP surgery - a crucial point in the difference between demand and supply that will be discussed later. Table 1 gives further examples of referral profiles for several specialties. Figures in table 1 come from a 10-year sample covering the period 1985-95.

2Ten years of data is required in order to obtain a true average in the face of considerable randomness in the actual monthly results.

Results have been adjusted for differing work days per month in various years and re-calculated for the working-day profile applicable to 2000-01. As can be seen, each specialty does indeed have a unique profile. Several specialties in table 1 have been taken to sub-specialty level to illustrate important driving forces behind referrals. For instance, the ear, nose and throat profile is close to the profile experienced for respiratory allergy. In this case the peaks and troughs of the sub-specialty are diminished when mixed with the wider range of conditions encountered within ENT, many of which may also be responding to the same causative sources as respiratory allergy.

To determine the impact of the different profiles of GP referral on the profile for the number of patients waiting longer than 13 weeks, it is important to weight the contribution of each specialty by the total number of patients experiencing a long wait. This is illustrated in table 2, where national figures have been used (see page 31).

3As can be seen, 91 per cent of patients waiting longer than 13 weeks come from just eight specialties.

For some specialties such as varicose veins (hence general surgery), dermatology (also allergy - respiratory, skin and other) and ophthalmology there are more GP referrals in the first half of the year. Referrals for varicose veins probably represents the extreme case, with 62 per cent of referrals occurring in the first half of the year.

Although trauma and orthopaedics constitutes around 25 per cent of all NHS outpatients waiting longer than 13 weeks, the referrals are fairly balanced, with 49 per cent of referrals in the first half of the year.However, the number waiting still reaches a peak in September each year.How can we explain this apparent discrepancy?

Consultant clinics are normally held on a set day each week - for example, Mr X's urology clinic is held on a Monday. Table 3 gives the number of workdays available in a year to clinics held on particular days of the week.From table 3 we can see that Monday and Friday clinics suffer from lost productivity due to public holidays and that 200001 has the minimum possible number of Mondays available.

The number of workdays in a year ranges from 251 to 255 with 2000-01 having only 252. This difference in the number of workdays available in different years partly explains why NHS productivity is higher or lower in particular years.

Returning to the case of trauma and orthopaedics, this specialty runs both general orthopaedic and fracture clinics. Given the more immediate demands of a fracture clinic (equivalent to all urgent appointments), they are not usually run on a Monday or Friday (for obvious reasons) leaving the mainly GPreferred orthopaedic patients to be seen on the days when potential annual capacity is lowest.

Access to a GP is not, however, subject to these constraints. For example, each GP practice usually has a range of GPs available at any time. If a condition is acute, the patient can then visit any member of the team of GPs in order to obtain a referral. The only limitation in this case is the number of working days in the week or month.

For these reasons GP referrals follow a pattern relating to the total number of workdays available in a week and month, while consultant first appointments follow the profile particular to the day on which the clinic is held.

For example, in 2000-01 some 47.8 per cent of working Mondays occur in the first half of the year, while 49.6 per cent of available working days occur in the first half of the year.

The number of patients waiting longer than 13 weeks is the equivalent of water added to a full dam running over the causeway. The difference between demand and supply therefore shows up in the number of patients waiting longer than 13 weeks.

In the example above it is 1.8 per cent (49.6 - 47.8) of the total demand which then inflates the number waiting longer than 13 weeks. This magnifying effect therefore leads to the appearance of an 'alarming' increase in numbers waiting over 13 weeks up to September followed by an equally rapid reduction over the next six months.

This difference is further increased by the effect of the summer holidays. In this instance, consultant appointments are greatly reduced during August and September while the opportunity to visit a GP is not. Adjusting for the effect of holiday periods gives only 45 per cent of available working Mondays in the first half of the year compared to 49.6 per cent of available working days.

Corresponding figures in 2000-01 for the other days are Tuesday (48.9 per cent), Wednesday and Thursday (47.9 per cent) and Friday (46.8 per cent).

Thus for all consultant clinics (irrespective of the day of the week on which the clinic may be held) there are always more opportunities for GP referral in the first half of the year than there are available outpatient appointments. The supply side of our equation -namely, consultant first appointments, therefore lags considerably behind the opportunity for GP referral during the first half of the year.

Hence the number of patients waiting for a first appointment (and hence waiting time) climbs to a September peak every year. In the second half of the year this pattern is reversed and so by the end of March the total number of patients waiting for their first consultant appointment returns almost back to the previous year-end total. Any change is accounted for in the difference between total demand and supply across the whole year.

In conclusion, the total number waiting for a first appointment always rises to a seasonal peak in September due to the higher relative opportunity to obtain a GP appointment during the first half of the year as opposed to a consultant appointment.

This seasonal peak, caused by the mismatch between supply and demand, is further magnified in particular specialties such as general surgery, dermatology and ophthalmology, where the seasonal profile of the disease(s) in that specialty leads to more than 50 per cent of referrals occurring in the first half of the year.

REFERENCES

1 Fleming D et al. Annual and Seasonal Variation in the Incidence of Common Diseases. Occasional Paper No 53. Royal College of General Practitioners, 1995. ISBN 085041615.

2 The Central Bureau of the Royal Berkshire Hospital. Manually Collected Raw Data Covering Referral to Individual Consultants and Sub-specialties Between 1985 and 1995.

3 Data is for March 2000. NHS website

4 Jones, R. Estimation of Annual Activity and the Use of Activity Multipliers. Health Informatics 1996; 2, 71-77.

5 Jones, R.How Many Patients Next Year? Healthcare Analysis and Forecasting, 1996. Reading, UK.