Vol2, No. 2
Printed in Great Britain
Family Practice
© Oxford University Press 1985
The Denominator for Audit in General
Practice
D M FLEMING
undertaken by an individual doctor. Between
each denominator, one possible source of bias is
entered; there are many others and some operate
at more than one level. The net effect of different
biases may be compensatory, but, equally, it may
be additive or even cumulative, hence inferences
drawn at one level cannot be applied at another
without first considering the impact of bias.
In general practice the age-sex register defines
the population. The discipline of maintaining an
accurate register is considerable and though
errors do occur,1-2 it remains the best source of a
practice population denominator. It permits
The interpretation of a measured value requires
reference to a standard. For some parameters,
for example body temperature, a reference
standard has been established by repeated
measurement, using an instrument which has
itself been calibrated against an absolute
standard. In using a thermometer we rely on the
accuracy of the instrument. In epidemiological
studies we count events, for example disease
episodes, but the interpretation of the count
depends on a reliable measure of the population
to which the count relates. In this paper the
problem of a reliable practice-based denominator
is considered. Without one we cannot make
comparisons. The paper is not concerned with the
numerator and its related issues, including such
issues as the accuracy of diagnosis, completeness
of count or adequacy of samples.
The usefulness of a population denominator
depends on limiting the potential for bias. In
Figure 1 possible denominators are considered
ranging from the national population through
stages down to the number of consultations
Denominators
Examples of bias
National or area
population
District of local
population
Practice registered
list size
Number of persons
consulting in practice
Ethnic minorities
Sex of doctor
Proximity of practice premises
Special interests of doctor
Number of consultations
Birmingham Research Unit of the Royal College of General Practitioners, Lordswood House, 54 Lordswood Road, Harborne,
Birmingham BI7 9DB.
FIGURE 1 Denominators and bias in practice statistics
76
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Fleming D M (Birmingham Research Unit of the RCGP, Lordswood House, 54 Lordswood Road, Harborne,
Birmingham B17 9DB). The denominator for audit in general practice. Family Practice 1985; 2: 76-81.
Different denominators for morbidity studies were compared from two large studies in Britain. From the
second national morbidity survey, data from 24 single-handed doctors showed a close correlation between
the denominators 'persons consulting' and 'list size' (r > 0.9) in both years of the survey, but a weaker
correlation between 'consultations' and 'list size' (r = 0.6). However, when examining rank order statistics
for visiting and out-patient referral rates, it was immaterial for most doctors which denominator was
chosen. Only for recorders with a consultation rate at the extremes of the range was the choice of
denominator critical to the interpretation of the data.
In the practice activity analysis study, based on 47 doctors and a mean of 284 consultations in two weeks,
the correlation between 'persons consulting' and 'total consultations' was 0.99. Thus the number of
consultations provided a satisfactory proxy for persons consulting in a two-week study.
These results justify the use of 'consultations' over two weeks as a denominator in general practice audit in
circumstances where rank order is appropriate for the interpretation of data.
THE DENOMINATOR IN GENERAL PRACTICE
METHOD
Data provided by singlehanded general practitioners recruited to the second national morbidity
survey3 and from practice activity analysis4 were
examined with particular reference to the
acceptability of the number of consultations as a
denominator, notably when using rank order
statistics. A variety of statistical methods were
used. Some data were described using the mean,
standard deviation, coefficient of variation
(standard deviation divided by mean) and
correlation coefficient. These statistics apply
chiefly to data which are normally distributed.
The standard deviation is a measure of spread of
a distribution. The coefficient of variation
permits comparison of variability in one set of
data with that in another; a value exceeding 0.5
indicates great variation and a value less than 0.1
little variation. The correlation coefficient is a
mathematical expression of the association
between paired sets of numbers; a value exceeding 0.9 is very high, exceeding 0.7 is substantial
and exceeding 0.5 is important. A value less than
0.3 is rarely of importance by itself even though it
may be highly significant statistically.
When the underlying distribution of data is not
known or when the distribution is not normal,
rank order statistics are preferable. These include
median values, centile distributions and rank
correlations. The significance of the rank correlation coefficient is similar to that of the correlation coefficient referred to above.
RESULTS
Second National Morbidity Survey Data
Twenty-five single-handed general practitioners
contributed data to the first two years of the
second national morbidity survey. The distributions of these practices for the rates of persons
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comparison between practices, especially if
standardization techniques are employed in
which the differing age-sex and social composition of the practices are recognized. Much
variation in data is determined by doctors, and
without the ability to look individually at doctors
—as opposed to practices—important differences
are missed. In addition, if performance review is
to have any place in medical education, we must
obtain satisfactory means of providing measures
of individual performance. In this context the
relativity of performance is often more important
than the absolute level.
77
consulting and for consultations per 1000
registered list are presented as histograms in
Figure 2 for each year. The registered list in the
national 'morbidity survey took account of
registrations for part of the year and was
calculated as the sum of patient days registered
divided by 365. In one practice the person consulting rate was 40°7o in both years of the study,
whereas in all other practices this value exceeded
60%. With this exception, the results from the
remaining 24 practices were normally distributed
in both years of the study; the analyses presented
here are based exclusively on these practices.
A mathematical analysis of the data from both
years is provided in Table 1, showing the mean
practice values, standard deviations and coefficients of variation. Table 1 also shows the
correlations between the values of the 'list' and
'persons consulting' and between the 'list' and
'consultations'. On average, approximately
10000 consultations were provided for 2000
persons consulting out of a list of 3000 patients.
The correlations between list size and number of
persons consulting were 0.% and 0.94 for years 1
and 2 respectively, and between list size and
number of consultations were 0.61 and 0.62. The
coefficient of variation was approximately 0.2
for all the statistics. The correlation between the
number of persons consulting in year 1 and the
number of patients registered at any time during
the study year (mean 3149) was 0.96—virtually
the same as that with the list defined above.
The mean practice rates for percentage of
persons consulting and number of consultations
per person are reported in Table 2. The correlations of practice rates in year 1 compared with
year 2 were high (r = 0.94 for 'persons consulting'
and 0.95 for 'consultations per person'). The
coefficient of variation for the 'persons consulting' rate (0.07) was less than that for 'consultation' rate (0.21).
The ranges of home visiting and out-patient
referral rates are detailed in Table 3, specifying
the median and the 20th and 80th centile rates.
The ranges of performance illustrated by the
factorial difference between the 20th and 80th
centiles were similar regardless of the
denominator.
In Table 4, the rank order of the study doctors
for the rates of home visits and out-patient
referrals are compared. These are presented in
quintile groups (low to high, A to E) using
'registered list', 'persons consulting' and 'con-
78
FAMILY PRACTICE—AN INTERNATIONAL JOURNAL
Year 1
10 r
_ _
Year 2
u
o
-o
X)
E
1
:3
<45
45 50 55 60 65 70 75 80 85 <45 45 50 55 60 65 70 75 80 85
Percentage of persons consulting
Percentage of persons consulting
Year 1
locto
10
25
«
XI
E
-
Year 2
.'•• f
}•
; • ' . < ; : ;
-
3
z
r
n
<2.5 2.5 3 3.5 4 4.5 5 5.5 6
Number of consultations per patient
1
<2.5 2.5 3 3.5 4 4.5 5 5.5
Number of consultations per patient
FIGURE 2 Distribution of single-handed doctorsfor percentage ofpersons consulting and consultations per patient in years 1 and
2 (n = 25 doctors)
TABLE 1 Consultation data for 24 single-handed general practitioners in the national morbidity survey: comparison of list size,
number of persons consulting and number of consultations in years 1 and 2
Year 2
Year I
Denominator
List size (no.)
Persons consulting
(no.)
Consultations (no.)
SD = standard deviation.
Mean
(SD)
Coefficient Correlation
of variation with list
Mean
(SD)
Coefficient Correlation
of variation with list
2935
(622)
0.21
_
2999
(635)
0.21
2052
10144
(407)
(2309)
0.20
0.23
0.96
0.61
2056
9994
(421)
(2611)
0.20
0.26
0.94
0.62
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.*"•: "3
79
THE DENOMINATOR IN GENERAL PRACTICE
TABLE 2
Consultation data for 24 single-handed general practitioners: comparison of percentage of persons consulting with
consultations per person
Year 1
Year 2
Denominator
Mean
(SD)
Coefficient
of variation
Mean
(SD)
Persons consulting (%)
Consultations per person (no.)
70.3
3.52
(4.8)
(0.73)
0.07
0.21
69.0
3.41
(5.5)
(0.73)
Practice Activity Analysis Data
Forty-nine doctors completed a specific practice
activity analysis investigating the distinction
TABLE 3
between the total number of consultations and
the number of patients seen in a two-week period.
The distribution by doctor according to the
number of consultations undertaken was close to
the normal (Figure 3). Two recorders reported
respectively 111 and 136 consultations during the
two weeks—less than half the mean number
usually encountered in practice activity analysis
data—and were therefore excluded from this
analysis. The mean number of consultations in
two weeks undertaken by the remaining 47
doctors was 284. Further information about the
results from individual practices is presented in
Table 6. Patients consulting for the first time
made up 89.5% of all consultations; this was a
highly consistent figure (standard deviation 3.4,
coefficient of variance 0.07). The correlation
between the number of persons consulting and
the number of consultations was 0.99.
DISCUSSION
In the national morbidity survey data the
information content about both the range of
home visiting and referrals to out-patient departments was similar regardless of the denominator,
yet the correlation between the number of consultations and the list size in individual practices
(0.62) was insufficient to justify the use of
number of consultations as a denominator when
comparing the rates between practices. The cor-
Distribution of practice results for home visiting and out-patient referral rates by list size, number of
persons consulting and number of consultations
Home visiting
List
Maximum
80th centile
Median
20th centile
Minimum
0.94
0.95
0.08
0.21
1445
686
520
407
134
Out-patient referrals
Persons
consulting Consultations
1988
968
771
604
161
328
189
160
126
49
List
219
130
85
69
43
Persons
consulting Consultations
301
186
123
98
67
54
38
25
20
13
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sultations' as denominators. The rank correlation
coefficient between practice rates for the number
of persons consulting and the list size was 0.97
and between number of consultations and list size
was 0.89.
Eight instances were identified in which a rank
order differed by five places or more (one
quintile) from that using the list size as
denominator: one involving 'persons consulting'
and seven involving 'consultations'. These differences occurred among the five practices for
which consultation data are summarized on
Table 5. Reference to the histograms in Figure 2
show that these consultation rate values are at the
extreme ends of the range: the three highest and
the two lowest recorded rates. With the exception
of practice 4, these practices were also at the
extremes of the range for number of persons consulting. Among all the rank order differences
identified here, only that for referrals in practice
5 presented confusion in interpretation of the
data, since this recorder was identified as being in
the highest group when using the list size or
number of persons consulting as denominators
but substantially nearer the median when using
number of consultations as the denominator.
Correlation
Coefficient
of variation year 1 vs year 2
80
FAMILY PRACTICE—AN INTERNATIONAL JOURNAL
TABLE 4
Rank order comparison using list size, number of persons consulting and number of consultations as
denominators
Rank order of out-patient referral rates
Rank order of visiting rates
Persons
consulting Consultations
Consultations
1
2
3
4
5
2
1
3
4
5
1
2
4
3
7
1
2
3
4
5
1
2
4
3
5
2
1
5
3
4
B
6
7
8
9
10
9
6
7
10
12
11*
9
8
6
21*
6
7
8
9
10
9
11
6
10
8
6
14*
10
7
9
C
11
12
13
14
14
11
13
S*
15
10
12
5*
11
12
13
14
7
12
13
15
11
12
15
20*
D
15
16
17
18
19
15
16
17
18
19
13
16
17
14
19
15
16
17
18
19
16
14
17
18
19
8*
3*
17
18
19
E(high)
20
21
22
23
24
20
22
21
23
24
20
22
18
24
23
20
21
22
23
24
20
21
22
23
24
21
22
16*
23
24
A (low)
List
Rank correlation
coefficient vs list
0.97
0.87
List
0.98
0.91
* Rank difference of five or more places compared with list.
TABLE 5 Consultation data in five practices showing rank
order differences when using alternative denominators for
expressing visiting (V) and referral (R) rates
Practice
Activity
Percentage of
persons
consulting
1
2
3
4
5
VandR
VandR
V
R
R
61.3
62.5
81.1
72.6
82.1
Number of
consultations
per person
2.34
2.74
4.51
4.92
5.76
relation between the number of persons consulting and the list size was high and it is debatable
which of these denominators should be preferred.
If the problems of the maintenance of an age-sex
register—such as have been outlined by Fraser1
and Bentsen2—could be overcome, then on
theoretical grounds the age-sex composition of
the practice is a more satisfactory denominator.
'Persons consulting' provides an acceptable
denominator5 where the age-sex register is of
suspect quality or in countries where formal
patient registration procedures are not necessary.
The improvement obtained by considering total
patients registered at any time during the year as
opposed to a population denominator taking
account of registrations for part of the year was
so small that for most purposes it is not necessary
to take the trouble to define this statistic
separately.
For the individual recording doctor in the
national morbidity survey it is immaterial from
the rank order statistics whether 'list' or 'persons
consulting* is used as the denominator. Despite
the limited direct correlation between number of
consultations and list size, the rank order correla-
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Persons
consulting
Quintile group
THE DENOMINATOR IN GENERAL PRACTICE
II
« 10
L
2
o
•a
e
z
5 -
149
199 249
299 349 399
Number of consultations in two weeks.
449
FIGURE 3 Distribution of doctors by number of consultations undertaken in two weeks (n = 49 doctors)
TABLE 6 Mean number of consultations with patients seen
for the first, second, third, fourth or more times in two weeks
(n = 47 recorders)
Consultations
Number of times the
same patient was seen
in two weeks
Mean
number
(SD)
Percentage
of total
One
Two
Three
Four or more
254
23
4
2
(56)
89.5
8.2
1.4
0.9
Total
284
(63)
100.0
Correlation of persons consulting with consultations = 0.99.
NB: Values shown to the nearest whole number.
tions of event rates based on these two denominators was high (0.9) and only in isolated instances
was the difference for any individual doctor
important for the interpretation of the data.
Those doctors whose differences were important
were all identifiable in consultation data as being
at the extremes for the statistics for 'consultations' per 1000 list or 'persons consulting' per
1000 list. The apparent difference between the
correlation of absolute values for 'consultations'
and 'list' and the rank correlation of the event
.rates using the two denominators reflects the
reduced variation in consultation rates compared
with that in visiting and referral rates. The
extremely high correlation of consultation rates
from one year to the next emphasizes the con-
sistency of doctor behaviour. A doctor's consultation pattern is fixed, though this does not
exclude the possibility of short and limited
disruptions of a regular pattern; a matter for
consideration when defining the sample period.
Consultation data from practice activity
analysis showed that the number of consultations
during two weeks is a satisfactory proxy for the
number of persons consulting in that period.
Thus, for practical purposes it is an acceptable
denominator for use in short-term studies
especially for audit purposes, where rank order
and the identification of extremes are important
for the interpretation of data. When interpreting
individual data, careful note should be taken of
the overall rate of consultations per 1000 list.
1
2
3
4
3
REFERENCES
Fraser B C. Patient movements and the accuracy of the
age-sex register. J R Coll Gen Pract 1982; 32:
615-622.
Bentsen B G. The pitfalls of the denominator: towards an
accurate estimation of a population at risk. Family
Practice 1984; 1:86-91.
Office of Population Censuses and Surveys/Department of
Health and Social Security/Royal College of General
Practitioners. Morbidity statistics from general
practice. Studies on medical and population subjects
no. 26. Second national study 1970-71. London:
HMSO, 1974.
Fleming D M. Practice Activity Analysis. Medical Education. Update 1982; 15 March.
Fleming D M. The population at risk. Allgemeinmedicin
International 1983; 3.
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