Het volume van chirurgische ingrepen en de impact ervan op ... - KCE

28 Volume Outcome KCE reports 113
These plots are less helpful when the majority of institutions have a very low volume
(one or two interventions) because all units will be concentrated on one dot, and so the
size of the dot needs to be adapted to the number of units on that dot. Also, for
procedures with low rate of events and units with small sample size, the graphic might
give the impression to be “squeezed” if a low volume units has 100% mortality,
The definition of funnel plots has four components. 89 In each unit (hospital or surgeon),
r events are observed out of a sample size n (cross sectional binomial data).
1. An indicator (summary statistic) which is the observed proportion of event
r/n.
2. A target proportion which is the average event rate θ0. It is given by the sum
of all events divided by the sum of all sample sizes.
3. A measure of the precision, in that case given by the unit sample size n.
4. The control limits that depend of the target θ0, of the sample size n and of a
given p-value. These limits are constructed such that the chance of exceeding
these limits for a « in control » unit is p. Usual sets of values for p are
p=0,001, p=0,999 corresponding to 3 SD (the usual limits in control charts
framework), and p=0,025, p=0,975 corresponding to 2 SD (the usual limits
set in the test of hypotheses framework). In the case of binomial cross
θ 0 ( 1−
θ 0 )
sectional data, the limits are given by y p ( θ 0,
n)
= θ 0 + z p
,
n
with zp as such that P(Z ≤ zp)=p for a standard normal distribution Z (z0.025=- 1.96).
Figure 3.4: An example of funnel plot, from Spiegelhalter et al. (2005) 89