A System Dynamics Approach to Analysing NHS Waiting Times
Ann van Ackere” and Peter Smith”
London Business School, “ University of York
The United Kingdom National Health Service (NHS) delivers 95% of the country’s health
care. It is a public sector organization which delivers health care free of charge at the point
of access. With the exception of emergency services, patients cannot refer themselves directly
to NHS hospitals. Instead they must be teferred-by a family practitioner, who acts as the
"gatekeeper" to hospital health care. If referrals to hospitals give rise to excess demand,
rationing takes place in the form of waiting lists for non-emergency procedures. There is a
small private sector which is used by some patients who have the means to bypass the NHS
queues.
The issue of NHS waiting lists and the associated problem of waiting times for elective
surgery has been a source of acute public and political concern since the inception of the NHS
in 1948. Although most patients were treated reasonably quickly (about 2/3 within 3 months)
there were always a small minority who had to wait very long times for surgery. In response
to this, the UK Government set up in 1991 a "Patient’s Charter" which, amongst other things,
placed a duty on local hospitals to ensure that all patients received treatment within two years
of being put on a waiting list. This has had a dramatic effect in eliminating the very long
waits experienced by some patients, and the Patient’s Charter has now been amended to
reduce waiting times for certain conditions still further.
Thus waiting times play a key role in the functioning of the NHS. On the demand side, a long
expected waiting time may persuade a patient to forego treatment or to seek private health
care. On the supply side, long waiting times reflect poorly on local management. In response
to long waiting times, management might therefore either devote more resources to inpatient
surgery, or seek to use those resources more efficiently.
Previous analyses of this problem mostly consider a static framework. Martin and Smith [1]
model waiting times for elective surgery, using comprehensive data for 1991-92. They
assume an equilibrium situation, and estimate a demand and a supply equation. The resulting
coefficients are estimates of the elasticity of the dependent variables (demand and waiting
time) with respect to the explanatory variables. This paper builds on this work by adding the
dynamic dimension, using a system dynamics approach. The estimates provided by Martin
and Smith enable meaningful parameterization of the model.
Figure 1 shows a simple causal loop diagram illustrating the key feedback structure, which
consists of two feedback loops: longer waiting times lead to pressure for more resources (and
more effective use of available resources), and lower demand, both of which yield shorter
waiting times. Figure 2 shows the stock and flow diagram, as well as the equations. The
waiting list increases by referrals, a reflection of demand. The list is depleted as patients are
treated. The treatment rate depends on the number of beds (a measure of capacity) and
efficiency (inefficiency is measured as the average length of stay). Changes in demand, beds
and inefficiency result from changes in the perceived waiting time, and their elasticity with
respect to waiting time. The elasticities of beds and inefficiency are assumed constant, while
the elasticity of demand depends on perceived waiting time in a highly non-linear way (see
figure 3). The “external change in beds" is used to subject the model to a step change in
resources (beds).
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Figure 4 shows the results of 4 simulation runs. Runs 1 and 2 consider a 10% increase in
resources, staring from an average waiting time of 3 and 4.5 months respectively. Runs 3 and
4 consider a 10% decrease in resources for the same cases. Note that combining cases 2 and
3 can be interpreted as transferring resources from. a ‘short wait’ region to a ‘long wait’
region.
Figure 4A shows that it is comparatively easy to achieve significant reductions in waiting time
when the initial waiting list is shorter: a reduction of 0.8 months (just over 25%) in run 1,
compared to a reduction of 0.5-months (barely 12%) in run 2. The deterioration resulting
from a reduction in resources is of the same order of magnitude for both cases: respectively
28% and 25% in runs 3 and 4.
Figure 4B shows the impact on demand: changes in resources are partially off-set by changes
in demand when the average waiting time lies in the "sensitive" region (with our
parameterization, between 3 and 5.5 months).
Figure 4C shows the internal pressures on the reallocation of resources when average waiting
times change due to a sudden change in resources. Only in mun 4 (long initial waiting time
and resource increase) does the externally induced change resist fairly well to internal
pressures.
The present model needs further refining. For instance, the time required for changes in
waiting time to affect demand, number of beds and efficiency is assumed to be the same, un
unrealistic assumption. Further work will consider a more detailed model of the demand side,
including referral patterns, and a more realistic representation of changes in resources.
Reference
[1] Martin and Smith, Modelling Waiting Times for Elective Surgery, 1995
Acknowledgment
We are grateful to Stephen Martin for providing us with further estimates of the various
elasticities, not included in [1]
Figure 1
Corba
Resources v=) Average waiting time Cy Demand
NU XU
Figure 2
Waiting list ase
Changes in divers ae Wang fst
Referrals Patients treated
Elasticity of demand &
Change in
Perceived|walting time
Inetfiaency
‘Change in perceived waithhg time
Beds
:xtemal change In beds Change in beds
e) = Kt nel Perceived waiting time
Change in perceived welting time “Tana: to:peresive, waking tre
Elasticity of beds
Inefficiency Wating Het
‘Change in inefficlency Cl Percetved_weiting_time(t) = Percsived_welting_timett- dt) + (Change_in_perosived_waiting_time)
a
INIT Percetved_waing_time = Walling_SsiPatients_treated (months)
rT f inet fic INFLOWS:
lasticity of inefficiency ne an sisiieite»
(Walting_time- Perceived SerPocabed eth teTine6, perch, wating efron pa mo
DD Watling. bei) = Wating_lat t+ (Referral - Paberts_trstod) * at
Changes in drivers INIT Weating_Bet = 300 {petierts}
(CO Bede(t) © Bedest - dt) + (Change_i_beda + Extemel_change_in_bede) * ot INFLOWS:
INIT Beds = 10 (beds) @ Reterraia = Demand (patients pec month)
INFLOWS, OUTFLOWS:
“8 Change_in_bede = “A Pationts_tealed = Beds/inetiiency {patients per month; see document for comment on
Elesticily_of_beds’Beds*Change_in_peroeived_watting_time/Percelved_watiing_time (beds units)
per month) ® O Time_to_pecceive_waiting_tme « 3 {monthe) ‘
W_ Extornal_change_in_bede * GRAPH(Time) © Waiting _time = Watting_KstPatients_treated (montha)
(8 00, 0.00), (10 0, 1.00), (11.0, 000), (12 0, 0 00)
GI Demandit) = Demandit - di) + (Change _in_demand) * ot
INIT Demand « 100 (patients per mort)
INFLOWS: -o7Tr TF
44 Change_In_demand = Elasticty_of_demend"Demand"Change_in_perceived_waiing_trme! . e
Figure 3
Perceived_waiting_tme (people per month) \
OO Ineticioncytt) = Inefiiclencytt - ot) + (Change_In_inefficieny) * dt
INIT inefficiency = 0.1 {monthe, inefficiency ia approximated by the average length of stay} Elasticity
INFLOWS: ot demand
4& Chenge_in_hefficieny =
Edesticly_of_inefficiency“Ineficiency"Chenge_in_perceived_walting_tme/Perceived_walin
{ime fmonthe pec month)
© Elestictly_of_bede = .29 {constant
© Elesticty_of inefficiency = .0o{constan
@ Etesticty_of = GRAPH(Perceived_weding_tie) “8
(0.00, 0.00), (0.5, 0.00), (1.00, 0.00), (1.50, 0.00), (2.00, 0.00), (2.50, 0.00), (3.00, 0.00), (3.50, fel St
0.09), (4.00, -0.4), (4.50, -0.4), (5.00, -0.113), (5.50, 0.00), (8.00, 0.00) 0.000 6.000
Percelved_welting_time
6.00
Figure 4
!
- i i i
A. Waiting time i !
3.00 : 7
.00
0.00 S00 15.00 30.00 45.00 60.00
Months
110.00 7 1
B. Demand H
| —2
100.00 =
+ iin 4
| { |
90.0000 15.00 30.00 45.00 60.00
Months
12.004 7 T }
i : i i
C. Beds :
:
10.0077*
3
8.00500 15.00 30.00 45.00 60.00
