1. Two queue or not two queue:
When and how to integrate HIV care and treatment into outpatient services in resource-limited settings
Sarang Deo1, Ariel Garcia2, Bettina Gardner2, Stewart E. Reid3,4,
Mallory Soldner2, Julie Swann2, Stephanie Topp3,4, Kezban Yagci2
(authorship is alphabetical rather than by contribution)
1
Kellogg School of Management, Northwestern; 2 H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of
Technology; 3 Centre for Infectious Disease Research in Zambia; 4 Schools of Medicine and Public Health, University of Alabama at Birmingham
Motivation/Introduction
Sub-Saharan Africa bears a disproportionate burden of the current global HIV/AIDS epidemic. In 2008, the region
accounted for 67% of HIV infections and 72% of the AIDS-related deaths worldwide[1]. Rapid growth in
international donor funding to combat the HIV epidemic has placed an enormous additional strain on already weak
public health systems and fueled the debate over vertical versus integrated (or horizontal) health systems and their
pros and cons [2]. In sub-Saharan Africa, typical vertical service delivery in primary health care clinics involves
separate departments for HIV, TB, routine outpatient care (OPD) and maternal and child health operating parallel to
each other. Integrated (or horizontal) systems, which exist in very few settings, may involve strengthened paper
referral systems between separate departments or a single clinic with harmonized staff and space and pooled
resources to serve multiple patient types under the same roof.
International donors and their implementing partners have typically favored vertical systems as they enable rapid
scale-up of higher quality and more reliable delivery of care in the short term, bypassing potential bottlenecks in
public health systems. In the longer term, however, vertical systems can lead to the diversion of human and material
resources towards individual diseases, potentially harming overall primary health outcomes for the future [3].
Moreover, disease-specific international funding may not be sustained at its current levels. As a result, there has
been a growing need for evidence of feasible integration strategies for HIV services in resource-limited settings [2].
Recent studies have investigated the impact of integration of TB and HIV care (via referral systems) on uptake and
access to care [4]. However, to our knowledge, very little work has been done to evaluate the impact of integration
on service delivery systems themselves, specifically focusing on integration of HIV and outpatient care.
Approach
In this study, we evaluate the integration of HIV care (referred to as Antiretroviral Therapy or ART clinics) with the
regular outpatient department (OPD) in a primary health care clinic in Lusaka, Zambia In Zambia, OPDs provide
episodic care to any presenting patient while the ART clinics provide chronic care to any clinically-eligible, HIV-
infected patient who requests enrollment [5]. While both OPD and ART clinics are Ministry of Health services,
ART clinics receive significant additional monetary and technical support from international donors, such as the
U.S. government, and through NGOs, such as the Centre for Infectious Disease Research in Zambia (CIDRZ).
Starting in September 2007, CIDRZ, in collaboration with the Lusaka District Health Management Team, initiated a
pilot to integrate OPD and ART clinics. Integration involved combining patient flows (which were served in a first
come, first served manner except for extreme medical emergencies), modifying physical space and cross-training
staff. The objective of integration was to improve HIV case finding and referral to care while reducing the
associated stigma of the disease, to improve quality of OPD care by leveraging ART experience and to reduce
patient waiting times by leveraging the potential economies of scale in an integrated system [6] since waiting times
can affect patients’ willingness to access services and adhere to treatment.
In this proposal, we focus on waiting times as our primary outcome measure and contribute a rigorous and
quantitative analysis of the integration of health systems in resource-limited setting. Specifically, we: (i) conduct an
empirical investigation of integration on patient waiting times; (ii) use simulation to provide concrete design
recommendations about when and how to integrate OPD and ART clinics, and examine clinic characteristics that
lead to more successful integration; (iii) complement empirical and simulation analysis with a theoretical
examination of queuing factors that can lead to increased waiting times for either or both classes of customers, e.g.,
if one customer class skips some steps in the process.
Data Description
We collected data over two, seven-day periods (pre-integration and six months post-integration) using a time and
motion study form attached to the medical file of every patient arriving prior to noon (which is when the vast
majority of patients arrive due to cultural and social reasons). This included type of patient visit, time of patient
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2. arrival, the start and finish times of interaction at each clinical station (vitals, triage, screening room, laboratory,
pharmacy, adherence, ART enrolment) and the time of exit taken as the finish time at the last station. We manually
entered the data into a spreadsheet, which we then analyzed to map clinic operations before and after integration,
estimate distributions of patient inter-arrival times and service times at each step, and derive approximate nurse
schedules and worker habits such as late arrivals or batch processing.
Results/Findings
Average process (consultation) times for ART patients were higher than for OPD patients for all rooms visited
during pre- and post-integration periods, suggesting ART patients are generally ‘slower’ to process. Preliminary
empirical evidence suggests that the waiting times of both patient types increased after integration. While the
literature documents similar increases when pooling patients with different service times [7, 8], the increase in
waiting time for the slower patient type (ART) remains surprising.
Empirical and Simulation Analysis
Given the observation periods of one week each, a direct empirical comparison of raw waiting times before and after
integration does not accurately reflect the impact of integration, because several other conditions (patient load,
patient-mix, and staff availability) might have changed. Hence, we identify statistically significant differences in
inputs (supply and demand) before and after integration and use simulation to aid accurate comparison of pre- and
post-integration systems. For instance, we find that staffing hours are statistically lower after integration and extra
process time is incurred for OPD patients after simulation. We also observe that “breaks” after integration are more
frequent, although these could include processing times between patients. However, even after controlling for
staffing levels, tnitial simulation results indicate the slower patient (ART) waiting times can increase after
integration, even with similar inputs.
We also use simulation to inform analysis of when and where to integrate and to evaluate ideas to improve the
current system. Fixing the initial resources in pre- and post- integration, we find that clinics with a patient mix of
greater than 30% ART patients will have a benefit in their integrations. Clearly, increasing resources decreased
waiting times, but we also found that wait reductions were possible by shifting the nurses schedules (without
increasing the total hours worked) to start on-time and consistently. Interestingly, if more OPD patients receive
provider-initiated HIV testing and counseling (PITC), which corresponds to fewer patients “skipping” a processing
step, then the wait times of ART patients decrease. We explore this further theoretically.
Theory: Process Skipping
Many pooling conditions can affect waiting times. Here, we analyze the impact of process skipping. In a serial
network of queues with multiple customer classes, we define an instance of process skipping as one in which some
proportion of a customer class skips a process step and later rejoins a common queue. Figure 1 below shows the
rooms (as identified in the clinic) visited by patients in the integrated clinic and highlights relevant instances of
queue skipping for each patient type: (i) when OPD patients stop at Room 3 for PITC, ART patients pass them; and
(ii) when ART patients stop at Rooms 6 and/or 8, OPD patients pass them. Process skipping results when
integrating two serial networks that share some but not all processing steps; yet to our knowledge, this topic has not
been explicitly studied in the literature. Mandelbaum and Rieman [9] investigate pooling in a queuing network, but
their work primarily deals with servers being merged into a single faster server. Skips are not considered. Since
many healthcare processes occur in a series of steps, understanding the implications of process skipping is essential
to understanding the impact on patient waiting times in the debate between vertical vs. integrated health systems.
When patients skip a process, it may seem intuitive that they benefit (as measured by a reduction in total waiting
time) by not having to wait in the queue they are skipping. However, we show that there are realistic cases where
skipping is beneficial and realistic cases where it is not. For example, as mentioned above, skipping was beneficial
to ART patients in our simulations when a high number of OPD patients visited Room 3 for PITC. That is, the
waiting time for the Room 4 queue was lower on average for an ART patient skipping PITC, than for an OPD
patient who visits PITC before Room 4, even though both patients wait in the same line.
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3. Figure 1: (Left) Process skipping by patient type in the clinic. Figure 2: (Right) Simulation results adjusting PITC % at integrated clinic
We study general models with process skipping and find that skipping may be detrimental to the skipper’s total
waiting time (no matter how many processing steps they skip) for some values of system utilization. For example,
consider again the case when ART patients skip past PITC in Room 3. Let the departures from Room 2 be batched
(e.g., if the nurse at Room 2 pulls multiple charts at a time) but not batched from Room 3. As long as the system is
stable at Room 4, ART patients are actually penalized in terms of waiting time by arriving at Room 4 in a batch
from Room 2, while those attending Room 3 have the batch broken-up. In such cases, skipping may be detrimental
if the following apply: (i) departures are batched from the last common processing step before those skipping and
those not skipping are separated, (ii) departures are not batched from the station immediately before the common
queue where the skipper and skippee rejoin, and (iii) the common queue where the skipper and skippee rejoin is
stable. This is one example of pooling conditions that can lead to increased waiting times for both classes of
patients. We conjecture that the variability of the choices made by workers (e.g., whether and how much patients
are batched), at the skipped stations or those prior, impacts whether a skip is beneficial for the patient type doing the
skipping or the patient type being skipped. In the proposed research paper, we will further investigate general
conditions, including characteristics of process skipping that can lead to increased waiting times for either or both
patient types.
Contribution
Our findings contribute quantitative research to the health policy debate about vertical vs. integrated systems by
investigating the impact on waiting time of integrating HIV care and treatment into routine outpatient care. In
particular, we offer both immediate and practical policy recommendations regarding ways to improve integrated
clinic operations and which clinics to prioritize for integration, assuming similar integration models are adopted.
We also advance the theoretical understanding of a practical, yet unstudied subcategory of pooling: process
skipping. We formalize the subcategory and investigate how instances of process skipping in the pooling of serial
systems (such as is common in healthcare integration) can be a benefit or detriment to waiting times for particular
patient types, rather than just average waiting times across patient types.
References
1. 09 AIDS Epidemic Update. 2009, World Health Organization.
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Jaids-Journal of Acquired Immune Deficiency Syndromes, 2009. 52: p. S3-S5.
3. Garrett, L., The challenge of global health. Foreign Affairs, 2007. 86(1): p. 14-+.
4. Harris, J.B., et al., Early lessons from the integration of tuberculosis and HIV services in primary care
centers in Lusaka, Zambia. International Journal of Tuberculosis and Lung Disease, 2008. 12(7): p.773-9.
5. Stringer, J.S.A., et al., Rapid scale-up of Antiretroviral therapy at primary care sites in Zambia -
Feasibility and early outcomes. Jama-Journal of the American Medical Association, 2006. 296(7): p. 782-
793.
6. International Center for AIDS Care and Treatment Programs (ICAP): Leveraging HIV Scale-up to
Strengthen Health Systems in Africa. in Bellagio Conference Report. 2008. ICAP, Mailman School of
Public Health, Columbia University.
7. Joustra, P., E. van der Sluis, and N.M. van Dijk, To pool or not to pool in hospitals: a theoretical and
practical comparison for a radiotherapy outpatient department. Annals of Operations Research, 2009.
8. Whitt, W., Partitioning customers into service groups. Management Science, 1999. 45(11): p. 1579-1592.
9. Mandelbaum, A. and M.I. Reiman, On pooling in queueing networks. Management Science, 1998. 44(7): p.
971-981
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