How Do Health Systems Address Patient Flow When Services Are Misaligned With Population Needs? A Qualitative Study

Background: Patient flow through health services is increasingly recognized as a system issue, yet the flow literature has focused overwhelmingly on localized interventions, with limited examination of system-level causes or remedies. Research suggests that intractable flow problems may reflect a basic misalignment between service offerings and population needs, requiring fundamental system redesign. However, little is known about health systems’ approaches to population–capacity misalignment, and guidance for system redesign remains underdeveloped. Methods: This qualitative study, part of a broader investigation of patient flow in urban Western Canada, explored health-system strategies to address or prevent population–capacity misalignment. We conducted in-depth interviews with a purposive sample of managers in 10 jurisdictions across 4 provinces (N = 300), spanning all healthcare sectors and levels of management. We used the constant comparative method to develop an understanding of relevant strategies and derive principles for system design. Results: All regions showed evidence of pervasive population–capacity misalignment. The most superficial level of response – mutual accommodation (case-by-case problem solving) – was most prevalent; capacity (re)allocation occurred less frequently; population redefinition most rarely. Participants’ insights yielded a general principle: Define populations on the basis of clusters of co-occurring need. However, defining such clusters demands a difficult balance between narrowness/rigidity and breadth/flexibility. Deeper analysis suggested a further principle: Populations that can be divided into homogeneous subgroups experiencing similar needs (eg, surgical patients) are best served by narrow/ rigid models; heterogeneous populations featuring diverse constellations of need (eg, frail older adults) require broad/ flexible models. Conclusion: To remedy population–capacity misalignment, health system planners should determine whether clusters of population need are separable vs. fused, select an appropriate service model for each population, allocate sufficient capacity, and only then promote mutual accommodation to address exceptions. Overreliance on case-by-case solutions to systemic problems ensures the persistence of population–capacity misalignment.


Background
Patient flow -ensuring that patients can move smoothly through the health system to obtain the care they need -is one of the greatest challenges facing healthcare today. The issue of flow is vast, intersecting with multiple dimensions of healthcare quality, 1 and is a theme of myriad improvement efforts in diverse areas. While emergency department (ED) crowding is its most recognizable symptom, stagnant flow may result from bottlenecks at any point along the continuum of care 2 ; as such, flow is widely recognized as a system problem that demands a system response. However, existing evidence is inadequate to guide decision-makers through this difficult, complex and potentially risky undertaking.
The literature has focused overwhelmingly on specific interventions to reduce input, accelerate throughput, or facilitate output from the ED or hospital. [3][4][5] However, it seems doubtful that such interventions hold the key to improving flow. The overall evidence base for flow interventions is weak: Although virtually every type of initiative has shown some promising results, very few can be confirmed as effective, considering the methodological shortcomings of the available studies and the high likelihood of publication bias. 6,7 Furthermore, no specific intervention, nor combination thereof, has been found to predict flow performance at the hospital level, and health systems with very poor performance may nonetheless boast a plethora of interventions. 9 A large systematic review suggested that interventions are often poorly matched to the actual causes of flow problems, noting that greater organizational and scholarly attention has been devoted to testing solutions than to understanding Implications for policy makers • Population-capacity mismatches were pervasive across all health jurisdictions studied. Of the three levels of response to such misalignment, the most superficial (case-by-case problem solving) was most prevalent, with less attention given to capacity (re)allocation and almost none to population definition. • This is the reverse of the order that should be adopted. Health system planners should first determine population needs, and then allocate capacity, using mutual accommodation only to address a limited number of exceptions. • While there is agreement that populations should be defined in terms of clusters of co-occurring need, trade-offs are involved in determining how narrowly/rigidly or broadly/flexibly these clusters should be defined. • A useful principle for managing these trade-offs is that relatively narrow/rigid definitions work for homogenous populations with similar needs (eg, surgical patients); while heterogeneous populations with diverse constellations of need (eg, frail elderly) require broad/flexible definitions. • We outline the features of appropriate service models for populations in which clusters of need are clearly separable (segmentation, specified services, sorting rules) vs. inevitably fused (fuzzy sets, fluid resources, funnels).

Implications for the public
All countries are working to improve the movement of patients through the health system so that they can obtain the care they need. Patients cannot move smoothly through the system unless available services are a good match for their needs. When service offerings do not match population needs, health system planners should first define all populations in need of care, then assign appropriate capacity. In practice, however, we found that mismatches were usually addressed by case-by-case problem solving, seldom by ensuring that services are first designed to fit population needs. This results in system inefficiency and unmet need. Defining the populations in need of care is a complex task involving many trade-offs. However, our findings suggest a guiding principle: Use relatively narrow/rigid definitions when it's possible to identify distinct subgroups with similar needs (eg, surgical patients), and broad/flexible definitions when needs are complex and overlapping (eg, services for seniors).

Key Messages
problems. 10 Moreover, when the underlying problem exists at the system level, it is unlikely to be amenable to localized solutions. 9 Improving the efficiency of one department within an interdependent health system does not necessarily improve system throughput, and may even have the unintended consequence of creating bottlenecks. 11 There has been growing interest in "whole-of-system" approaches to flow, 10 as reflected in research on system-level leadership/management practices (eg, data-driven management, performance accountability 8 ) and system-wide strategies (eg, enforcement of ED length-ofstay targets 12,13 ) that may improve flow performance. However, to date there has been limited attention to the issue of system design. This gap is critical, because if the system is not designed to provide "the right care to the right patients, " it is highly unlikely to be able to provide care at "the right time. " The theme of system design pervades the theoretical literature on flow: The Theory of Constraints 14 and the Theory of Swift Even Flow 15 emphasize the need for system-level re-engineering to address the bottlenecks and sources of variability that impede the smooth flow of people or materials through a process. Such theory, derived from the field of operations management, has had an indelible influence on researchers' understanding of healthcare wait times and flow. [16][17][18] In practice, however, reengineering is usually applied to discrete parts of the healthcare system, not to the system as a whole. 11,19 Looking beyond the flow literature, the general literature on delivery system redesign points to the need for new models of care to address shifting patterns of population need. 20 In particular, it has long been recognized that many health systems, having been developed to address acute medical problems, are misaligned with growing needs for complex and continuing care. 21,22 However, since such misalignment is not typically conceptualized as a flow issue, the implications for flow have received little examination.
A recent explanatory case study yielded a model for conceptualizing system design in relation to patient flow: the population-capacity-process model. 9,23 According to this model, patient flow depends on clearly identifying all populations in need of care and directing each to suitable capacity through a streamlined, reliable process. Here, population refers not to a demographic group but to those who share a need or set of needs; defining a population by needs facilitates identification of the most appropriate capacity (physical and human resources) to meet those needs, and development of an efficient process whereby the intended patients can access this capacity. 9 The study, which probed the source of one health system's intractable flow problems, identified a fundamental misalignment between service offerings and population needs. 23 Symptoms of such population-capacity misalignment included frequent identification of patients for whom no suitable service existed, habitual assignment of patients to a suboptimal service because the appropriate one was full (eg, "off-servicing"), and conflict between programs and/or sites as to who should take responsibility for certain categories of patient. As the underlying problem existed at the level of system design, even evidence-informed, well-managed flow initiatives fell far short of their desired impacts. Moreover, the failure of specific flow interventions could be linked to their neglect of one or more of the three domains: population, capacity, and/ or process. 9 Research in other organizations has corroborated these findings at the micro (initiative) level. 24,25 At the macro level, however, there is a need to explore the potential problem of population-capacity misalignment in other health systems, not limited to exceptionally poor performers.
One might suppose that most systems avoid misalignment through periodic assessment and/or forecasting of population needs and incorporation of this information into the planning cycle. Indeed, many countries and provinces use forecasting to inform workforce planning 26 ; many hospitals and health systems conduct community health needs assessments 27,28 ; and some use mathematical modelling to guide the distribution of physical capacity. 29,30 However, prevailing approaches to forecasting may be of limited value in helping systems adapt to changing needs, as models typically factor in only demographic trends and current patterns of utilization, not shifts in epidemiology or provider productivity. 26 Meanwhile, health system planners may not take action on the findings of needs assessments, or may respond with superficial changes. 27,31 To the extent that planning processes are biased towards the reproduction of existing arrangements, they may fail to correct misalignment.
This qualitative study undertook an open-ended exploration of how healthcare managers engage with the issue of population-capacity (mis)alignment. The research questions were: 1. How do health systems address and/or avoid populationcapacity misalignment? 2. What principles can be derived for optimal system design?

Study Design and Context
This study was a core component of a multi-jurisdictional research project designed to explore in depth how health systems can achieve maximal improvement in patient flow. The Western Canadian Flow (WeCanFlow) study, which spanned the 10 urban health regions/zones of Canada's four western provinces, was designed in partnership with decisionmakers from all participating jurisdictions and funded by the Canadian Institutes of Health Research. In keeping with an integrated knowledge translation approach, decision-makers were involved in identifying relevant research questions, giving feedback on recruitment materials and interview guides, identifying potential participants, and reviewing and interpreting findings. In Canada, health is a provincial/territorial responsibility; within many provinces, regionally based bodies (eg, health authorities) are responsible for the funding and delivery of hospital, community, and long-term care, as well as mental and public health services. The participating regions were disparate in size, structure, history, and political context, 32 affording an ideal opportunity to explore system-level issues.
The overall project was originally conceived as a mixedmethods comparative case study; its objective was to quantitatively assess inter-regional differences in flow performance and qualitatively explore factors differentiating high from low performers. System design was chief among the factors of interest; other factors included specific flow initiatives and aspects of social/organizational context. However, quantitative analysis revealed that inter-regional performance variation was not sufficiently large or consistent to permit comparison of performance-based subgroups. As preliminary qualitative analysis also suggested more crossjurisdictional similarities than differences, we decided to treat the qualitative dataset as a whole rather than as ten separate cases (while of course remaining attentive to any regional variation).
Approval was obtained from all relevant bodies for ethical and operational review in Manitoba, Alberta, Saskatchewan, and British Columbia, including one university (harmonized) research ethics board per province and the operational review committee of each participating region. All participants signed a consent form.

Data Collection
The primary data source consisted of in-depth interviews with 300 managers and quality improvement staff with current or recent responsibility for patient flow and/or involvement in flow initiatives. Participants included ~20-45 purposively sampled personnel from each region and 5 from extraregional bodies such as provincial ministries and quality councils. We sought representation of different levels of management (regional, organizational, departmental, etc) and organizations (eg, hospitals, programs), and a mix of strategic and operational roles. In keeping with our understanding of patient flow as an issue that spans the continuum of care, we recruited participants from all sectors, not only acute care. The sample was 60% female and predominantly at (39%) or above (45%) the Director level.
Potential participants were identified from organizational charts and by key decision-makers. Email addresses were gathered by a member of the participant's own region (researcher or decision-maker) who had access to the organizational directory, and were not shared with the full team. The local member sent each recruitee a personalized email introducing the study and inviting them to contact the research coordinator; reminders were sent 2-3 weeks later if necessary. A few additional participants were identified through snowball sampling. The overall response rate was 67%; region-specific rates ranged from 35%-88%.
Most of the interviews, typically 45-60 minutes in length, were conducted in person at the participant's office or a location of their choice; telephone was used for individuals who were unavailable during the site visit, and for one region where the site visit was cancelled due to weather. While most interviews were individual, in a few cases 2-3 colleagues chose to participate together.
Interviews were conducted between April 2016 and April 2018 by a trained, Master's or PhD-prepared interviewer. All interviewers were or had recently been embedded researchers in one of the participating regions; as such, they had experience working with decision-makers and were known to some participants, but were not in a supervisory role over any. Participants were aware that the research was intended to help Western urban health regions improve flow across the continuum of care, and that decision-makers planned to use the findings.
The semi-structured interview guide included questions about flow strategies, system design and organizational context, including participants' current and past involvement in flow initiatives, and perspectives on what had (not) worked well. Interviews were audio-recorded and transcribed. For the broader study, interview data were supplemented by document review and non-participant observation of flow meetings/ events, but these methods did not contribute to the present sub-study except as a source of contextual information.

Data Analysis
Interview data were entered in NVivo 11. In a preliminary round of analysis ("bucket coding"), two researchers contentanalyzed each interview independently to identify extracts related to the issue of population-capacity (mis)alignment; disagreements were resolved by consensus. Selected extracts were analyzed using the constant comparative method. 33 Themes were identified inductively; then, codes were (re) categorized and elaborated using the population-capacityprocess model as a sensitizing concept. Analysis relied on an iterative process of constant comparison between extracted quotations, full transcripts, contextual information, relevant literature, and the evolving coding scheme; this was led by one researcher with frequent team discussion of emerging interpretations. Contradictions in the dataset were explored through the technique of dialectical analysis 23 : when a disagreement was identified, we sought to ascertain the axis of conflict, then identify a principle that could synthesize two opposing viewpoints. All authors reviewed an initial draft report; as an additional measure to ensure trustworthiness, a revised draft was circulated to the full study team (comprising 31 health-system decision-makers and 17 researchers), with a request for review and commentary.

Symptoms of Population-Capacity Misalignment
All of the above-noted symptoms of population-capacity misalignment were reported in all regions (see Table 1). "Offservicing" (admitting patients to beds intended for a different population) was widely practiced despite its recognized limitations; off-servicing from medicine into surgery was most common. Participants in each region reported difficulty finding suitable programs for complex high-needs clients, particularly those with psychosocial/behavioural issues. Participants also described conflict surrounding the eligibility criteria of both acute and community programs, although several noted that overt conflict had decreased over time.
Overall, the theme of population -capacity misalignment as a problem requiring ongoing management emerged from the great majority of interviews.
Strategies for Addressing Population-Capacity Misalignment Analysis of actions taken or proposed by participants suggest three main categories of strategies used to manage population-capacity mismatch in the face of these challenges: mutual accommodation (case-by-case problem-solving); adding or repurposing capacity to better match observed need; and redefining patient populations.
Mutual accommodation -finding ways to accommodate needs of individual patients without changing the design or allocation of capacity -emerged as the most common strategy. Not only was it reported to occur ad hoc, it was institutionalized through such initiatives as bed meetings (at which staff negotiated the distribution of new admissions), overcapacity protocols (which mandated the use of off-service and/or unfunded beds), and regular meetings between acute and nonacute personnel to determine discharge destinations for patients with complex needs. Every region had implemented at least one (typically several) such interventions, and the majority of participants mentioned their role in easing flow. Some expressed pride that staff collaborated to accommodate patients, though many recognized such processes as an unfortunate "work-around. " "In the in-patient world we have no choice: every bed is a space where we can put a patient. And until we design hospitals that are [at] 85% capacity we're always going to run into this trouble … Yeah, these are all work-arounds. And it's always not as good as it could be" (P10130). While mutual accommodation was sometimes used to compensate for the lack of any program for which the patient was eligible, more commonly a suitable program existed but was fully subscribed, necessitating a "bed shuffle" (P4104). The daily "juggling" (P2202) of beds was often described as timeconsuming and frustrating for managers and staff. Mutual accommodation strategies were also associated with risks (eg, off-servicing medical to surgical may result in cancellations to the surgical slate, or in the provision of suboptimal care) which required mitigation strategies (eg, protection of the surgical slate). These issues are discussed in greater depth in a separate paper on interventions for overcapacity management. Outside the acute sector, the process of mutual accommodation was less frenetic but still time-consuming and potentially frustrating.
"It seems like we have to go through a lot of work before people actually come together and have a conversation and a meeting … to problem-solve, versus sitting in your office with an email and knowing that you're going to have to go back to your team and explain why you're okay with this person who doesn't fit the mandate coming in and, 'Did you lose the meeting? Is that what happened?'" (P2104). Few participants spoke of attempting to eliminate the need for frequent mutual accommodation; there appeared to be an assumption that the system would/could not be designed to ensure that service offerings were closely aligned to patterns of population need.
The second category of strategies, adding or repurposing capacity to better match the observed distribution of patient needs (see Table 2), was also well-reflected in every region. Each province had expressed a policy commitment to "shift care into the community, " and participants from all regions reported certain investments in postacute, transitional and/or home-based care. Typically, capacity-based strategies entailed expansion of already-existing services, although in a few cases capacity had been developed for newly identified populations (eg, persons with substance-abuse issues). Realignment of the hospital "bed map" to "right-size departments" was also reported in most regions, and undertaken regularly by at least two.
Although capacity-based strategies were within the repertoire of all regions, they were subject to fiscal and logistical constraints. Across jurisdictions, participants desired more capacity expansions than their region had been able to fund, and reallocation of resources was perceived as challenging ("our biggest challenge is … yes, we wanna support people at home, but it does come at a cost, and we find that the cost just never comes from acute … because acute has their own issues" [P1215]).
The least prevalent strategy consisted of redefining populations in order to allocate capacity and designing processes accordingly. Although over one-third of participants contributed data related to population (re)definition, only a handful could point to examples in which it had actually occurred. The common theme of these few success stories was the combination of atomized programs in order to better serve patients.
" "We got funded to do this, and then a few years later we got funded to do that, and by the way, don't mix the two or you'll lose your funding" (P9205).
Although positive examples were rare, many participants offered guidance on population redefinition by critiquing existing arrangements or exploring hypothetical scenarios. As their comments focused on what should be avoided in defining populations, we have termed the emerging themes "The Five Don'ts": Do not (1) separate similar needs, (2) separate needs that occur together, (3) use arbitrary cut- off points, (4) separate needs closely sequenced in time, (5) combine dissimilar needs (see Table 3 for examples of each principle as identified by participants). These negative principles can be synthesized into one broader, positive principle: Define populations in terms of co-occurring need; that is, group patients who need essentially the same human and physical resources even if their characteristics differ in other ways.
Trade-offs in System Design While there was broad consensus on the principle that services should be designed around clusters of co-occurring need, in practice the task of defining such clusters was experienced as challenging. Some participants made explicit reference to inherent trade-offs in defining populations, capacity, and process; at other times these trade-offs became apparent in comparing diverse perspectives on opposite sides of an apparent controversy. Underpinning each of the trade-offs (see Table 4) was found a common theme: the need to strike a balance between specificity and rigidity on the one hand, and breadth and flexibility on the other.

Trade-offs in Defining Populations
Two trade-offs were identified in defining populations. First, programs must make a trade-off between over-including and over-excluding patients -the sensitivity-specificity trade-off. Participants clearly described the hazards of both exclusivity and inclusivity, and discussed their challenges in negotiating the balance between them. While some suggested that maintenance of strong, specific criteria inevitably resulted in exclusion of patients with atypical needs, others noted the benefits of defining clear, specific clusters of patient need, noting that earmarking capacity for each cluster improves efficiency and effectiveness of care. Second, health system planners face a trade-off between designating too few programs (resulting in poorly-tailored services for diffuse populations) and too many (resulting in difficulty matching inflexible capacity to variable demand) -the carve-out trade-off. We found some consensus that carving out specialized services worked better where patient volumes were higher: The higher patient volume, the greater likelihood of maintaining steady demand for each type of service.

Trade-offs in Defining Capacity
Participants also discussed the trade-off between too much flexibility in deployment of capacity and too little -the bespoke trade-off. While flexibility can enable customization to meet the needs of individual patients -promoting personcentred care -overly fluid resources may easily be deployed inefficiently. Participants suggested that, where possible, designing services around cohorts of patients with similar needs is more cost-effective than an individualized approach.
The considerations involved in defining population and capacity interact: If a population is to be defined broadly, then the capacity assigned to that population must be defined either flexibly (fluid resources) or very generously, to accommodate a shifting "fuzzy set" of needs. Conversely, if a program intended to serve a broad population defines its capacity narrowly, many patients will de facto be excluded because "we don't do that here. "

Trade-offs in Defining Process
Finally, when discussing the challenges of finding appropriate care for patients, participants identified a trade-off between eliminating bottlenecks early vs. late in the process -the bottleneck trade-off. Participants commonly noted that a sorting model, in which referring providers learn each program's eligibility criteria and contact one after another until their patient is accepted, creates bottlenecks at the point of referral. Several suggested moving to what could be called funnel models, in which a receiving program with broad scope takes responsibility for placing each referred patent in the most appropriate sub-program and/or providing direct service to patients for whom no suitable program exists. However, the convergence of diverse patients on one large funnel can create a bottleneck at the point of assessment, and adds a needless extra step for those patients who could easily have been sent directly to the right program. There was no apparent consensus as to how numerous or broad the funnels should be or which patients should use them.
We found striking similarities in experiences and perspectives across regions, irrespective of their size or organizational structure; however, informants from regions that were in the throes of restructuring provided more observations relevant to population definition. Hospital leaders and medical directors contributed the most on this topic; lower-level managers and QI personnel the least. Although participants expressed diverse opinions on the desirability of narrow/rigid vs. broad/flexible ways of defining populations, the issue did not appear to be highly polarized; that is, perspectives varied not only between but within groups (eg, sites, programs), and several participants said they could "see both sides" of a tradeoff. However, we noted that narrow/rigid vs. broad/flexible models tended to be advocated in relation to different patient populations. The former were most commonly recommended for surgical patients (especially elective surgery, which lends itself to pathways and predictability) or conditions defined by an acute event, such as stroke. The latter were most commonly recommended for heterogeneous populations resistant to sub-grouping, especially those characterized by multiple, continuing needs and diverse patterns of comorbidity (eg, frail older adults).

Discussion
Across the sample of regions, participants reported the same three strategies for addressing population-capacity misalignment, and in the same order of prevalence: mutual accommodation, capacity (re)allocation, and population (re) definition. It would seem logical, in light of the populationcapacity-process model, 9 for systems to first define populations on the basis of need, then allocate sufficient capacity to each population, and only then promote mutual accommodation to handle the few inevitable exceptions. Instead, we observed the reverse pattern: Process solutions were the default option; capacity-related reforms were undertaken sometimes (but not as often as needed); and no region had taken a systematic, comprehensive approach to defining populations. This pattern likely reflects the relative level of difficulty of the three strategies. Mutual accommodation is a caseby-case approach that operational managers can undertake independently on a daily basis, with no major structural, policy, or budgetary implications. Capacity allocation, in contrast, entails system-level change, which must be pursued by strategic decision-makers on a longer planning horizon. Population redefinition requires that systems actually be redesigned, an even more complex and disruptive prospect. Furthermore, although we identified a simple principle to guide the definition of populations -namely, group patients on the basis of clusters of need -the task of identifying such clusters is not so simple in practice. Health system planners confront a host of trade-offs as they struggle to define populations and the associated service models in ways that are neither too narrow and rigid nor too broad and flexible. Yet, without effective redefinition of populations, population-capacity misalignment seems guaranteed to persist, with associated patient risk and waste to the system. Mutual accommodation is a classic example of the ineffective application of nonsystem-level solutions to system-level problems; capacity (re) allocation offers a superior solution, but will yield limited benefit unless program boundaries are aligned with clusters of need. How, then, should planners approach the challenging enterprise of population redefinition?
If our findings are to be converted into practical guidance for system design, it is necessary to derive a general principle for managing the identified trade-offs. No participant articulated such a principle. However, the finding that narrow/ rigid models tended to be recommended for homogeneous populations and broad/flexible models for heterogeneous models provides an important clue: It suggests that the optimal balance point in each of the trade-offs may depend on the nature and distribution of needs in the target population. On this basis, we advance the following supposition: The greater the separability of clusters of need, the greater precision can and should be applied when defining population, capacity, and process.
Although the separability of clusters of need is a continuum, not a binary construct, for the sake of clarity we will define two ideal-types of populations: those in which clusters of need are clearly separable (S populations) and those in which they are unavoidably fused (F populations). Findings suggest that the two types of populations demand different approaches to system design: S populations, which can be divided into homogeneous, needs-based groups with high coverage and low overlap, are best served by relatively narrow/rigid definitions; F populations, which feature diverse, overlapping constellations of need, require broad/flexible definitions. Accordingly, for S populations, it is most efficient to apply what we call the three Ss of system design: segmentation (create a separate program or stream for each cluster), specified services (provide a fixed set of services within each program or stream), and sorting rules (define policies to manage common types of exceptions). F populations, in contrast, demand the three Fs of system design: fuzzy sets (defining clusters of needs in general terms, avoiding arbitrary or excessively specific criteria), fluid resources (facilitating add-ons to core services for rapid tailoring), and/or funnels (making the initial 'gate' to services as wide as possible, with the onus on the receiving program). Figure offers a visual representation of service models for S vs. F needs.
It may sometimes be possible to identify a cluster of "S" needs in a population that otherwise has "F" features (eg, for gastric banding surgery in the bariatric population). Under such circumstances, it would seem desirable to use an S model for the well-defined, time-limited needs, while ensuring that an F model exists to manage the open-ended needs (cf. Christensen et al, on differentiation of services for different categories of need). 34 The three Ss of system design are highly congruent with the flow literature. S strategies aim to reduce within-program variability in patient needs (segmentation) and care activities (specified services), and to increase the speed of patient assignment (sorting rules); in this way they address both of the domains identified by the Theory of Swift, Even Flow. 15 The strategy of segmentation/streaming, which derives from queuing theory, underpins many flow interventions, 35,36 and the carve-out trade-off has been discussed from an operations research or process engineering perspective. 18 However, this literature does not appear to address the issue of clusterresistant populations. While some research suggests that process engineering methodologies such as Lean are most likely to achieve gains when applied to populations with relatively narrow, homogeneous sets of needs, 37 it is unclear to what extent such methodologies (and the theories that inform them) are truly applicable to complex populations. Meanwhile the growing literature on centralized/pooled waiting lists offers some support for the idea that narrow-funnel models can improve access to a defined service, but this literature has not addressed broad-funnel models. 38,39 The three Fs of system design are congruent with leading models of integrated care for seniors and persons with continuing care needs. 20,40 Two key features of such models are a single point of entry with a common assessment process (funnel) and a shared resource envelope across sectors (fluid resources). 41 The integration literature recognizes that not all patients require integrated care, nor is it cost-effective to spread high-intensity services beyond their intended population; thus there is a need to draw program boundaries -and an accompanying risk of creating gaps, silos, and fragmentation. 42 However, it is essential that integrated models be available to patients who require them; otherwise, the burden of complex, open-ended needs will continue to fall on services ill-equipped to meet them, notably EDs. 43 The overall principle of defining programs around identified clusters of need is congruent with leading work on delivery-system redesign, such as the Porter and Lee proposal for creation of Integrated Practice Units. 44 Our research builds on this conceptual foundation by proposing that health system planners should first examine how tightly or loosely needs are clustered within the population(s) to be served. Although there are several statistical methods for analyzing clustering of individuals or characteristics, [45][46][47][48][49] research to date has not compared populations in terms of separability of clusters. Studies of older adults with multimorbidity have yielded conflicting results as to whether this population can be accurately subcategorized, and, if so, what these categories might be. [50][51][52] Further research is required in this area. A key challenge will be collecting data to support such analyses, as most administrative datasets include data on patient characteristics, diagnoses, and interventions received, but not necessarily needs. Our finding that all regions showed evidence of populationcapacity misalignment supports Kreindler's 23 conjecture that this problem is not unique to one poorly performing system but afflicts health systems in general. In contrast to Kreindler, 23 we did not observe severe, intractable conflict of the "Your Order Is My Chaos" variety. Most regions appeared to mitigate conflict through intensive processes of mutual accommodation; in Kreindler's earlier study, the region examined appeared to lack sufficient central authority to enforce such processes, and allowed conflict to persist unmanaged. We suggest that intergroup conflict is merely one potential symptom of population-capacity misalignment, and that the latter, not the former, should be considered the hallmark of this "paradox of patient flow. " In summary, our findings suggest that population-capacity misalignment might best be tackled through the following process: First, assess whether clusters of need are S or F; second, design services around clusters of need using S or F models as appropriate; third, assign capacity according to the observed distribution of needs. Any unforeseeable configurations of need should then -and only then -be dealt with through mutual accommodation.

Limitations
This study has a number of limitations. None of the study sites had conquered their patient flow problems, and all were in Western Canada. In a recent 11-country comparison, Canada ranked last on timeliness and below average on coordination of care. 53 Population -capacity misalignment may be particularly severe in the fragmented Canadian system, in which policymakers have typically lacked strong mechanisms to influence the delivery of care despite holding the funding envelope. 54 There is a need to extend research on population-capacity (mis)alignment to higher-performing countries. However, as ED crowding is an international problem 10 and patterns of patient need are not country-specific, we believe that the identified principles for system design will prove transferable beyond Canada.
Our sample was restricted to management: While many participants were also practicing clinicians, we did not obtain perspectives of frontline providers or service users; incorporation of these perspectives would enrich future work. There is also a possibility of respondent bias: Although we recruited a diverse sample of individuals with strategic or operational responsibility for flow across the continuum of care, those who chose not to participate may have had differing perspectives. We also note that only a portion of each interview was focused on system design, and we did not explicitly ask participants, "Should we change the way we think about defining populations and, if so, what are the correct principles for doing so?" However, as the interview questions and probes afforded multiple opportunities for participants to address population redefinition, we believe that the relative paucity of data on this strategy reflected an actual gap in system-design thinking/practice within our sample, rather than a gap in the interview guide.
While an exploratory, interpretive approach enabled preliminary theory generation, the emerging theory must be tested through further research, and with systems exhibiting a greater range of performance. We were able to identify principles for system design, but not to assess the effectiveness or feasibility of any particular way of operationalizing these principles (eg, models advocated by certain participants). Consequently, our findings cannot be used to recommend specific system design initiatives. The breadth and flexibility of study design did, however, facilitate generation of novel concepts and hypotheses, which we offer for further exploration.
Finally, in focusing on the underexplored issue of population-capacity misalignment, we do not mean to imply that this is the only possible cause of flow problems, much less that adding capacity is always part of the solution. Poor performance may instead reflect inefficient use of capacity, 18 or weak execution and coordination of improvement initiatives. 8 Only local investigation can ascertain the most important contributing factors within a particular system. 10

Conclusion
Population-capacity misalignment will continue to adversely affect patient flow until health services are redesigned to match observed clusters of population need. Our findings suggest that system redesign should be guided by the following fundamental principle: Select S or F service models according to whether clusters of need are "separable" or "fused. " However, we found little evidence that this principle was being applied in practice. Instead, health systems may wastefully provide S populations with F models, or, more commonly, attempt to serve F populations with a miscellany of S models, leaving providers with the slow, frustrating task of reinventing the system for each atypical patient. Robust F models could effectively meet the needs of heterogeneous populations, such as the "fuzzy set" of community-dwelling older adults with continuing care needs. The consequence of failure to develop such models can be observed in the ED, which sees an ever-growing volume of complex patients whose needs are not being met elsewhere. 43 As a result, a service originally intended to provide rapid care instead becomes the ultimate F model: a giant funnel offering unlimited resources to a population with no eligibility criteria. Thus, until we invest in F models where they are most efficient and appropriate, we will continue to use them where they are most inefficient and inappropriate.