!!!!

Health Care Supply Chain Analytics An analysis of Plexxus hospital consumption data to identify

opportunities for supply chain efficiencies and savings

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!Peter (Yinan) Zhang

500597806 !!!!

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Table of Content

Executive Summary 4

Introduction 5

Background 6

1.1 Challenges & Solutions 6

1.2 Access to Data 7

1.3 Supply Side Data 7

1.4 Demand Side Data 8

1.5 Data-mining & Forecasting 8

Literature Review: Group Purchasing Organization 9

2.1 Supply Chain Cost Reduction 9

2.2 Key Issue in Healthcare Supply Chain — Standardization 9

2.3 Virtual Centralization of the Healthcare Supply Chain 10

2.4 Supply Chain Management Integration and Implementation 12

2.5 Supply Chain Management Integration 12

2.6 Supply Chain Management Implementation 14

2.7 IT in the Management of Healthcare Supply Chain — RFID 14

2.8 Making Business Sense 15

Literature Review: Ontario Healthcare Funding Reform 16

3.1 Healthcare Funding Reform and its Impact on UHN 16

3.2 Health System Funding Reform (HSFR) 16

3.3 Health Based Allocation Model (HBAM) 17

3.4 Service Component 18

3.5 Unit Cost Component 19

3.6 Getting to Hospital Expected Expenses 22

3.7 Quality Based Procedures (QBP) 23

Statistical Methods & Data Analysis 24

4.1 Data Collection 24

4.2 Data Cleaning 24

4.3 Data Subsection 26

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4.4 Top 10 Purchased Items 26

4.5 Individual Item Purchasing Pattern 27

4.6 Daily Number of Transactions 29

4.7 Linear Regression between Daily Number of Transactions and Daily Net Value 31

4.8 Testing Assumptions of Linear Regression Model 35

4.9 Forecasting and Prediction 37

Application & Implication 39

5.1 Benchmarking 39

5.2 Forecasting Demand 39

5.4 Implication for UHN 40

Conclusion & Further Research 41

Reference 42

Appendix A 44

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Executive Summary

The Ontario Health System Funding Reform (HSFR) ushered in a completely new system in

which to allocate funds to Ontario hospitals. Unlike before, hospitals have to analyze and justify

the cost associated with health service provided. Plexxus is a group purchasing organization for

Ontario hospitals, and the organization wants to find a way to identify tangible and realizable

hospitals savings for the hospitals it serves.

!The Health Based Allocation Model (HBAM) under HSFR is most relevant to the goal of

Plexxus. HBAM represent 40% of total hospital funding, and it does not tie in with clinical

outcomes. Expected service multiplied by expected unit cost per service determines expected

funding for a hospital. Since Expected service level is determined by the Ministry of Health,

hospitals can only control the expected unit cost component. Moreover, two major components

of unit cost per service are overhead cost and medical supply cost, but overhead cost is difficult

to negotiate, therefore focusing on medical supply cost is most appropriate for finding savings

opportunity.

!For this research paper, data collected from Plexxus are sub-sectioned into only gloves category

due to its ease of calculation and the commodity nature. This research is focused on one of the

Plexxus hospital organizations, University Health Network (UHN) which is one of the largest

and most complex hospital organizations in Ontario and perhaps all of Canada. Cyclicality is

observed in both the daily number of transactions processed by Plexxus, and the daily net value

($ CAD). There is close similarity between the movement of daily net value and the number of

transactions. A linear regression model containing daily net value as the dependent variable, and

daily number of transactions is created. R2 is 0.92, indicating a high statistical relationship. The

linear equation: Expected Daily Number of Transaction = e-1.5012 + 0.65826±0.02256 * log (Daily Net Value)

can be used to estimate the output variable.

!This equation can be used as a benchmarking tool for Plexxus to determine transaction

processing efficiency of Plexxus, and facilitate forecast of the number of transactions. The latter

application can aid UHN in controlling transaction cost associated with commodity products

such as gloves.

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Introduction

!This report is the continuation of the 2013 research supported by Plexxus regarding healthcare

supply chain analytic. In addition, University Health Network (UHN) representatives are

involved with this study, and requested a contextual study on the healthcare supply chain

efficiency within their hospitals.

The purpose of this study is to “identify tangible and realizable hospital savings for a sample of

items used by UHN”, and “successfully test and document a repeatable process that Plexxus can

provide as a part of its value proposition” (Edmison, Mouradov, Popescu & Sulatycki, 2014).

Several recommendations issued from the 2013 research indicated that data quality, data sources,

data consistency, and data attributes are major challenges for Plexxus. In addition, analytic

technologies are limited to Excel Pivot Tables and tools from the Plexxus SAP system (Edmison,

Mouradov, Popescu & Sulatycki, 2014). However, these challenges are ameliorated as of today,

and further statistical and quantitative approach could be applied on the issue of healthcare

supply chain efficiency.

Building on the proof-of-concept effort in the original research, this report focuses on the

financial implication of supply chain efficiency on hospital finance (i.e. the Health System

Funding Reform), various statistical and quantitative methods (e.g. linear regression, time series

forecasting) suitable for the task at hand, and final recommendations and statistical models built.

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!

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Background

1.1 Challenges & Solutions !On January 2012, Ontario Ministry of Health and Long-Term Care introduced the Health System

Fund- ing Reform (HSFR), which replaced the current global funding system that is based on

historic costs of hospitals. The HSFR intends to replace 70% of the global funding with Quality-

Based Procedures (QBP), and Health Based Allocation Model (HBAM), which represent 30%,

40% of the total funding respectively (MOHLTC, 2014).

These unforeseen changes in the way hospitals in Ontario are being funded had placed enormous

pressure on the management team to adapt their current financial and operating plans. These

changes in funding will also likely to have a lasting impact on how budget control and

organizational process will be planned in the future.

The key for hospitals to accommodate this significant funding change is the ability to analyze

and forecast supply and demand of healthcare services, and be able to have a quantitative way of

managing cost associated with satisfying the demand, given limited resources.

Given appropriate data, we can model the relationship between demand and supply using

regression analysis and decision tree analysis; in the sense that given existing services UHN

provide (demand), and the existing resources (supply), the management team can anticipate the

resources needed. This provides tangible savings for UHN since over-staffing and/or excess

inventories could be avoided.

As for Plexxus, UHN's resource-need estimate would inform product purchasing and negotiation,

resulting in more informed and methodical purchasing procedures. Moreover, provided that

Plexxus had to manage the purchases for multiple hospitals, optimal product mix could prove

challenging, since product standardization process maybe arduous, and the amount of products

and hospital needs are different. This could be solved by adapting linear optimization algorithm,

which minimizes total cost of purchase given the constrains and requirement of different hospital

budgets and needs.

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Before delving into the details of our literature review and methodology, we have to evaluate the

feasibility of obtaining appropriate data from UNH and Plexxus.

1.2 Access to Data !We categorized our data needs into supply-side and demand-side. The analogy being drawn here

is that, one can view the healthcare sector as a vibrant economic system, with its own supplies

and demands. The demand side represents the multifarious health needs of our citizens, and the

supply side represents the ability and capacity of hospitals to meet those needs.

By using the supply and demand analogy, we can align this research to the HSFR guideline,

which aims to bring supply and demand into equilibrium (MOHLTC, 2014). Moreover, our

search for data can be streamlined, and our findings could be placed within the context of

hospital funding system.

1.3 Supply Side Data !Supply side data refer to any data involved in providing healthcare services (e.g. gloves, nurses),

and clinical metrics. These data pertain any quantitative information from the ERP system of

Plexxus (i.e.SAP), reporting database of UHN (e.g. Discharge Abstract Database, National

Ambulatory Care Reporting System), and any relevant data from UHN's electronic health

records.

For example, Plexxus has the purchasing data of hospital commodity products such as gloves, IV

solutions; UHN maintains records of overhead costs, and patient discharge data. In addition,

certain internal hospital performance metrics such as patient turn-over rate, hospital-related

infection rate, and average waiting time, also prove to be reliable source of data.

Supply side data are linked to HSFR, and the individual investigation in the supply side will

prove invaluable to the Health Based Allocation Model (HBAM) section of HSFR, which

requires hospitals to provide “utilization estimates and multi-year forecasts by program, detailed

analysis of resource use, including profile of highest use population providers’ costs and

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expenses, including detailed information on hospitals’ unit cost variance for each of its care

types.” (MOHLTC, 2014)

1.4 Demand Side Data !Demand side data comes from UHN, Statistics Canada, and Ontario Ministry of Health and

Long-Term Care. These data include metadata of patient diagnosis groups, population growth,

and census information.

Under HBAM, a number of publicly available inputs (e.g. expected population growth, health

care access pattern, etc.) are used to predict how many services each hospitals are expected to

provide in a given year, and what should be the cost benchmark for each service rendered (Born

& Dhalla, 2012).

1.5 Data-mining & Forecasting !Having identified reliable source of data, there are two objectives to be achieved. For UHN,

forecasting and modelling will be conducted using decision-tree model, and regression analysis.

For Plexxus, product mix optimization will be calculated using linear optimization algorithm.

An example of forecasting and modelling for UHN is as follows. It can hypothesized that there is

a causal relationship between glove and alcohol swab utilization rate and hospital-related

infection rate, controlling for patient diagnosis and condition. Statistical test will tell us whether

this relationship holds true or not. If there is indeed a causal relationship, adjustment of input

variables (e.g. the type of gloves used, or the frequency of alcohol swabs used) will change the

output variable (i.e. the rate of hospital-related infection rate).

Using Plexxus' data, linear optimization allow us to find the product mix that minimizes total

cost. For instance, given the constant costs of gloves, and different purchase portfolio and

budgets for these gloves by different hospitals, we can satisfy both conditions by solving for the

amount of gloves that should be purchased for each category of gloves.

!

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Literature Review: Group Purchasing Organization

!2.1 Supply Chain Cost Reduction !Many models exist within the healthcare supply chain, such as simple supplier to contractor

relationship, group purchasing organizations, and consolidated service centre (Vries & Huijsman,

2011). The cost saving opportunity for hospitals relies on the selection of appropriate model, and

an understanding of the processes of supply chain management. This literature review

encompasses: a) key issue in healthcare supply chain; b) virtual integration of the healthcare

supply chain; c) theories of supply chain management integration and implementation; d) IT

application example and potential in the healthcare supply chain; e) the business case for

healthcare supply chain integration.

2.2 Key Issue in Healthcare Supply Chain — Standardization !Standardization of healthcare supplies reduces costs by increasing bargaining power of hospitals,

reducing time and efforts needed to negotiate and re-negotiate contracts, and improving health

outcome of patients. Many ills and inefficiencies in the supply chain can also be greatly

diminished ( McKone, Sweek, Hamilton & Willis, 2005).

Other than providing updated infrastructure and equipments, healthcare supply chain for

commodity products such as gloves and surgical sutures provides hospitals with an untapped

source of financial saving (Roark, 2005). In the primary and tertiary healthcare setting, the

typical supply budget represent 25% to 30% of the operating cost. This budget is largely

determined by physician preferences other than budgetary considerations, therefore, cost

reduction efforts and benchmarking prove difficult (Roark, 2005).

One of the cause for this conundrum is because regular frontline professionals are not normally

trained in business processes. They also believed that maximum availability of medical supplies

is crucial to the lives of their patients, therefore sacrificing patient safety due to cost

consideration is unacceptable (Rahimnia & Moghadasian, 2010). Group purchasing

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organizations (GPO) such as Plexxus are critical gatekeepers and have the bargaining power to

ensure supply chain efficiency.

GPOs negotiate contracts and manage supplier relationships, they are responsible for obtaining

optimal price for the hospitals (Vries & Huijsman, 2011). Hospitals, in turn, still have to

purchase in bulk in order to maintain the con- tract price obtained by GPOs (Brennan, 1998).

However, such contract arrangement may lock hospitals into position as commodity prices drop,

and such purchasing flexibility may reduce the adoption of new innovations (Roark, 2005).

Moreover, anti-trust and price manipulation allegations had been concerns regarding GPOs, and

both the U.S. and Canadian government have regulations concerning the quantity and total

purchase from GPOs (Roark, 2005).

Shipping and delivery represent a large portion of the overall spending, since hospitals use

thousands of types and brands of medical equipments. In addition, the projection of the demand

of equipments is difficult to measure, therefore leading to supply chain inefficiencies (Roark,

2005). In a way, it is the method of negotiating contract and managing logistics that determine

the saving opportunities, less so to do with the actual benchmarking. Standardization of

equipments, on the other hand, provide the area of greatest savings. Many industries have

realized reduction of cost by removing the “transactions costs” between switching between

standard (Brennan, 1998; Vries & Huijsman, 2011).

Other than cost saving, standardization can sometimes improve patient outcome. For instance, by

standardizing pressure ulcer dressings, there is noticeable reduction in the incidence of

nosocomial pressure-ulcers (Roark, 2005). In the case of healthcare related supplies, such

approach will be deemed appropriate first in the regional level, municipal level, and eventually

national level. The following section provides frameworks on how to create a GPO-like supply

chain structure to foster standardization, and circumvent the problems discussed above.

2.3 Virtual Centralization of the Healthcare Supply Chain !While diagnostic and treatment breakthrough are constantly evolving, the delivery method of

healthcare through the three tiers (primary, secondary, tertiary) of healthcare has been relatively

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stable for decades (Parker & DeLay, 2008). Following similar trend, medical supplies also

enjoyed tremendous improvement regarding their safety, ease-of-use, and efficacy. Nevertheless,

the supply chain structure of medical supplies had remained the same (Parker & DeLay, 2008).

One way of improving the supply chain structure is through using virtually centralized supply

chain management. A prominent example of this is a consolidated service centre (CSC).

Differing from the group purchasing organizations (GPO) discussed in the previous section, CSC

is not only focused with contracting, procurement and customer services, but also distribution

(Parker & De- Lay, 2008). Other benefits of CSC include:

• Networking opportunities for participating hospitals, sharing best practices, and products

experiences.

• Exceptional pricing and order accuracy, and lowered operation expenses associated with

individual supply chain management.

• Encourage standardization and volume aggregation, thus reducing inventory, lower

distribution costs, and reduce transportation costs.

• Provide medium to small sized facilities with the benefit of bargaining power previously

enjoyed only by large hospitals.

• Freeing management attention towards clinical quality instead of budgeting by

outsourcing supply chain to CSC (Parker & DeLay, 2008).

!There are several steps to take in order to form a CSC from the ground: “partner with other

regional hospitals, standardize products, foster a spirit of cooperative competition, leverage

partnerships, centralize material management, share consulting resources, and elevate materials

management leadership.” (Parker & DeLay, 2008). The salient points are hospital partnerships,

standardization, and leveraged partnership.

Hospital Partnerships: hospitals from proximal geographical locations should form regional

CSCs (Parker & DeLay, 2008). The resulting aggregation of purchasing power will not only

secure optimal prices from suppliers, but also establish consistent relationship with those

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suppliers. In addition, as demands fluctuate, supplies can be swapped between partners for better

inventory control (Brennan, 1998). Such CSCs can also be sub-specialized according to

specialty, for instance, family physicians within the same city could form a CSC to request for

items commonly used in that setting.

Standardization: commodity products such as gloves, dressings, and sutures should be

standardized to secure maximized purchasing bulk. The identification and categorization of

commodity products should be done collaboratively, and the final decision of the selection of

products should be based on evidence (e.g. peer reviewed journals). Other specialized, high-price

physician items such as generic medications, imagining devices should be the second priority of

standardization (Vries & Huijsman, 2011). The end goal of standardization is to reduce the

number of suppliers thus increasing bargaining power and complexity of contracts. Even in the

case that standardization does not take place, the process of sharing evidence will stir the CSC

towards commonality of choice (Parker & DeLay, 2008).

Leveraged partnership: some hospitals may have dealings with other supply chain partners other

than GPOs, such as distributors, and progressive suppliers. Hospitals should leverage the

knowledge and experience of these partners (Parker & DeLay, 2008). However, there would be

difficulties in this endeavour due to conflict of interests, as CSC would exert greater pressure on

existing suppliers or terminate existing unfavourable contracts.

2.4 Supply Chain Management Integration and Implementation !With the framework of CSC in mind, the next hurdle lies in how to integrate existing supply

chain divi- sions of hospitals into a CSC. A comprehensive literature review has been done by

Damien Power (2005) at the University of Melbourne to address this issue.

2.5 Supply Chain Management Integration !The three elementary components of integrated supply chain are information systems, inventory

management, and supply chain relationships (Power, 2005). The basis of integration can be

defined by “co- operation, collaboration, information sharing, trust, partnerships, shared

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technology and a fundamental shift away from managing individual functional process, to

managing integrated chains of processes” (Power, 2005, p. 253).

Information System: Information flow between organizations are driven by both hardware and

software technology. Examples of hardware technology include telephone, fax machines, etc.,

and software technology are represented by tabulation software (Excel) and enterprise resource

planning (ERP) software (Lee, Lee & Schniederjans, 2011). These information technologies

reduce the complexity of communication and provide details and comparison between

organizations (Power, 2005). Miscommunication can break the basis of integration such as trust,

and collaboration. Other more practical impacts of asynchronous IT are: excessive inventories,

untimely planning, and increased logistical costs (Power, 2005).

Physical logistics: having an integrated supply chain means that organizations can have

accelerated response rate of market demand, and at the same time holding on to minimum level

of inventory. This reduced cycle in supply chain often translate business advantages (Power,

2005). IT again comes into the fore as the most important factor that determines the success of

improved logistics. Physical distribution centres depend on IT to optimize best in-bound, out-

bound routings. IT also provides a way of benchmarking suppliers, and allows CSC to decide

which suppliers to keep or drop.

Partnerships, alliances and cooperation: supply chain analysis and a clear identification of

common interests between parties are essential to align the objectives of organizational partners

(Power, 2005). Upper management attentions are needed to ensure full-cooperation. Before the

full fledging of CSC, trust can be developed directly through negotiations and stakeholder

meetings, and in directly through commitments in smaller purchases. One of the challenges of

partnerships is when “the benefits ‘pool’ with some members at the detriment of others” (Power,

2005, p. 257). However, in the case of CSC, hospitals’ interests converge towards cost-reduction,

and the “benefits pool” of the hospitals and of suppliers are mutually exclusive.

!!!

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2.6 Supply Chain Management Implementation !Key criterion of supply chain management implementation are suitable selection of IT, and the

use of “third-party providers for both transportation and information management” (Power, 2005,

p. 258). A successful implementation example in a European company elucidate seven critical

success factors that are applicable for CSC (Power, 2005, p. 258):

1. a committed organization, from the board down;

2. effective programme management;

3. consistent, pre-emptive communications;

4. positive action to identify and manage key risks before they become issues;

5. a well-defined and managed programme baseline, changed as necessary;

6. a succession of manageable delivery millstones to maintain momentum and confidence;

7. an actionable, owned, manageable and measurable set of business benefits.

!CSC will rely heavily on the selection and deployment of appropriate IT, the next section discuss

the usage of radio frequency identification devices (RFID) in the healthcare supply chain.

2.7 IT in the Management of Healthcare Supply Chain — RFID !Radio frequency identification devices (RFID) are electronic signal senders embedded into or in

close proximity of a product or shipment (Kumar, Swanson & Tran, 2008). They can track the

location of product which in turn can improve information passed onto supply chain managers,

thus benchmarking and optimizing supply chain efficiency (Smith & Flanegin, 2004). Three

ingredients are essential for CSC to provide the cost saving it purports: prices, logistic efficiency.

CSC already provides a platform to track pricing, RFID can control for logistic efficiency.

Kumar, Swanson & Tran (2008) studied the cost benefit analysis of applying RFID in the

healthcare supply chain setting. They found that the benefits of RFID are invaluable, such as

“reduced time, effort, and patient deaths” (p. 78). However, the cost of implementing RFID at

this stage surpasses the value it generates. Even so, outsourcing RFID management to a three-

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party, for example Amazon, could potentially solve the cost consideration. We can see that the

fruition of CSC relies on IT, physical logistics, and partnerships.

2.8 Making Business Sense !What ties everything together is whether a business case exists in improving healthcare supply

chain efficiency (Brennan, 1998). Economic savings, economic investment, and noneconomic

factors should be included in the CSC proposal.

Economic savings: economic benefits are not necessarily related to cash flow, it could be savings

that are gained from reductions of inefficiencies. A financial assessment should be conducted,

and specific cost savings and assumptions should be clarified (Brennan, 1998). Scenario analysis

needs to be included to indicate the time-sensitivity of proposed plan. If operational changes are

proposed, the scenario analysis should reflect the impact of these changes on anticipated returns

(Brennan, 1998).

Economic Investment: the proposal should include forecasting of capital and personnel

investments required to fully or partially implement CSC. Transactions costs, such as relocation

fees, travelling, train- ing, and organizing costs should be fore-sought (Brennan, 1998).

Non-economic factors: CSC’s impacts on existing supplier relationship, management shortages,

change managements, should be evaluated. It is important to note that hospitals are non-for-profit

organizations, and non-economic benefits should be quantified and distributed among frontline

healthcare professionals (Brennan, 1998).

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Literature Review: Ontario Healthcare Funding Reform !3.1 Healthcare Funding Reform and its Impact on UHN !The Health System Funding Reform (HSFR) is the driving force behind the need for this report,

and the funding formula and rationale are essential to the replicability of this research finding to

other hospitals. HSFR will be discussed in detail in the following section.

3.2 Health System Funding Reform (HSFR) !Ontario's healthcare system is shifting towards a patient-based funding system instead of a global

one, and the HSFR is implemented in 2012 by the Ontario Ministry of Health and Long-term

Care (MOHLTC) in order to fulfill the requirement set by the Excellent Care for All Act passed

in 2010. This entails that HSFR will eventually account for 70% of the total funding provided to

hospitals, and the remaining 30% will still be rationed out on a global basis (MOHLTC, 2014).

Traditionally, each hospital’s fund allocation is determined by historical spending patterns,

inflation, and one-off negotiations between hospital executives and civil servants (MOHLTC,

2014). Even though this global funding provides stable budget for hospitals, it does not provide

financial incentives for those hospitals to increase efficiency. In addition, some hospitals have

been more successful at negotiating with unions than others, and critics of global budgeting

argue that these negotiations lead to some hospitals receiving more than their fair share of

resources. (Born & Dhalla, 2012; Sutherland, 2011).

HSFR's patient-based funding takes measures to provide more equitable and evidence-based

fund allocation by taking into consideration population metrics, numbers of patients actually

served, evidence-based quality of service and population needs (MOHLTC, 2014).

HSFR contains two components: Health Based Allocation Model (HBAM), and Quality-Based

Procedures (QBP), each dealing with funding equality and evidence-based practice issues. The

current funding allocation has not reached the proposed proportion yet, as only certain items on

QBP had been implemented. Figure 1 illustrates the present breakdown of HSFR (MOHLTC,

2014).

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3.3 Health Based Allocation Model (HBAM) !HBAM represents 40% of total funding sanctioned by HSFR, and its purpose is to provide an

evidence-based, and health based funding formula. HBAM estimates hospital's future expenses

based on a Service Component and a Unit Cost Component (MOHLTC, 2014).

The Service Component estimates the amount of market share a hospital has among the total

health service providers (HSP). The Unit Cost Component calculates expected unit cost for

hospitals based on regression equations specific to each hospital and modules. The total

Expected Expenses is derived from the product of the Service Component and the Unit Cost

Component. Then the total Expected Expenses for one hospital is divided by total Provincial

Expected Expenses to determine HBAM Expected Share represented as a percentage. This

percentage is then multiplied to the actual provincial healthcare funding to derive the finally

funds allocation to each hospitals (MOHLTC, 2014). The relationship of the formula is shown

below:

Service Component * Unit Cost Component=HSP HBAM Expected Expense HSP HBAM Expected Expense/ Total Provincial HBAM Expected Expenses= HBAM Expected !

Share HBAM Expected Share * MOHLTC funding = Actual funding to individual HSP !Moreover, HBAM has five modules of clinical areas which only three are fully in effect

(discounting HBAM for Community Care Access Centres, which handles community health and

17

Full Implementation

HSFR Phased-in Over Time

HBAM

Global Funding QBP

Current Pre-HSFR

Global Funding HBAM Global

Funding

QBP

Example: Hospital Changes Over Time

17

Figure 1. Current HBAM distribution (left), target HBAM distribution (right)

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home care). These modules are: acute inpatient & day surgery, complex continuing care,

emergency department, inpatient rehabilitation, and inpatient mental health (MOHLTC, 2014).

In the case that expected funding is insufficient or that HBAM cannot model HSP’s true expense,

mitigation strategy and special provisions for technical insufficiency will be in situ. The final

released funds are allocated from MOHLTC to the Local Health Integration Network (LHIN)

which subsequently get passed on to HSP (MOHLTC, 2014).

3.4 Service Component !The Service Component includes four stages, and it estimates the approximate marketshare of

HSP based on population and census information. This is to ensure that HSP’s services and

capacity are adjusted to the demand of the population (MOHLTC, 2014). For instance, if the

prevalent condition in the Milton region is mostly cardiac related, extra X-ray machines and

technicians for the Milton General Hospital would be considered wastage.

HBAM collects data from HSP and databases such as Discharge Abstract Database, National

Ambulatory Care Reporting Systems, and Ontario Cost Distribution Methodology. This

information is used to inform the Person Profile, Expected Weighted cases, Growth Adjustment,

and HSP Market Share stages of the Service Component (MOHLTC, 2014).

Person Profile is consists of all hospital services received by a person that are covered by OHIP,

and that person’s socioeconomic status extrapolated from census data. An aggregate of Person

Profiles from a HSP is then categorized into Modelled Expected Weighted Cases and Non-

Modelled Actual Weighted Cases (MOHLTC, 2014).

Modelled Expected Weighted Cases are common ailments and expected services provided for

those ailments. The details of the models are not disclosed publicly but the variables used are

disclosed: age & gender, socio-economic census, and rurality (MOHLTC, 2014).

If a patient has indigestion and sought out treatment, his/her visit for this specific condition will

be compared to others’ with the same condition (thus called “modelled”), and the average time

and resource that are dedicated to this indigestion are assigned to this his/her “case” without

consideration of the actual time and resources spent. The assumption here is that the variation of

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costs eventually cancel each other out because these modelled cases are so numerous that

statistically, it makes sense to take the average without fixation on individual cases.

Non-Modelled Actual Weighed Cases are special services that may or may not be provided for a

unique population, and they do not represent typical Ontario cases. These cases can not be

modelled either due to low frequency or complexity. Organ transplant, Aboriginal health, and

neonatal patients are such examples (MOHLTC, 2014).

Non-Modelled cases and Modelled cases are combined for for a case mix, which in turn

undergoes Growth Adjustment. HBAM uses publicly available predictions of population

parameters such as demographical shifts, immigration, and emigration, to calibrate the forecast

for case mix (since HBAM is concerned with future budget). The lowest rank of such population

data is based on regional census data collected by Statistics Canada, and at this level, census

divisions match with corresponding LHIN operational boundaries, so that population projections

reflect concise health needs of census population (MOHLTC, 2014). On top of that, in order to

account for patients seeking health service outside of their census area, Growth Adjustment will

take the patients census data from their most recent residence and augment to the case mix

(MOHLTC, 2014).

The last stage in the Service Component of HBAM is calculating HSP Market Share. All Ontario

HSPs’ expected weighted cases (Non-modelled cases plus Modelled cases) will be calculated

using the previous three stages (with the exception of Inpatient Mental Health and Complex

Continuing Care), however, individual HSP’s expected weighted cases are subject to change

(MOHLTC, 2014).

3.5 Unit Cost Component !The Service Component measures expected units of services delivered by HSP, and the Unit Cost

Component estimates the unit costs that correspond to the expected units of services.

Specifically, HBAM uses linear regression to find HSP’s expected unit costs, which measures the

relationship between multiple changing variables (MOHLTC, 2014). However, linear regression

does not differentiate between clinical setting and specific cost variables of HSPs. Therefore, cost

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modifiers are applied to different clinical settings (i.e. modules) in order to recognize HSP

characteristics.

Since the detailed linear regression formulae are not publicly released, several hypotheses will be

given here as plausible methodologies of the linear regression formulae used.

1) Total costs of all hospitals in Ontario are normalized by total services provided by HSPs.

2) Cost variables are separated by LHINs, and total costs of all hospitals are normalized by total

services provided by HSPs in one LHIN.

3) Individual HSP’s historical costs are analyzed, and the resulting formulae discounts cost

abnormalities.

Hypothesis 1 over-generalizes cost factors to a provincial level that are not useful in informing

distinctive cost structures of HSPs, population clinical needs, nor geographical differences.

Hypothesis 3 does not deviate too much from the previous global funding system, and it

discounts the fact that there are similarity between HSPs and possible benchmarking of

reasonable cost levels. Hypothesis 2 is the most likely scenario since it combines the benefits

from both hypothesis 1 and 3, while mitigating their deficiencies.

14 Local Health Integration Networks (LHINs) are created by MOHLTC in 2006, and their

purpose is to plan, integrate and fund HSPs (LHIN, 2014). LHINs work closely with local HSPs

and communities, and they ensure the correct coordination of HSPs to deliver optimal tax-dollar

values. They study the healthcare needs, trends and best practices. LHINs also negotiated with

HSPs regarding the services HSPs provide, and the terms and conditions are reinforced through

formal and legal agreements. By segmenting HSPs costs using LHINs, regional health needs are

well defined and controlled for, and HSPs are expected to justify their costs according to those

regional health needs (MOHLTC, 2014). A linear regression based on hypothesis 2 is shown

below:

!

Page !21

∑ Cost of HSPs from Toronto Central LHIN = ⍺ * services provided in Acute Inpatient & Day

Surgery + ß * services provided in Emergency Department + … + ei

⍺ = expected total cost of Acute Inpatient & Day Surgery

ß = expected total cost of Emergency Department

Expected Unit Cost of Acute Inpatient & Day Surgery = Total cost of Acute Inpatient & Day

Surgery / Total services provided in Inpatient & Day Surgery

Within the regression model, there will be other variables that are statistically significant in

explaining the total cost of HSPs, and these variables are the Cost Modifiers. For example, taking

into consideration the number of medical interns and the rurality of the HSP, the unit cost of the

emergency department of a small rural HSP will be higher compared to that of an inner city ER

department. There are five Cost Modifiers that are either activate or deactivated across five

modules of HBAM (MOHLTC, 2014) (Figure 2).

!The formula that demonstrates the Cost Modifiers are as follows:

Module Teaching Rural Geography

Economy of Scale (size)

Specialized Services

HSP type

Acute Inpatient & Day Surgery ✓ ✓ ✓

ER ✓Complex

Continuing Care (CCC)

✓ ✓ ✓

Inpatient Rehabilitation

✓ ✓ ✓

Mental Health ✓ ✓ ✓

Figure 2. Cost Modifiers for 5 HBAM modules

Page !22

∑ Cost of HSPs from Toronto Central LHIN = ⍺ * services provided in Acute Inpatient & Day

Surgery + ß * services provided in Emergency Department + ∂ * number of interns + µ *

number of employee + π * population density of the LHIN + … + ei

⍺ = expected total cost of Acute Inpatient & Day Surgery

ß = expected total cost of Emergency Department

∂ = Cost Modifier for teaching HSPs

µ = Cost Modifier for Economy of Scale

π = Cost Modifier for Rural Geography

In conclusion, there are five Expected Unit Costs for each HBAM module, and they are adjusted

by Cost Modifiers. For the year of 2012, Expected Unit Costs do not apply to small HSPs and

Mental Health module, and HBAM Expected Unit Cost equals to the actual unit cost (MOHLTC,

2014).

3.6 Getting to Hospital Expected Expenses !With the Expected Service and Expected Unit Cost estimated for five HBAM modules, a final

HBAM Expected Cost is calculated (MOHLTC, 2014).

For each of the five modules of HBAM, there are five HBAM Expected Costs. Actual service

provided and cost of the CCC and Inpatient Mental Health modules are used instead of the

Expected Service and Expected Unit Costs. This is due to HBAM’s inability to estimate the costs

correctly within a acceptable margin of error (MOHLTC, 2014). Non-HBAM Expenses are costs

associated with out patient clinic or expected growth in service capacity. Five HBAM Expected

Costs plus Non-HBAM Expenses equals HBAM Overall Hospital Expected Expenses. Each

individual HSP will have a HBAM Expected Share calculated based on HBAM Overall Hospital

Expected Expenses (MOHLTC, 2014).

HBAM Expected Share (%) = HSP HBAM Expected Expense / Total Provincial HBAM Expected

Expenses

Page !23

HBAM Expected Share is represented as a percentage point, and HSP’s Expected Share times

the actual funding allocated by MOHLTC equals to the final dollar amount individual HSP will

receive.

Final dollar amount = HBAM Expected Share * MOHLTC funding

This process is done to ensure that, were there any universal changes in the case models or

readjustment to the inputs of the Service Component or Unit Cost formulae, there will be no

need to recalculate HBAM Overall Hospital Expected Expenses (MOHLTC, 2014).

3.7 Quality Based Procedures (QBP) !QBP have similar funding structure as HBAM where the Expected Service for clinical

procedures, such as cataract surgery, times the Expected Unit Cost equals to the expected

funding HSP will receive. QBP concerns with clinical outcome and evidence based practice, and

not medical products, therefore detailed information will not be provided here.

!!!!!!!!!!

Page !24

Statistical Methods & Data Analysis

4.1 Data Collection !Data from the Plexxus supply chain ERP (SAP) regarding purchasing orders were collected by

the researcher, and the data span from April 2013 to April 2014. The SAP data were converted

into spreadsheet format for Microsoft Excel program, and the final Excel file contains 20

variables, and 629692 observations. Figure 3 represents an example of one of these observations.

!4.2 Data Cleaning !Certain variables are either not useful or distracting for the purpose of cost analysis. For

example, SAP Material refers back to the original location of the data extracted, and this piece of

information is not needed unless a double-checking of data-quality is required. Therefore the

researcher decided to only contain meaningful quantitative data such as PO Quantity, and

relevant categorical variables such as Recipient/Department Name.

Figure 3. One observation of purchase order from Plexxus

Purchasing Document

Company Code Document Type Document Type Description

Created On

1000000000 1000 XC Ad-hoc STO to DC 2013-04-01Vendor Vender Name Purchasing Group Currency Line Item1000000 Hospital Admin. PLX CAD 10000

Key Account Assignment

SAP Material Material Description

Plant

400000000000000 K 333333 TIP BULB Suction 1000Material Group Material Group

DescriptionVendor Material

NumberManufacturer Part

NumberPO Quantity

24444444 Medsrug General D00000M D11111M 50Order Unit Net Price Per Order Price Unit Net Value

EA 22.22 1 BX 13444Currency Cost Centre Recipient Recipient/

Department NameReference: !Contract

CAD 10000000 11BB4-Unit ICU DCCWXT2304Vendor Vender Name Purchasing Group Currency Line Item1000000 Hospital Admin. PLX CAD 10000

Reference: Contract line item Reference: Purchasing Info Record34442 42235

Page !25

There are also redundant variables in the dataset, for example, Currency appears three times in

the data set. Interchangeable variables, such as Material Group and Material Group Descriptions,

also encumber data analysis. The redundant and interchangeable variables are also removed from

the original dataset, resulting in 10 variables shown in figure 4 .

Four currencies are used for purchasing purposes by Plexxus: Canadian Dollar, Euro, British

Pound, and U.S. Dollar. 98% of all transactions are done using the Canadian Dollar, and 2.2%

are done via U.S. Dollar. There are only three transactions through Euro and British Pound, and

the total net value of these transactions are only $ 2,254 CAD out of $700 million. Due to the

insignificant share of other currencies, the researcher converted USD, EUR and GBP in to CAD

using July, 2014 conversion rate.

Data inconsistencies exist around Net Price and Net Value in the dataset. The formula for

calculating Net Value is PO Quantity times Net Price. However, for certain observations, this

formula does not hold. On closer inspection, two main issues arise: Net Price conversion units

inconsistency, and Order Unit variations.

Most observations use dollar as a base unit, but a minority uses cents. This unit base error is

corrected by applying Original Price/10 formula to affected observations. Also, there are five

Order Units: BX, CA, EA, PK, PR, (i.e box, case, each, package, pair) and the Net Price/Order

Unit calculation is different for PR. This is corrected by applying Original Price*0.005 to the

affected observations. Finally, Net Value is checked by using the Adjusted Net Price times PO

Quantity, and IF formula in Excel.

!

Created On Currency Material Description

PO Quantity Order Unit

2014-05-30 CAD Glove Procedure S 40 BXNet Price Per Order Price Unit Net Value Recipient/

Department Name30 1 BX 1200 Medicine

Figure 4. Cleaned observation of purchase order from Plexxus

Page !26

4.3 Data Subsection !The scope of this research is only concerned with commodity products, which are specifically

IV products, gloves, and sutures & staples. These products are consistent with the 2013

research. However, the only analysis that will be presented in this report focuses on the gloves

category.

4.4 Top 10 Purchased Items !There are 57 different types of gloves being purchased and the total net value is $455,307.76

(CAD). The top 10 types of gloves represent 60% of the total spending, one out of the ten is

surgical glove and the rest being examination gloves (Figure 5).

!The average amount spent on individual glove type is $7,717, and the range starts from $68.2 for

GLOVE WORK COTTON, to $36,046 for GLOVE EXAM CURAD TEXTURED PF SMALL.

!$36,046.30!! !$36,005.90!!

!$32,063.19!!

!$30,072.55!!!$28,338.13!!

!$24,989.35!!!$23,237.82!! !$22,482.60!!

!$20,557.56!!!$19,017.67!!

!$/!!!!

!$5,000.00!!

!$10,000.00!!

!$15,000.00!!

!$20,000.00!!

!$25,000.00!!

!$30,000.00!!

!$35,000.00!!

!$40,000.00!!

GLOVE!EXAM!CURAD!

TEXTURED!PF!SMALL!!!!!!!

GLOVE!SURG!DERMAPRENE!

PF!SZ!6!!!!!!!!!!!!

GLOVE!EXAM!NIT!FGRTXT!PF!SNSCRICE!

BLU!M!!

GLOVE!EXAM!NITRL!TXT!PF!LF!CURAD!BLU!!

M!!

GLOVE!EXAM!CURAD!

TEXTURED!PF!MEDIUM!!!!!!

GLOVE!EXAM!NITRL!TXT!PF!LF!CURAD!BLU!!

L!!

GLOVE!EXAM!NITRL!TXT!PF!LF!CURAD!BLU!!

S!!

GLOVE!NITRILE!EXAM!PURPLE!MED!

BX100!!!!!!

GLOVE!EXAM!NIT!FGRTXT!PF!SNSCRICE!

BLU!L!!

GLOVE!EXAM!SYN!STRETCH!PFREE!UNIV!

3G!M!!!

Figure 5. Top 10 items in terms of total net value

Page !27

The quartiles are: Q1 $483, Q2 $2,225, Q3 11,368 (Figure 6). The box-

plot shows that purchasing amount varies the least below median at

$2,252. This means that below the median, the Net Value differences

between each glove types are small. For instance, GLOVE EXAM

NITRILE PF MFLX XCEED BLU S with a annual net value of $978 only

has 1 dollar difference to the item next to it, while $2,500 more GLOVE

EXAM CURAD TEXTURED PF MEDIUM are purchased compared to

the item below it.

Glove types beyond the upper whisker represent really far-lying values that

are not expected from the rest of the data. However, in this case,

those data points are of interest, since outlier values often lead to

intriguing explanations. On top of that, these data represent high

value purchases, therefore any potential findings for cost reduction will lead to greater total

dollar saved compared to that for lesser net value items. The top 10 items in terms of total net

value will be analyzed in the next sections.

4.5 Individual Item Purchasing Pattern !The daily net values of each item are plotted against time, and two types of purchasing patterns

are observed. The first type of pattern is cyclical. Figure 7 is a typical time series graph for the

!

!!

0

10000

20000

30000

Net

Val

ue ($

CAD

)

!$#!!!!

!$200.00!!

!$400.00!!

!$600.00!!

!$800.00!!

!$1,000.00!!

!$1,200.00!!

!$1,400.00!!

2013#04#01!

2013#04#08!

2013#04#15!

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2014#03#06!

2014#03#14!

2014#03#24!

GLOVE&EXAM&CURAD&TEXTURED&PF&SMALL&(Total&Net&Value&$36,046.30)&&

Figure 6. Box-plot of Net Value

Figure 7. Purchasing

pattern for one of the top

purchased items in terms of net

value

Page !28

top 10 purchased items, and there are regular intervals where the daily net value rises an falls.

This can be explained by the fact that as gloves are being depleted, automatic orders will be

make from the hospital to Plexxus.

The second type of purchase pattern is associated with average infrequent purchases combined

with the few large purchases (figure 8). This is likely associated with stockpiling practices

common in certain department (e.g. specimen procurement) or attributable to unpredictable

events (e.g. flu immunization).

!!!!!!!!!

!!!!

!$#!!!!

!$2,000.00!!

!$4,000.00!!

!$6,000.00!!

!$8,000.00!!

!$10,000.00!!

!$12,000.00!!

2013#04#03!

2013#04#19!

2013#04#24!

2013#05#06!

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2013#05#22!

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2014#03#12!

2014#03#27!

GLOVE&EXAM&NIT&FGRTXT&PF&SNSCRICE&BLU&L&&(Total&Net&Value&$&$20557.56)&

&

Figure 8. Purchasing pattern for one of the top purchased items in terms of net value

Page !29

4.6 Daily Number of Transactions !The daily number of transactions is defined as the number of items being purchased disregarding

ordering quantity and price. There are no extreme values, and the maximum number of orders

placed in a given day is 55 (Figure 9).

One thing to note is that there is a pattern of cyclicality presenting in frequency of purchases.

Figure 10 shows a three-weeks segment from the figure above.

!!!!!

0"

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Num

ber'o

f'transac/o

n'

0"

10"

20"

30"

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50"

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Mon" Tue" Wed" Thu" Fri" Sat" Mon" Tue" Wed" Thu" Fri" Sat" Mon" Tue" Wed" Thu" Fri" Sat" Mon" Tue" Wed"

Num

ber'o

f'transac/o

n'

Figure 9. Daily number of transactions over time

Figure 10. Three-weeks segment of daily number of transactions

Page !30

The purchase amount is at minimum on Mondays, increases over the week and decreases close to

Saturday. Plexxus does not open for operation on Sundays.

Figure 11 is taken from the same three-weeks segment, however net value is being measured

here. The same cyclicality pattern is also observed. This figure also ensures that unit price

differences between items do not confound daily net value.

In fact, another insight is gained from comparing the two graphs: the daily net value can predict

the daily number of transaction, not knowing which item and how many are sold that day.

Despite the different measuring units, the direction, shape, and magnitude of the curves share

close resemblance. Also, there should be no relationship between the number of transactions and

net value, since there are multiple items/price being order per day and the exact quantity per item

is not given in the two graphs. Lastly, on an “eye-ball” inspection on the product mix and PO

quantity, there are no regularity of the types of products nor PO quantity to be found. In sum, all

these considerations point to the direction that two unrelated variables correlate somehow, and

the statistical tests of this relationship is given below.

!

!$#!!!!

!$500.00!!

!$1,000.00!!

!$1,500.00!!

!$2,000.00!!

!$2,500.00!!

!$3,000.00!!

!$3,500.00!!

!$4,000.00!!

Mon! Tue! Wed! Thu! Fri! Sat! Mon! Tue! Wed! Thu! Fri! Sat! Mon! Tue! Wed! Thu! Fri! Sat! Mon! Tue! Wed!

Net$Value

$

Figure 11. Three-weeks segment of daily net value

Page !31

4.7 Linear Regression between Daily Number of Transactions and Daily Net Value !Two columns of data, one represents the number of transactions, the other total net value, are put

in the statistical software R! for further processing. Linear regression method is used, since there

seemed to be a simple linear relationship between number of transactions and net value.

Figure 12 is the box-plots for our two variables, and there are seven outliers in Net Value, and

one in Number of Transactions. Theses outliers may affect the outcome of linear model since the

goodness of fit R2 is heavily influenced by outliers.

!!!!!!!!

Figure 13 shows the two scatterplots with or without these outliers. Two analyses are done in the

following sections with and without the removal of outliers.

In addition, the shape of the scatterplots is funnel like, indicating that data transformation using

logarithms is warranted. Logarithm will improve the linearity of data since it reduces the

variance of data due to the difference between unit of measurements. For example, when

comparing one variable that is measured in billions of dollar, and the other variable that is

0

10000

20000

30000

Net.Value

0

20

40

Num

ber.of.Transaction

Figure 12. Box-plots for Daily Net Value (left), and Daily Number of Transactions

Page !32

measured in thousands of dollars, logarithm will with enable you to find the order of magnitudes

(e.g. the exponent of 102), which downplays the absolute differences in measurement.

0

1000

2000

3000

4000

0 20 40Number of Transaction

Net

Val

ue

1

2

3

0.0 0.5 1.0 1.5Log(Freqency of transtions)

log(

Net

val

ue)

0

10000

20000

30000

0 20 40Number of Transactions

Net

Val

ue

1

2

3

4

0.0 0.5 1.0 1.5log(Number of Transactions)

log(

Net

Val

ue)

Figure 13. Scatter-plots of Daily Net Value verses Daily Number of Transactions. Outliers removed (left), outliers not removed (right)

Figure 14. Scatter-plots of log Daily Net Value verses log Daily Number of Transactions. Outliers removed (left), outliers not removed (right)

Page !33

Figure 14 shows the scatterplots of two datasets, the one on the left with the removal of outliers,

and the one on the right without the removal of outliers, in logarithmic terms. Even though the

scatterplot on the right still shows outliers, however, the degree to which it affects the rest of the

data is diminished greatly.

There are two linear regression models processed in the statistical software R — one model

removed outliers, the other did not. The resulting two linear equations are:

1) log(Daily Number of Transactions)= -1.50120 + 0.65826*log(Daily Net Value)

p-value<2e-16; R2 = 0.92; modified R2= 0.927699422 (Outliers removed)

2) log(Number of Transactions)= -1.64738 + 0.64654*log(Net Value)

p-value<2e-16; R2 = 0.88; modified R2= 0.928497103 (Outliers included)

Both p-values are <2e-16, which are significant, meaning that our model results are not obtained

based on chance. However, it is the R2 value that tells us the the goodness of fit of our model, in

other words, how much of the change in net value is explained by change in number of

transactions. R2 values are 0.92 and 0.88, which means 92% (or 88%) of the change in net value

can be attributed to change in number of transactions to the respective models.

However, we are dealing with log-log models, and the resulting R2 values does not express the

true measurement of change in net value, since the the interpretation of log-log models result in

measurement in elasticity (i.e. the % change in one value verses the % change in the other). The

ultimate method of deriving a true R2 value in log-log model is to take the log(Net Value)

outcome and manually calculate R2 (Shazam,1995).

The equation for R2 is:

!In practice, the Number of Transaction actual value is put in the equation 1) and 2), for example:

Page !34

log(Daily Number of Transactions)= -1.50120 + 0.65826*log(Daily Net Value)

Daily Net Value = 399

log(Daily Number of Transactions)= -1.50120 + 0.65826*log(399)

log(Daily Number of Transactions) = 2.4413

Daily Number of Transactions = e2.4413

Expected Daily Number of Transactions ≈ 11

After obtaining Expected Net Value for all the input variable of Number of Transactions, the

following calculations are carried out:

∑i (Expected Daily Number of Transactions - Mean of Actual Daily Number of Transactions)2 =

SSregression

∑i (Actual Daily Number of Transactions - Mean of Actual Daily Number of Transactions)2 =

SStotal

R2 = SSregression / SStotal

The modified R2 value for equation 1), the model with outliers removed, is 0.9276; the modified

R2 value for equation 2), the model without outliers removed, is 0.9254. Model 1 (with outliers

removed) is preferable, since the original R2 is identical with modified R2 value, hence more

reliable. Model 1 is also less computationally demanding, because the above transformation from

log to actual value can be discarded.

The final formula to derive Daily Number of Transaction, given Daily Net Value is:

!Expected Daily Number of Transaction = e-1.5012 + 0.65826±0.02256 * log (Daily Net Value)

!

Page !35

4.8 Testing Assumptions of Linear Regression Model !Before accepting our model, four factors regarding the assumptions of linear regression model

have to be considered: linearity, independence of the errors (free from autoregression),

homoscedasticity, and normality of error distribution (Duke University, 2014).

In order to check linearity, the scatterplot from

previous section is used (figure 15).

After log transformation, it can be observed that

the observations fits symmetrically around the

diagonal regression line, indicating linearity

between the two variables.

Linear regression should also be free of

autoregression. Autoregression is a problem

frequently encountered when analyzing time-

series data, where today’s value is correlated

with yesterday’s value. Two additional tests

were completed to rule out this problem.

In the first test, a time sequence indicator (dummy variable) is introduced, which indicate the

order of the two variables (figure 16). Then Time is used as an additional independent variable

beside Number of Transactions in order to predict Net Value. If autoregression exists, then Time

would be a statistically significant variable. The p-value of Time is 0.613, indicating that Time is

not a related variable.

1

2

3

0.0 0.5 1.0 1.5Log(Freqency of transtions)

log(

Net

val

ue)

Time Net  ValueNumber  of  Transac3ons

1 399.15 10

2 995.97 28

Figure 15. Scatter-plots of log Daily Net Value verses log Daily Number of Transactions.

Figure 16. Example of creating a dummy variable (Time) to test autoregression

Page !36

Another more established test is the Durbin-Watson (DW) test which measures the possible

correlation in predictor errors from a regression analysis. A DW test of 2 means that there is no

autoregression, while a DW > 2 indicates a negative correlation, and DW < 2 points to a positive

correlation(Jank, 2011). An associated p-value measures the validity of DW test. The results

shows that DW = 2.0432 and p-value = 0.6464. Even though there is a finding of slight negative

correlation in the predictor errors, but p-value is not statistically significant. In conclusion, after

running the two tests above we are sure that autocorrelation is not present in our model.

Homoscedasticity is the condition where

all random variables in the sequence or

vector have the same finite variance.

Series violation of this condition will

result in over-estimation of R2 value.

Homoscedasticity is tested by plotting the

residuals versus fitted values (predicted

values). The residuals in figure 17 did not

get larger (i.e., more spread-out) as a a

function of the predicted value. In other

words, the variables have similar variance

(distance from the circle in the figure to

the line).

The violation of normality of the error distribution assumption in linear regression means that the

estimation of coefficients and the calculation of confidence intervals are violated. Since the least

squared method for determining line of best fit is based on minimization of squared error, if there

are large outliers in the error distribution, those numbers will disproportionally influence the line

of best fit (Duke University, 2014).

1.5 2.0 2.5 3.0 3.5

0.002

0.010

0.050

0.200

1.000

5.000

Spread-Level Plot for RegModel.1

Fitted Values

Abs

olut

e S

tude

ntiz

ed R

esid

uals

Figure 17. Residuals from the linear regression plotted against predicted value.

Page !37

Visually, a Q-Q plot will inform us of the normality of error distribution. Figure 18 shows that

our model error distribution is not perfectly randomly distributed (a randomly distributed error

will show up as a straight diagonal-line).

However, we should still assume normality of

error distribution, since the error distribution is

only skewed on the high value end, which

means there are high-value outliers affecting

the linear regression, but the existence of these

outliers are already acknowledged and justified

for in previous section.

The four assumptions of linear regression are

satisfied, therefore the validity of the our model

is assured.

4.9 Forecasting and Prediction !Regression analysis alone cannot guarantee the predictive ability of the linear equation, since

historical data cannot be used to forecast without a major assumption that future data will lie in

the same parameter as historical data (Williams, 2011). This means that although forecast can be

generated using historical data, but the utility and validity of the forecast can be cast in to doubt

if the conditions of the historical data are violated in the future. For instance, a cyclical pattern is

observed in the sales of gasoline, and a forecast was created based on this pattern. If the macro-

economical condition changes in the future, the forecast will not stand.

One method of circumventing this problem is to randomly segment historical data into three

partitions: training, validation, and testing (Williams, 2011). The training partition will generate

the linear equation, and validation and testing partitions are used as future data to affirm the

forecast ability of the linear equation. This method does not completely eliminate the uncertainty

-3 -2 -1 0 1 2 3

-2-1

01

23

4

QQ Plot

t Quantiles

Stu

dent

ized

Res

idua

ls(R

egM

odel

.3)

Figure 18. QQ plot of the error distribution.

Page !38

of future data parameter. However, it is the best method available to simulate a future-like

condition, compared to strictly using historical data (Williams, 2011).

The dataset for gloves is randomly

partitioned by the ratio 70:15:15 (for

training, validation, and testing

respectively) in the program Rattle.

Figure 19 displays the relationship

between predicted (y-axis) and observed

values (x-axis). Predicted values are

generated using linear equation derived

from the training partition, while

observed values are taken from the

testing partition. The dotted blue line is a

hypothetical equation if perfect

correlation exist between the observed

and predicted values (i.e. the linear

equation perfectly predicts future data). Another

linear equation is calculated based on the position of predicted and observed values using

ordinary least squares method, presented by the solid blue line.

Visually, the more resemblance there are between the two lines, the stronger the predictive power

of the linear equation have. Numerically, the predictive strength of the new linear equation is

described by pseudo-R2 . Pseudo-R2 is the value which measure the correlation between the

predicted and observed values, and the closer this value is to 1, the better the linear equation

predicts the data in testing partition (Williams, 2011). Pseudo-R2 equals to 0.9392 in this case,

and it is a sign that the linear equation derived from the training partition has close to perfect

accuracy in predicting the log of Daily Net Value/Daily Number of Transactions. The linear

equation derived from the training partition is virtually identical compared to the equation

derived in previous section.

1.0 1.5 2.0 2.5 3.0 3.5

1.5

2.0

2.5

3.0

3.5

Log.Net.Value

Predicted

Linear Fit to PointsPredicted=Observed

Pseudo R-square=0.9392

Predicted vs. Observed Linear Model

Model data.xlsx [test]

Rattle 2014-Jul-25 05:51:03 peterzhangFigure 19. Scatter-plot between predicted value and

observed values.

Page !39

Application & Implication

!There are two major applications of the linear equation: benchmarking efficiency of Plexxus, and

facilitating forecast of demand. Furthermore, the latter application can aid UHN in controlling

transaction cost associated with commodity products such as gloves.

5.1 Benchmarking !The strong statistical relationship between daily net value and daily number of transactions can

act as a formula to benchmark Plexxus’ efficiency in dealing with daily transactions. Daily

number of transactions can be viewed as a performance metric for the ability of Plexxus to

handle hospital requests. In addition, the daily number of transactions does not specify the type

and quantity of gloves being processed, therefore Plexxus does not need to worry about the

variability of those two factors.

For instance, given a certain amount of daily net value, Plexxus can derive the expected daily

number of transactions. When the observed number of transactions for that day deviates

significantly from expected number of transactions, Plexxus gains the information that the

normal performance level is not being reached, and can investigate further of the cause of such

deviation.

5.2 Forecasting Demand !The available daily net value data shows cyclicality

on a weekly basis, and this pattern can be used for

forecasting by the Holt-Winters seasonal method

(Athanasopoulos & Hyndman, 2014). The blue line

in figure 20 shows the rough forecast of daily net

values for two weeks ahead, and the grey area

represent 95% confidence interval of the forecast.

Under the condition in which the relationship

Forecasts from HoltWinters

5 10 15

01000

2000

3000

4000

Figure 20. Time series forecast using Holt Winters method.

Page !40

between daily number of transactions and net value is unknown, a separate forecast has to be

conducted and fine-tuned. However, only one set of forecast need to be made, and the values can

be transformed between the two variables.

The forecasted daily number of transactions is a forecasted demand for Plexxus, and Plexxus can

plan and optimize its resources based on forecasted demand. For example, if the average quantity

(e.g. boxes) per transaction can be calculated, and the average cost per quantity (e.g.

transportation, handling, processing fees) can also be known, then the forecasted number of

transactions times the average quantity per transaction, times the average cost per quantity will

give Plexxus a forecast of the daily cost per day based on demand. To further illustrate, consider

the example:

Average quantity per transaction= 10 boxes

Average cost per box = $100

Forecasted number of transactions = 10

Forecasted daily transaction cost = 10 * $100 * 10 = $10,000

Similar forecasting of daily transaction cost can be applied with UHN data when more UHN

specific information becomes available.

5.4 Implication for UHN !Recalling from previous discussion of HBAM, Expected Unit Costs is the only variable UHN

can affect since Expected Services are determined by the government. Expected Unit Costs

includes overhead expenses and medical supply costs. Overhead expenses are difficult to

negotiate due to union presence (Born & Dhalla, 2012), therefore medical supply costs is one

area UHN could find savings opportunity.

The demand of specialty medical supplies, such as prosthetics, is hard to forecast due to its

irregularities, leaving the forecast of commodity products demand/associated costs in the

Page !41

forefront. Moreover, Plexxus already achieved significant purchasing power to ensure optimal

pricing for commodity products, as a result, only the forecast of associated costs of commodity

products would be useful. Therefore, when negotiating with LHIN on the topic of Expected Unit

Costs, being able to control transaction cost of commodity products will prove to be valuable.

Conclusion & Further Research

!Descriptive statistics and analyses of glove purchasing data are given in this report based on

purchasing order data from Plexxus. A linear regression equation between the daily number of

transactions and daily net value of transactions is found and validated, which can be used for

benchmarking and forecasting purpose. However supply side data from UHN and the Ministry of

Health could not be obtained to this date. A more comprehensive analysis using these additional

data is warranted, and tangible cost savings and a repeatable process would be identified.

Only linear regression method is used in this report, and additional forecasting and data-mining

methods would bring us closer to the goal of this research of finding cost saving opportunity for

UHN. Decision-tree and neural network techniques can be used to evaluate commodity

consumption rate related to clinical outcome; time-series analysis such as autoregressive

integrated moving average model (ARIMA) and Hold-Winter seasonal method could be

conducted on both patient turn-over rate and expected admissions; multi-variate regression and

logit regression can be used on categorical variables.

Immense opportunities are available for applying data-mining techniques to hospital related data.

Discoveries of hidden relationships between variables and applying the relationship to the

finance of hospitals would be the future of healthcare analytics.

!!!

!

Page !42

Reference

!Athanasopoulos, G. & Hyndman, R.J. (2014). Forecasting: Principles and Practice. !Born, K. & Dhalla, I. (2012). Ontario hospital funding: confusion for 2012/2013. Retrieved from: http://healthydebate.ca/2012/02/topic/cost-of-care/ontario-hospital-funding-confusion !Brennan, C.D. (1998). Integrating the healthcare supply chain. Healthcare Financial Management, 52(1), 31-34. !Charted Institute of Management Accountants (2014). Time Estimates as Cost Drivers. !Coghlan A. (2013). Using R for Time Series Analysis. Retrieved from: http://a-little-book-of-r-for-time-series.readthedocs.org/en/latest/src/timeseries.html !Duke University. (2009). Testing the assumptions of linear regression. Retrieved from: http://people.duke.edu/~rnau/testing.htm !Edmison, J., Mouradov, I., Popescu, A. & Sulatycki J. (2014). Health Care Supply Chain Analytics: An analysis of Plexxus hospital consumption data to identify opportunities for supply chain efficiencies and savings. Jank, W. (2011). Business Analytics for Managers. Springer. NY. !Kumar, S., Swanson, E. & Tran, T. (2008). RFID in the healthcare supply chain: usage and application. International Journal of Health Care, 22(1), 67-81. !Lee, S.M., Lee, D. & Schniederjans, M.J. (2011). Supply chain innovation and organizational performance in the healthcare industry. International Journal of Operations & Production Management, 31(11), 1193-1214. !McKone-Sweet, K. E., Hamilton, P. & Willis, S. B. (2005). The ailing healthcare supply chain: a prescription for change. The Journal of Supply Chain Management. !Power, D. (2005). Supply chain management integration and implementation: a literature review. Supply Chain Management: An International Journal, 10(4), 252-263. Parker, J. & DeLay, D. (2008). The future of the healthcare supply chain. Healthcare Financial Management, 62(4), 66-69. !Roark, D.C. (2005). Managing the healthcare supply chain. Nursing Management. !

Page !43

Rahimnia, F. & Moghadasian, M. (2010). Supply chain legality in professional series: how to apply decoupling point concept in healthcare delivery system. Supply Chain Management: An International Journal, 15(1), 80-91. !Sutherland, J. M. (2011). Hospital Payment Mechanisms: an Overview and Options for Canada. !Smith, A. D. & Flanegin, F.R. (2004). E-procurement and automatic identification: enhancing supply chain management in the healthcare industry. International Journal of Electronic Healthcare, 1(2). !Shazam (1995). An Introductory Guide to Shazam. Comparing linear vs. log-linear models. Retrieved from: http://shazam.econ.ubc.ca/intro/olslog.htm#predict Vries, D. & Huijsman R. (2011). Supply chain management in health services: an overview. Supply Chain Management: An International Journal, 16(3), 159-165. !Ontario Ministry of Health and Long-term Care. (2014). Classification of Hospitals. Retrieved from: http://www.health.gov.on.ca/en/common/system/services/hosp/hospcode.aspx#groups !Ontario Ministry of Health and Long-term Care. (2014). Health Data Branch Portal. Health System Funding Reform Online Self-study Modules 1-8. Retrieved from: https://hsimi.on.ca/hdbportal/hbam !Ontario’s Local Health Integration Networks (2014). About LHINs. Retrieved from: www.lhins.on.ca !Pataricza, A., Horvath, G., Kocsis, I. & Gati, K. (2011). Time Series Analysis and Order Prediction with R. Retrieved from: http://www.inside-r.org/howto/time-series-analysis-and-order-prediction-r !Quick-R. (2012). Regression Diagnostics. Retrieved from: http://www.statmethods.net/stats/rdiagnostics.html !Williams G. (2011). Data Mining with Rattle and R. The Art of Excavating Data for Knowledge Discovery. Springer. NY. !!!!!