Department of Family and Community Medicine, University of Toronto, Ontario, Canada
Institute for Clinical Evaluative Sciences, Toronto, Ontario, Canada
Dalla Lana School of Public Health, University of Toronto, Ontario, Canada
Centre for Research on Inner City Health, The Keenan Research Centre in the Li Ka Shing Knowledge Institute of St. Michael's Hospital, Ontario, Canada
Department of Health Policy, Management and Evaluation, University of Toronto, Ontario, Canada
Pediatric Oncology Group of Ontario, Toronto, Ontario, Canada
Abstract
Background
Emergency departments are medical treatment facilities, designed to provide episodic care to patients suffering from acute injuries and illnesses as well as patients who are experiencing sporadic flareups of underlying chronic medical conditions which require immediate attention. Supply and demand for emergency department services varies across geographic regions and time. Some persons do not rely on the service at all whereas; others use the service on repeated occasions. Issues regarding increased wait times for services and crowding illustrate the need to investigate which factors are associated with increased frequency of emergency department utilization. The evidence from this study can help inform policy makers on the appropriate mix of supply and demand targeted health care policies necessary to ensure that patients receive appropriate health care delivery in an efficient and costeffective manner. The purpose of this report is to assess those factors resulting in increased demand for emergency department services in Ontario. We assess how utilization rates vary according to the severity of patient presentation in the emergency department. We are specifically interested in the impact that access to primary care physicians has on the demand for emergency department services. Additionally, we wish to investigate these trends using a series of novel regression models for count outcomes which have yet to be employed in the domain of emergency medical research.
Methods
Data regarding the frequency of emergency department visits for the respondents of Canadian Community Health Survey (CCHS) during our study interval (20032005) are obtained from the National Ambulatory Care Reporting System (NACRS). Patients' emergency department utilizations were linked with information from the Canadian Community Health Survey (CCHS) which provides individual level medical, sociodemographic, psychological and behavioral information for investigating predictors of increased emergency department utilization. Six different multiple regression models for count data were fitted to assess the influence of predictors on demand for emergency department services, including: Poisson, Negative Binomial, ZeroInflated Poisson, ZeroInflated Negative Binomial, Hurdle Poisson, and Hurdle Negative Binomial. Comparison of competing models was assessed by the Vuong test statistic.
Results
The CCHS cycle 2.1 respondents were a roughly equal mix of males (50.4%) and females (49.6%). The majority (86.2%) were youngmiddle aged adults between the ages of 2064, living in predominantly urban environments (85.9%), with midhigh household incomes (92.2%) and welleducated, receiving at least a highschool diploma (84.1%). Many participants reported no chronic disease (51.9%), fell into a small number (05) of ambulatory diagnostic groups (62.3%), and perceived their health status as good/excellent (88.1%); however, were projected to have high Resource Utilization Band levels of health resource utilization (68.2%). These factors were largely stable for CCHS cycle 3.1 respondents. Factors influencing demand for emergency department services varied according to the severity of triage scores at initial presentation. For example, although a nonsignificant predictor of the odds of emergency department utilization in high severity cases, access to a primary care physician was a statistically significant predictor of the likelihood of emergency department utilization (OR: 0.69; 95% CI OR: 0.630.75) and the rate of emergency department utilization (RR: 0.57; 95% CI RR: 0.500.66) in low severity cases.
Conclusion
Using a theoretically appropriate hurdle negative binomial regression model this unique study illustrates that access to a primary care physician is an important predictor of both the odds and rate of emergency department utilization in Ontario. Restructuring primary care services, with aims of increasing access to undersupplied populations may result in decreased emergency department utilization rates by approximately 43% for low severity triage level cases.
Background
Emergency departments are medical treatment facilities, designed to provide episodic care to patients suffering from acute injuries and illnesses as well as patients who are experiencing sporadic flareups of underlying chronic medical conditions which require urgent medical attention
Increased patient volumes at emergency departments, resulting from changes in patient preference/demand characteristics, decreasing supply of emergency department resources (eg. treatment facilities, physicians, nurses), or long term structural changes to patient case mix as a result of demographic trends have resulted in documented challenges in the delivery of emergency department services. These challenges include: increasingly long wait times, ambulance diversions, and crowding. Despite considerable research in this area, a lack of consensus exists as to the most appropriate strategies for addressing these problems. A review of available literature can sometimes illustrate contradictory findings regarding the characteristics of those individuals whom exhibit increased (sometimes coined "inappropriate") demand for emergency department services. One area of controversy is whether lack of access to a primary care physician in the community is attributable to increased utilization of emergency department services. In an Ontario based study, Chan
Another distinguishing feature of this study is the methodology employed to assess the factors' contributing to demand for emergency department services. Previous studies have either dichotomized the count of emergency department visits at some threshold (indicating nonfrequent users versus frequent users) and modeled the transformed outcome using logistic regression
Methods
Data Sources and Study Population
The Canadian Community Health Survey (CCHS) cycles 1.1 to 5.1 are national surveys which have been conducted by Statistics Canada from 2000 to 2010
In the province of Ontario CCHS respondents were asked to provide their Ontario health card numbers and to consent to linkage of their CCHS responses with personal health care utilization data. Those consenting in cycles 1.13.1 were linked to the Ontario Registered Persons Database (RPDB), the province's health care registry. Once linked with the RPDB, health card numbers were used to link respondents with feeforservice billing claims that physicians report to the Ontario Health Insurance Plan (OHIP). These data were collected for 20002001 and 20022003 observation periods. Approximately 94% of all physician encounters in the province are included in this database. A small number of physicians are salaried employees and hence do not directly bill OHIP for patient encounters. Records of all emergency department visits were also submitted to the Canadian Institute for Health Information (CIHI) as part of the National Ambulatory Care Reporting System (NACRS), for which close to 100% of emergency department claims in the province are included. The data were accessed at the Institute for Clinical Evaluative Sciences (ICES) as part of a comprehensive research agreement with the Ontario Ministry of Health and LongTerm Care (MOHLTC).
The study setting of Ontario is Canada's most populous province and the second largest province in terms of geographic area. The study population was restricted to individuals between the ages of 20 and 79 years to avoid proxy responses that could be assigned to children and older seniors. The cycles 2.1 collection period was January 2003 through December 2003 and cycle 3.1 was January 2005 through December 2005.
Outcome Variables
The number of emergency department visits during the 365 day interval following the interview date were tallied for fiscal years 2003 through 2006 for each individual respondent of CCHS cycle 2.1 and 3.1, and counted using the NACRS database. The scrambled Ontario health card number was used as a unique key to link individual level medical, sociodemographic, psychological and behavioral data from the CCHS 2.1 and 3.1 to emergency department visit data. We defined a potentially avoidable emergency department visit as one with a Canadian Triage and Acuity Scale (CTAS) score of 4 or 5 (less urgent), where the patient was not admitted to the hospital following observation by the physician. We defined an unavoidable emergency department visit, as one with a CTAS score of 1, 2 or 3 (urgent) and no diagnostic code indicating an injury. We assume these emergency department visits are unlikely treatable in a primary care environment. We excluded emergency department visits where the patient left without being seen and excluded transfers (i.e., kept the first emergency department visit when there was a transfer) and pregnant women. Outcome variables for each participant are the number of less urgent and the number of urgent emergency department visits. In regression models, participants with no emergency department visits were included with zero visits for both less urgent and urgent emergency department visits.
Assessment of Comorbidity
We used the John Hopkins University Ambulatory Care Groups Case Mix Adjustment System (version 7) to summarize the degree of comorbidity experienced by Ontarians during the two year period prior to the interview date. This software reads in international classification of disease (ICD) codes from physician and hospitalbased claims and categorizes patients as having up to 32 different Ambulatory Diagnostic Group (ADG) labels. An individual can be assigned to multiple ADG's depending on their respective diagnoses. We collapsed the 32category variable into three categories, specifically: individuals falling into 05, 69 and greater than 9 ADG's. This three level categorical variable was used as an indicator of comorbidity in all subsequent analyses.
The Ambulatory Care Groups Case Mix Adjustment software also generates Resource Utilization Bands (RUB), which estimate expected resource utilization. Patient level RUB categorization is determined through consideration of age, sex, and disease diagnoses. Different categories of RUB are associated with different levels of expected resource use and overall cost to the health care system over a given period of time. RUB values vary from 05, with higher values associated with higher utilization levels. For this study, RUBs were categorized as ≥ 4 (very high), 3 (high), 2 (medium), and 01 (low). The ACG measures were determined using two years of diagnostic data (fiscal year 2003 and 2004) from physician and hospitalbased claims.
Predictors
Individuallevel variables that were included in the regression models were gender (male, female), age (2044, 4564, 6579), total household income (low {less than $20,000}, medium {$20,000$59,999}, high {more than $60,000}), education (low {not completed high school}, medium {high school completion and some postsecondary education} and high {university degree}), number of chronic medical conditions (0, 1, >1) from the following list (asthma, fibromyalgia, arthritis/rheumatism, back problems, high blood pressure, diabetes, epilepsy, heart disease, and cancer), perceived health status (poor/fair, good, verygood/excellent), number of ADG's (05, 69, >9), RUB status (01, 2, 3, 45), access to a primary care physician in the community (no, yes), and location of primary residence (rural, urban).
Analytic Methods
Population studies which seek to estimate demand for emergency department services or hospitalization typically exhibit a large proportion of zeroes, representing the persons that do not use any of the services being investigated during the observational period of interest. Factors influencing the demand for these services are routinely modeled using Poisson or negative binomial regression. While the negative binomial regression model does not impose as stringent a set of restrictions on the conditional meanvariance relationship as the Poisson model, neither is ideal for handling data with a large proportion of zeroes. Failure to account for the mass of zeros that are occurring at a greater proportion than would be predicted by either the Poisson or negative binomial models may result in biased parameter estimates and misleading inferences. Several methods are proposed for analyzing data with excess zeros, including: the ZIP, ZINB, HP and HNB regression models. Given the lack of use of these models in emergency medical research we will describe each method below.
Before proceeding to any multiple regression modeling, descriptive statistics were generated to characterize the sample under investigation. For continuously distributed variables we presented means and standard deviations; whereas, for categorical variables we presented counts and percentages.
Regression Models for Count Outcomes
Perhaps the most parsimonious and widely implemented method for modeling count data in the public health sciences is Poisson regression. The Poisson regression model assumes that the number of events (y_{i}) experienced by patient i follows a Poisson distribution:
where μ_{i }represents the conditional mean response of a given patient, which is assumed to depend on a set of observed data (x_{i}) and an estimated vector of coefficients (β). Mathematically, this relationship takes the following form:
Taking the natural logarithm of the conditional mean allows for the response under consideration to vary linearly as a function of observed predictor variables multiplied by the effect of their corresponding regression coefficients. Various numerical maximization methods exist for iteratively estimating the values of the coefficient vector, β, and the associated covariance matrix. variance Estimates are typically found by finding the parameter estimates that maximize the following loglikelihood function:
Since the natural logarithm of the likelihood function for the Poisson regression model is globally concave, a unique maximum can be found if it exists
A less parsimonious, but more flexible extension to the Poisson regression model is the negative binomial regression model. The negative binomial regression model does not assume that the conditional variance of the response is equal to the conditional mean. A simple extension to the specification of the Poisson conditional mean leads to a negative binomial regression model, which is illustrated below:
Above, the conditional mean for the Poisson model has been adjusted by adding an individual specific random term, ε_{i}, that is assumed to be uncorrelated with the observation vector, x_{i}. Typically one assumes that
Above, μ_{i }represents the mean number of events that is expected for an individual with observation vector xi, u represents the negative binomial dispersion parameter and Γ(·) represents the gamma function. Determination of regression coefficients in negative binomial regression proceeds by maximizing the following loglikelihood function with respect to the unknown parameters:
The negative binomial regression model is a useful model for accounting for data in which unobserved heterogeneity or temporal/spatial correlation is present; however, it is not necessarily an optimal model for dealing with data that contain an excess mass of zeroes at the corner of its empirical distribution.
Zero Inflated Poisson (ZIP) regression models were introduced by Lambert
Similarly, for zeroinflated negative binomial model, the probability density function is given by:
For both the ZIP and ZINB models the probability of an excess zero, ψ_{i}, the is modeled using logistic regression (although, any binary regression framework will suffice). As a result, the probability of an excess zero is given by:
In other words, the probability of an excess zero is a function of some observed linear predictor, η_{i}, which itself is formed from a set of predictor variables, z_{i}, multiplied by their associated logistic regression coefficients, ε(nb. the set z_{i}, in the logistic of model need not equal the set of variables, x_{i}, in the Poisson or negative binomial component regression models). For the ZIP model the conditional mean and variance are:
For the ZINB model, the conditional mean is the same as for the ZIP model; however, the conditional variance differs. The equations for both the conditional mean and variance of the ZINB model are given below:
Considering ψ_{i }as the probability of excess zeroes, it can be observed that as ψ_{i }tends toward zero then the probability densities, as well as the conditional mean and variances of the ZIP and ZINB models converge toward the corresponding formulas for the Poisson and negative binomial models, respectively
Here
One issue with the application of zeroinflated modeling strategies for emergency department demand is that interpretively some of the zeroes in ZIP/ZINB models are considered to be structural; whereas, others are assumed to arise as a result of a sampling process. Conceptually, it is hard to imagine even the healthiest individuals in the Ontario population not being "at risk" for an emergency department visit and hence representing a structural zero. As a result, even though the ZIP and ZINB models may fit our data well, a more parsimonious explanation of the phenomena under investigation can be derived using a hurdle modeling approach.
Hurdle models account for excess zeroes but are specified and interpreted slightly differently than the ZIP and ZINB models discussed above. The hurdle regression approach was introduced by Mullahy
Above, z_{i }and γ represent the respective variables and coefficients associated with the zero/nonzero (hurdle) process. The xi and β are the respective variables and coefficients associated with the count process. Lastly, the
If we purport to use a Bernoulli density to model the probability (ψ_{i}) of a zero versus a nonzero (1  ψ_{i}) count, coupled with a left truncated Poisson density (with mean μ_{i}) for the count process, then our overall hurdle Poisson (HP) density looks as follows:
Similarly, if we purport to use a Bernoulli density to model the probability (ψ_{i}) of a zero versus a nonzero (1  ψ_{i}) count, coupled with a left truncated negative binomial density (with mean, μ_{i}, and negative binomial dispersion parameter, υ) for the count process, then our overall hurdle negative binomial (HNB) density looks as follows:
Again, regression coefficients are estimated through determination of the coefficients which maximize the following loglikelihood functions
Intuitively, the hurdle approach to handling excess zeroes in medical utilization data is appealing as predicted zeroes are not interpreted as a mix of structural and sampling zeroes. Rather, the first component of the hurdle approach can be used to model whether a person does or does not decide to seek emergency services over the time interval of our study. This process can be modeled using a binary regression framework, such as logistic or probit regression. Given that a person does decide to seek emergency services, the number of visits they make to the emergency department can then be modeled using a left truncated Poisson or negative binomial distribution.
Comparing Regression Models for Count Outcomes
Vuong
And let
The Vuong statistic is asymptotically distributed as a N(0,1) variable. Calculating a normal based random confidence interval can be used to assess whether model 2 is favored over model 1, whether model 1 is favored over model 2, or whether insufficient evidence exists to claim either model is favored over the other
Statistical Computing
All statistical computation was carried out using SAS version 9.2 (SAS Corporation; Cary, North Carolina). For all regression modeling we used Proc NLMIXED, specifying the likelihood equations, as shown above, and maximizing them directly using numerical methods. Maximization began from various starting points and the final gradient vectors and hessian matrices were investigated to ensure proper convergence of estimated model parameters.
Results
Descriptive statistics for our sample are presented in Table
Demographic characteristics of CCHS cycle 2
variable
CCHS 2.1
CCHS 3.1
N
%
N
%
Female
14086
49.6
14012
49.1
Male
12607
50.4
12648
50.8
Age 2044
10958
51.6
11549
50.0
Age 4564
9888
34.6
9627
36.3
Age 6580
5847
13.8
5484
13.7
Income High
10882
55.1
6739
42.4
Income Medium
10867
37.2
10140
47.4
Income Low
3113
7.7
2948
10.2
Education High
13903
55.4
15177
60.2
Education Medium
7214
28.7
6704
25.9
Education Low
5233
15.9
4655
13.8
No chronic condition
11808
51.9
11890
52.3
One Chronic conditions
7488
27.3
7557
27.2
Two or more chronic conditions
7397
20.8
7213
20.5
Self rated health excellent or very good
14384
56.8
15438
60.5
Self rated health good
8299
31.2
7484
28.2
Self rated health fair or poor
3998
11.9
3721
11.3
ADG 05
15888
62.3
16158
63.3
ADG 69
7823
28.4
7646
27.3
ADG 10+
2982
9.3
2856
9.4
RUB 0, 1
3433
14.1
3408
14.0
RUB 2
4251
17.7
4382
18.3
RUB 3
13871
52.6
13921
51.8
RUB 4, 5
5138
15.6
4949
15.9
Had regular doctor
24391
91.4
23995
90.5
Didn't have regular doctor
2296
8.6
2656
9.5
Rural
5471
14.1
5409
14.0
Urban
21222
85.9
21251
86.0
Emergency department utilization was determined for each respondent, one year following their respective CCHS 2.1 and 3.1 interview dates. A summary of the respondents utilization patterns was stratified by triage scale, with triage scale rankings 13 collapsed into a single category (high severity) and triage scale rankings 45 collapsed into a separate category (low severity). Emergency department utilization rates were recorded for both CCHS cycles 2.1 and 3.1 and presented in Table
Proportion of persons visiting the emergency department (ED) at least once in a given year and the rate of emergency department visits conditioned on using the emergency department.
CCHS 2.1
CCHS 3.1
Triage 13
Triage 45
Triage 1 3
Triage 45
% ≥ 1
ED visit
Mean (SD)
% ≥ 1
ED visit
Mean (SD)
% ≥ 1
ED visit
Mean (SD)
% ≥ 1
ED visit
Mean (SD)
Female
9.6
1.46(22.69)
11.7
1.57(27.52)
11.8
1.48(17.92)
11.6
1.50(19.52)
Male
10.0
1.51(21.30)
11.3
1.55(25.29)
11.0
1.49(24.51)
11.6
1.50(20.92)
Age 2044
8.3
1.45(30.23)
12.5
1.49(24.08)
9.9
1.49(27.00)
12.3
1.50(21.49)
Age 4564
9.7
1.45(17.02)
9.8
1.56(24.29)
11.2
1.40(16.38)
10.1
1.46(19.09)
Age 6580
15.2
1.62(15.82)
11.9
1.87(33.37)
17.3
1.63(16.88)
12.9
1.60(18.96)
Income High
8.1
1.39(19.60)
9.7
1.43(22.52)
10.5
1.47(28.39)
11.5
1.41(20.12)
Income Medium
11.1
1.52(24.35)
12.8
1.64(25.27)
13.2
1.48(15.60)
12.5
1.60(19.30)
Income Low
15.0
1.63(16.91)
15.3
1.75(23.12)
18.0
1.88(24.83)
15.5
1.94(24.66)
Education High
8.6
1.38(15.73)
9.8
1.54(25.85)
9.9
1.46(22.94)
10.6
1.43(18.98)
Education Medium
10.1
1.57(32.25)
12.2
1.51(23.47)
11.8
1.39(16.59)
12.2
1.50(19.52)
Education Low
13.5
1.61(19.13)
15.9
1.69(30.88)
16.8
1.66(21.57)
14.2
1.74(23.23)
No chronic condition
7.3
1.34(26.11)
10.1
1.48(24.12)
8.5
1.39(20.07)
10.1
1.39(18.72)
One Chronic conditions
9.8
1.54(21.51)
11.5
1.59(26.08)
11.8
1.48(26.00)
12.1
1.43(16.89)
Two or more chronic conditions
16.0
1.60(18.67)
15.0
1.68(29.29)
18.2
1.62(18.05)
14.7
1.78(23.56)
Self rated health excellent
7.5
1.27(12.41)
10.3
1.42(19.85)
8.8
1.37(15.80)
10.0
1.40(17.52)
Self rated health good
10.3
1.47(19.79)
11.4
1.59(28.31)
11.8
1.37(16.98)
13.1
1.47(18.19)
Self rated health fair/poor
19.6
1.89(31.19)
17.4
1.92(34.36)
24.1
1.86(29.94)
16.4
1.92(25.68)
ADG 05
6.8
1.35(17.19)
9.5
1.40(18.45)
7.8
1.32(15.25)
10.2
1.36(14.85)
ADG 69
12.0
1.43(16.71)
13.2
1.59(27.46)
14.4
1.41(16.20)
12.2
1.60(20.23)
ADG 10+
23.1
1.84(32.50)
19.8
2.03(38.61)
27.1
1.93(31.97)
19.1
1.85(30.32)
RUB 0, 1
4.6
1.20(11.38)
8.0
1.38(18.22)
6.6
1.28(14.38)
9.0
1.30(13.12)
RUB 2
6.5
1.39(21.66)
10.3
1.32(15.15)
6.5
1.25(9.74)
9.5
1.26(11.94)
RUB 3
9.1
1.37(15.53)
10.9
1.53(23.31)
10.9
1.35(15.17)
11.5
1.48(17.67)
RUB 4, 5
20.6
1.74(28.71)
18.1
1.88(36.03)
22.9
1.83(29.22)
16.5
1.82(27.83)
Had regular doctor
10.1
1.50(22.52)
11.5
1.55(26.84)
11.4
1.48(21.47)
11.4
1.47(19.54)
Didn't have regular doctor
7.2
1.31(13.33)
11.6
1.68(23.54)
10.9
1.54(18.51)
13.0
1.78(23.93)
Rural
10.1
1.45(13.81)
17.9
1.70(26.50)
11.4
1.39(13.87)
16.6
1.55(15.47)
Urban
9.8
1.49(23.69)
10.4
1.53(26.53)
11.4
1.50(22.62)
10.8
1.49(21.59)
These statistics are summarized for both low and high severity cases and CCHS cycles.
Histogram of the number of Triage 13 (urgent) and Triage 45 (less urgent) emergency department (ED) visits
Histogram of the number of Triage 13 (urgent) and Triage 45 (less urgent) emergency department (ED) visits.
Rate ratios, odds ratios (where applicable), and 95% confidence intervals for the six count regression models applied to triage scale 13 and triage scale 45 emergency department visits, from combined CCHS cycles 2.1 and 3.1 data, are presented in Table
Regression models for CCHS 2
Poisson
Negative Binomial
Zero Inflated Poisson
Zero Inflated Negative Binomial
Hurdle Poisson
Hurdle Negative Binomial


Binary
Count
Binary
Count
Binary
Count
Binary
Count
RR (95% CI)
RR (95% CI)
OR (95% CI)
RR (95%CI)
OR (95% CI)
RR (95% CI)
OR (95% CI)
RR (95% CI)
OR (95% CI)
RR (95% CI)
Male
1.17, (1.121.22)**
1.16, (1.101.23)**
1.11,(1.011.21)*
1.09, (1.021.16)*
1.26,(0.961.65)
1.13, (1.051.22)**
1.17, (1.101.23)**
1.09, (1.021.16)*
1.17, (1.101.23)**
1.09, (0.971.22)
Female










2044 years
1.19, (1.121.26)**
1.14, (1.051.24)**
0.90,(0.801.02)
1.25, (1.141.37)**
0.66,(0.401.09)
1.21, (1.091.35)**
1.09, (1.001.08)*
1.26, (1.151.38)**
1.09, (1.001.18)*
1.23, (1.051.44)**
4564 years
0.94, (0.890.99)*
0.94, (0.871.01)
0.84,(0.750.94) **
1.06, (0.971.15)
0.76,(0.461.26)
0.96, (0.871.05)
0.90, (0.830.97)**
1.06, (0.971.15)
0.90, (0.830.97)**
1.06, (0.921.22)
> 65 years










RUB 2
1.31, (1.171.47)**
1.30, (1.141.48)**
1.08,(0.811.43)
1.23, (0.951.58)
1.11,(0.582.12)
1.24, (0.931.66)
1.27, (1.111.45)**
1.23, (0.951.58)
1.27, (1.111.45)**
1.24, (0.891.72)
RUB 3
1.65, (1.491.83)**
1.62, (1.441.82)**
1.15,(0.891.48)
1.46, (1.161.83)**
1.25,(0.702.24)
1.45, (1.121.88)**
1.54, (1.361.74)**
1.46, (1.171.83)**
1.54, (1.361.74)**
1.50, (1.122.01)**
RUB 45
2.54, (2.252.85)**
2.49, (2.162.86)**
1.32,(1.001.75)
2.04, (1.602.59)**
2.04,(0.844.98)
2.13, (1.622.81)**
2.23, (1.932.58)**
2.05, (1.612.60)**
2.23, (1.932.58)**
2.23, (1.613.09)**
RUB 1










ADG 69
1.45, (1.371.54)**
1.45, (1.351.56)**
1.52,(1.341.73) **
1.06, (0.961.17)
4.44,(2.169.13) **
1.08, (0.941.23)
1.50, (1.391.62)**
1.06, (0.961.18)
1.50, (1.391.62)**
1.07, (0.921.25)
ADG 1032
2.22, (2.052.39)**
2.18, (1.962.43)**
1.82,(1.552.15) **
1.43, (1.271.62)**

1.51, (1.291.78)**
2.17, (1.952.41)**
1.44, (1.281.63)**
2.17, (1.952.41)**
1.56, (1.281.91)**
ADG 05










Income Low
1.46, (1.371.56)**
1.46, (1.341.59)**
1.11,(0.981.27)
1.34, (1.221.48)**
0.89,(0.591.34)
1.45, (1.291.63)**
1.37, (1.251.49)**
1.35, (1.221.49)**
1.37, (1.251.49)**
1.47, (1.251.74)**
Income Med.
1.16, (1.101.22)**
1.19, (1.111.27)**
1.04,(0.941.16)
1.14, (1.051.24)**
1.47,(1.052.05) *
1.09, (1.001.20)*
1.14, (1.071.22)**
1.14, (1.051.24)**
1.14, (1.071.22)**
1.19, (1.041.35)*
Income High










Educ. Low
1.17, (1.111.23)**
1.20, (1.111.29)**
1.23,(1.101.38) **
1.02, (0.941.10)
1.28,(0.851.93)
1.15, (1.041.26)**
1.21, (1.121.30)**
1.01, (0.931.10)
1.21, (1.121.30)**
1.08, (0.941.24)
Educ. Med.
1.04, (0.991.09)
1.06, (0.991.13)
1.09,(0.981.21)
0.98, (0.901.07)
1.16,(0.841.60)
1.02, (0.931.12)
1.06, (0.991.14)
0.98, (0.901.06)
1.06, (0.991.14)
1.00, (0.871.14)
Educ. High










SRH Poor or Fair
1.96, (1.852.08)**
1.91, (1.762.08)**
1.36,(1.191.55) **
1.57, (1.431.73)**
0.91,(0.581.43)
1.99, (1.802.20)**
1.82, (1.681.97)**
1.58, (1.441.74)**
1.82, (1.681.97)**
1.73, (1.482.01)**
SRH Good
1.21, (1.171.30)**
1.21, (1.131.29)**
1.07,(0.951.20)
1.16, (1.051.27)**
0.72,(0.530.93) *
1.30, (1.181.42)**
1.19, (1.121.28)**
1.16, (1.061.27)**
1.19, (1.121.28)**
1.18, (1.021.35)*
SRH Excellent or Very Good










Access Doctor
0.92, (0.851.00)*
0.92, (0.831.02)**
0.88,(0.751.05)
1.01, (0.881.15)
0.77,(0.481.25)
0.97, (0.831.13)
0.90, (0.811.00)
1.01, (0.891.15)
0.90, (0.811.00)
0.99, (0.881.23)
No Doctor










1 Chronic Condition
1.13, (1.071.20)**
1.13, (1.051.22)**
0.99,(0.881.12)
1.13, (1.021.24)*
1.06,(0.761.48)
1.10, (0.991.22)
1.09, (1.011.17)*
1.13, (1.031.25)*
1.09, (1.011.17)*
1.19, (1.031.39)*
>2 Chronic Conditions
1.19, (1.111.26)**
1.21, (1.121.31)**
1.24,(1.091.42) **
1.02, (0.921.13)
1.80,(1.102.95) *
1.10, (0.981.23)
1.22, (1.131.33)**
1.02, (0.921.13)
1.22, (1.131.33)**
1.07, (0.911.26)
No Chronic Condition










Rural
0.97, (0.921.02)
0.99, (0.931.07)
1.00,(0.891.12)
0.99, (0.911.08)
1.73,(1.082.75)*
0.90, (0.820.99)*
0.99, (0.921.06)
0.98, (0.901.07)
0.99, (0.921.06)
0.98, (0.851.12)
Urban










*Statistically significant at 0.05 level
**Statistically significant at 0.01 level
Regression models for CCHS 2.1 and 3.1 combined. Triage scale 45.
Poisson
Negative Binomial
Zero Inflated Poisson
Zero Inflated Negative Binomial
Hurdle Poisson
Hurdle Negative Binomial


Binary
Count
Binary
Count
Binary
Count
Binary
Count
RR (95% CI)
RR (95% CI)
OR (95% CI)
RR (95%CI)
OR (95% CI)
RR (95% CI)
OR (95% CI)
RR (95% CI)
OR (95% CI)
RR (95% CI)
Male
1.10, (1.061.14) **
1.11, (1.051.17)**
0.94,(0.881.01)
1.16, (1.101.23)**
0.23,(0.070.81) *
1.15, (1.081.21)**
1.05, (1.001.11)
1.15, (1.091.21)**
1.05, (1.001.11)
1.20, (1.091.33)**
Female










2044 years
1.88, (1.791.98)**
1.82, (1.681.97)**
1.52,(1.371.68)**
1.38, (1.291.49)**
1.78,(0.437.35)
1.78, (1.641.93)**
1.80, (1.671.95)**
1.38, (1.291.49)**
1.80, (1.671.95)**
1.42, (1.231.63)**
4564 years
1.18, (1.121.24)**
1.16, (1.071.25)**
1.11,(1.011.22) *
1.10, (1.021.18)**
0.45,(0.111.81)
1.18, (1.091.27)**
1.16, (1.081.25)**
1.10, (1.021.17)**
1.16, (1.081.25)**
1.08, (0.951.24)
> 65 years










RUB 2
1.25, (1.151.36)**
1.22, (1.101.36)**
1.16,(0.981.38)
1.09, (0.941.26)
3.16,(0.7413.44)
1.16, (1.021.31)*
1.21, (1.091.34)**
1.11, (0.961.29)
1.21, (1.091.34)**
1.13, (0.911.41)
RUB 3
1.61, (1.501.74)**
1.55, (1.401.71)**
1.19,(1.021.39) *
1.37, (1.201.55)**
3.98,(0.9416.84)
1.47, (1.321.65)**
1.46, (1.331.61)**
1.41, (1.241.60)**
1.46, (1.331.61)**
1.48, (1.221.80)**
RUB 45
1.79, (1.631.95)**
1.69, (1.491.91)**
1.28,(1.071.54)**
1.42, (1.231.65)**

1.53, (1.331.75)**
1.59, (1.411.80)**
1.48, (1.281.71)**
1.59, (1.411.80)**
1.56, (1.231.98)**
RUB 1










ADG 69
1.39, (1.331.46)**
1.37, (1.281.47)**
1.09,(0.991.20)
1.30, (1.211.39)**
0.11,(0.020.55) **
1.45, (1.351.56)**
1.30, (1.211.38)**
1.30, (1.211.40)**
1.29, (1.211.38)**
1.39, (1.231.57)**
ADG 1032
2.19, (2.042.34)**
2.16, (1.942.41)**
1.27,(1.111.45)**
1.84, (1.672.02)**
0.07,(0.010.48) **
2.29, (2.042.55)**
1.80, (1.622.00)**
1.84, (1.672.02)**
1.80, (1.621.99)**
2.21, (1.832.65)**
ADG 05










Income Low
1.62, (1.531.71)**
1.53, (1.401.66)**
1.18,(1.061.32) *
1.40, (1.291.51)**
0.22,(0.070.73) *
1.58, (1.451.73)**
1.45, (1.331.57)**
1.41, (1.311.53)**
1.45, (1.331.57)**
1.47, (1.261.70)**
Income Med.
1.32, (1.271.38)**
1.30, (1.231.38)**
1.07,(0.981.16)
1.25, (1.181.33)**
0.63,(0.261.50)
1.32, (1.241.41)**
1.24, (1.171.31)**
1.26, (1.181.34)**
1.24, (1.171.31)**
1.31, (1.181.46)**
Income High










Educ. Low
1.27, (1.211.33)**
1.26, (1.171.35)**
1.21,(1.101.32) *
1.12, (1.051.19)**

1.20, (1.111.29)**
1.27, (1.191.36)**
1.11, (1.041.18)**
1.27, (1.191.36)**
1.12, (0.991.27)
Educ. Med.
1.08, (1.031.12)**
1.08, (1.021.15)*
1.08,(0.991.17)
1.03, (0.971.10)
6.40,(1.3929.47) *
1.04, (0.971.11)
1.09, (1.031.16)**
1.02, (0.961.09)
1.09, (1.031.16)**
1.02, (0.911.14)
Educ. High










SRH Poor
1.50, (1.421.58)**
1.51, (1.391.64)**
1.07,(0.971.19)
1.41, (1.311.52)**

1.49, (1.371.61)**
1.32, (1.221.43)**
1.42, (1.321.53)**
1.32, (1.221.43)**
1.62, (1.411.86)**
SRH Good
1.16, (1.111.20)**
1.14, (1.071.22)**
1.05,(0.971.15)
1.10, (1.031.17)**
0.62,(0.311.27)
1.16, (1.081.23)**
1.12, (1.061.19)**
1.11, (1.041.18)**
1.12, (1.061.19)**
1.14, (1.021.27)*
SRH Excellent










Access Doctor
0.58, (0.550.61)**
0.61, (0.560.67)**
0.86,(0.780.96) *
0.69, (0.640.74)**
3.49,(1.657.38) **
0.58, (0.530.64)**
0.69, (0.630.75)**
0.67, (0.620.72)**
0.69, (0.630.75)**
0.57, (0.500.66)**
No Doctor










1 Chronic Conditions
1.10, (1.051.15)**
1.09, (1.021.17)*
1.18,(1.081.30) *
0.97, (0.911.04)
1.68,(0.803.52)
1.07, (1.001.15)
1.14, (1.071.22)**
0.97, (0.901.04)
1.14, (1.071.22)**
0.92, (0.821.04)
>2 Chronic Condition
1.25, (1.191.32)**
1.26, (1.161.36)**
1.25,(1.131.38)**
1.06, (0.991.14)

1.19, (1.101.29)**
1.27, (1.181.37)**
1.06, (0.991.14)
1.27, (1.181.37)**
1.08, (0.941.24)
No Chronic Condition










Rural
1.59, (1.531.65)**
1.61, (1.521.71)**
1.56,(1.441.69)**
1.16, (1.101.23)**

1.55, (1.451.65)**
1.64, (1.551.74)**
1.16, (1.101.23)**
1.64, (1.551.74)**
1.23, (1.111.37)**
Urban










*Statistically significant at 0.05 level
**Statistically significant at 0.01 level
Vuong Likelihoodratio statistics comparing nonnested models. Triage scale 13
Poisson
NB
ZIP
ZINB
HP
HNB
Poisson

NB
3.66

ZIP
4.76
4.97

ZINB
4.27
4.36
3.82

HP
4.77
5.00
3.43
3.81

HNB
4.25
4.32
3.81
2.69
3.80

*Values < 2 indicates the row model had significantly better fit than the column model.
*Values >2 indicates that column model had significantly better fit than the row model.
Vuong Likelihoodratio statistics comparing nonnested models.
Poisson
NB
ZIP
ZINB
HP
HNB
Poisson

NB
3.82

ZIP
5.30
6.25

ZINB
4.58
4.75
4.06

HP
5.36
6.34
3.92
4.02

HNB
4.58
4.74
4.07
2.18
4.03

Triage scale 45.
*Values < 2 indicates the row model had significantly better fit than the column model.
*Values >2 indicates that column model had significantly better fit than the row model.
Similarly, when the Vuong test is applied to the combined CCHS cycle 2.1 and 3.1 dataset, stratified by low severity (triage scale 45) emergency department visits, the results suggest that the HNB model is a good fit for these data (Table
Discussion
Poisson regression is a commonly employed method for analyzing count data. Our results illustrate that the Poisson regression model is a candidate model for analyzing the number of emergency department visits observed in the CCHS 2.1 and 3.1 datasets; however, alternative methodologies exist which may yield better fits to the observed data. Extra variation in the count data can be handled by extensions to the familiar Poisson model or by using a NB regression approach. Health utilization data, such as the number of emergency department visits made by an individual during a fixed window of followup time, are typically characterized by a large proportion of zeroes, representing those individuals who exhibit zero demand for the service during the study interval. Further, some individuals exhibit large demand for emergency department services, resulting in an empirical distribution of counts with a long right tail and extraPoisson variation. Modified Poisson and NB regression models are able to deal with both extra variation (overdispersion) and the excess of zeros which are typically observed in medical utilization data. The HNB model is an extension of the NB model (which itself, is an extension of the Poisson model) and is a natural choice for modeling data that exhibit both extra variation and excess of zeros, especially when zeros are structural. Although the NB regression model fits these data well, and has fewer estimated parameters than the HNB model, we tend to favor the slightly more complex hurdle model. The theoretical framework of the HNB model is an ideal choice for modeling medical utilization data as it allows researchers to simultaneously interpret the factors which influence the odds of using the medical service and the rate/intensity at which utilization occurs in those who do exhibit positive demand for the service.
Our results demonstrate the suitability of both the NB model and the HNB model for analyzing emergency department demand in the CCHS cycle 2.1 and 3.1 datasets. As an aside the ZINB model also fit these data well; however, the zeroes in this model are a mix from the Bernoulli component of the model and the count component of the model, and hence interpretation is not as simple. The Vuong test, which is designed for comparing nonnested regression models, suggests the HNB model is the most appropriate approach to modeling emergency department demand in this study.
The impact of covariates on the odds of visiting the emergency department for a less severe visit (triage scale 45) versus a more severe visits (triage scale 13) are quite different. For example, gender is not associated with the likelihood of emergency department utilization in the analysis characterized by less severe visits. However, male gender is statistically significantly associated with increased odds of at least one emergency department visit in the analysis stratified by more severe cases. This result indicates the importance of stratifying our analyses according to the severity of the triage scale, as the factors influencing the emergency department utilization may vary as a function of the severity of a cases initial presentation.
The impact of access to a primary care physician on emergency department utilization rates is an interesting finding in our analysis. Once again, the impact of this covariate differs according to the severity of presentation. For more severe cases (triage scale 13), having access to a family doctor did not influence the odds of emergency department utilization, nor did it impact the rate of utilization in those who demonstrated positive demand for the service over the study interval. For less severe emergency department visits (triage scale 45) we estimate that having access to a primary care provider significantly reduces the likelihood (OR = 0.69) of a visit. Further, given that a visit occurs, the rate of utilization is also significantly lower in those with access to a primary care provider (RR = 0.57). From a policy perspective, this finding suggests that having access to a primary care provider has the opportunity to reduce more than 40 percent of less urgent emergency department visits. Hence, strategies to increase the supply/access to primary health care professionals may result in reduced demand for emergency department services and fewer issues related to crowding, wait times and variable quality of care in Ontario's emergency departments.
To our knowledge this study is a unique population based Canadian study, which links a large national survey to provincial health utilization databases to assess the impact of individual level characteristics on the emergency department demand. Our sample size is large and outcome measures are complete. Results of this study are based on regression models that are theoretically appropriate and statistically had the best fit compared to other potential models which were investigated. Some of the findings of this study have important policy implications and if adopted may result in reducing the number of less urgent emergency department visits that are occurring in Ontario.
One limitation of our study is that we did not examine the impact of contextual factors, such as: accessibility to nearby walk in clinics, the number of primary care providers in a respondents' census tract or postal code region or the distance to nearest emergency department at the area level. Nor did we stratify our analyses according to other pertinent factors, such as: the day of the week (weekday versus weekend) or the time of the day. An advanced multilevel modeling framework can be extended to the HNB regression model fit to these data to assess the impact of contextual factors on the likelihood and intensity of emergency department visits when the impact of individual level characteristics are adjusted for. Similar methodological approaches can be adopted for stratified analyses.
Conclusions
Demand for emergency department services can be appropriately modeled using simple extensions to count based regression models, such as the HNB model. This model simultaneously accounts for excess zeroes, a skewed empirical distribution (extravariation) and unobserved heterogeneity that is common in medical demand data. Additionally, the two component interpretation of the hurdle models makes them ideal for understanding factors which affect those who experience no demand for emergency department services versus those persons that experience positive demand for emergency department services.
This analysis also revealed that the factors which influence the likelihood and intensity of emergency department services vary according to the severity of initial presentation. Some important factors that differed between the two stratified analyses were access to a primary care physician and urbanversusrural residence. While access to a primary care physician was an irrelevant factor on both the odds and intensity of emergency department utilization in high severity cases, this factor was a statistically significant predictor of the likelihood and rate of emergency department services in low severity cases. Our findings suggest that access to a primary care physician could reduce the odds of a low severity emergency department visit by approximately 31% and further reduce the rate of low severity emergency department visits by approximately 43%. This suggests that restructuring health care services in Ontario, such that access to primary care physicians is enhanced, may result in a reduced number of low severity cases presenting in the emergency department.
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
RM performed the analysis and interpreted the results. RM and CM drafted the paper. MA and BZ cut the data. RM and RHG conceptualized the research. All authors read and approved the final manuscript.
Acknowledgements
This study was supported by the Institute for Clinical Evaluative Sciences (ICES), which is funded by an annual grant from the Ontario Ministry of Health and LongTerm are (MOHLTC). The opinions, results and conclusions reported in this paper are those of the authors and are independent from the funding sources. No endorsement by ICES or the Ontario MOHLTC is intended or should be inferred.
Prepublication history
The prepublication history for this paper can be accessed here: