Wait time is the difference between the time a patient arrives in the emergency department (ED) and the time an ED provider examines that patient. Wait time is a problem faced by both patients and hospitals. The mean wait time in EDs increased 25%, from 46.5 minutes in 2003 to 58.1 minutes in 2009. [1] The time it takes a patient to see a doctor (wait time) can be critical to the patient’s health and to a hospital’s service quality. Clinically, prolonged ED wait times may result in protracted pain and suffering and in delays in diagnosis and treatment. Many factors, such as ED overcrowding, can affect the wait time. Overcrowding in EDs may also place patients at greater risk for medical errors. (refer to American College of Emergency Physicians web site “Fact Sheets”)

Many studies examining ED wait times have used data from the National Hospital Ambulatory Medical Care Survey (NHAMCS, see http://www.cdc.gov/nchs/ahcd/about_ahcd.htm). Conducted by the National Center for Health Statistics (NCHS) annually since 1992, NHAMCS collects data about sample visits made for medical care to EDs and outpatient departments (OPDs) of a national probability sample of non-Federal, general and short-stay hospitals. The survey is a component of the National Health Care Survey, which measures health care utilization across a variety of health care providers. There are two micro-data files produced from NHAMCS and released for public use, one for OPD visits and one for ED visits. [2]

Wait time is a topic of many publications by staff at NCHS and researchers from different organizations. A majority of the publications use descriptive statistics or quote results from annual Emergency Department Summaries using NHAMCS, such as that released by NCHS for 2007 [3]. Those summaries report total numbers of visits in the following intervals: fewer than 15 minutes, 15 to 59 minutes, 1 hour but less than 2 hours, 2 hours but less than 3 hours, 3 hours but less than 4 hours, 4 hours but less than 6 hours, 6 hours or more, not seen by a physician, and missing blank. They also give a median wait time (e.g., 33 minutes in 2009 [1]).

To further analyze wait time using NHAMCS data, some statistical model-based methodologies were also introduced. [4], [5], [6]

In [4], multivariate linear regression methodology was applied to the NHAMCS 1997 to 2004 ED data. The change in wait time to see ED physicians was evaluated for all adults, patients diagnosed with acute myocardial infarction (AMI), and patients whose triage personnel designated as needing “emergent” attention. SURVEYFREQ and SURVEYREG procedures were used in SAS to better adjust for NHAMCS’s complex sample design.

In [5], multivariate logistic regression was used to estimate the association between wait time and the patient’s age, sex, payment status, and geography of that visit using NHAMCS 1997 to 2006 data. Wait times were analyzed for visits with diagnoses of acute pancreatitis, appendicitis, cholecystitis, and upper gastrointestinal hemorrhage (UGIH). For these analyses, the association between the patient’s race/ethnicity and frequency of delay relative to triage assignment was evaluated by year.

In [6], both descriptive statistics and linear regression analysis were conducted. Data for ED visits by patients 15 years of age or less from 1997 to 2000 were examined. Sample weights were applied to the identified patient records to yield national estimates. For the purposes of that study, ED wait time was analyzed for 3 major groups, i.e., non-Hispanic white (NHW), non-Hispanic black (NHB), and Hispanic white (HW). Using a linear regression analysis with logarithmically transformed wait time as a dependent variable and with adjustment for potential confounders, including hospital location, geographic region, and payer status, the study found that NHB and HW patients waited longer than NHW patients..

This paper will examine the 2009 NHAMCS micro data on ED visits that were publicly released by NCHS. The data include hospital, patient, and visit characteristics for each visit. The sample ED visits from a hospital are treated as a cluster and hospitals are mutually independent. Wait time was collapsed into discrete values based on 15-minute intervals. The resulting frequency plots showed a Poisson distribution for the wait time. A Poisson regression model was fitted to the data with wait time as the dependent variable; hospitals as subject variables (all visits to one hospital as a cluster); patient’s arrival time, arrival by ambulance, age, race/ethnicity, hospital location, etc. as covariates. Because of an overdispersion problem associated with the Poisson model for the data set, a negative binomial regression model was used to fit the data instead.

The authors have found that neither generalized linear models (to which both Poisson regression model and negative binomial regression model belong) nor the treatment of ED visits to each hospital as a cluster have been examined in the literature on ED wait time. The objective of this study is to find a fitting model to examine characteristics associated with ED wait time.”

Scientific questions concerning wait time for ED patient visits are broad. Most of them can be answered with descriptive statistics, but some of them require statistical inference based on a statistical model.

Examples of descriptive statistics are: what’s the average wait time, what’s the median wait time, what’s the average wait time for females, at what time of the day is the wait time longest, etc. Those questions could be answered by applying SAS, R or other statistical software directly to the ED visit data. For a complex multistage survey like NHAMCS, the PROC SURVEYFREQ procedure in SAS is quite useful to produce those results. Also, the wait times published in NCHS annual Emergency Department Summaries report frequently used statistics on wait time by time intervals.

When one investigates the attribution of some independent factors on ED wait time, one needs to adjust for confounding factors to avoid the possibility of spurious relationship. For example, according to many publications [4], [6], racial minority patients have longer wait times than their white counterparts. However, a majority of racial minority patients live in metropolitan areas, and hospitals in metropolitan areas have on average longer wait times than hospitals in non-metropolitan areas [1], [4]. One should adjust for hospital location when investigating the differences in mean wait times between racial groups. Statistical modeling and statistical inferences are required to answer those kinds of questions.

To compare differences in ED wait time between population subgroups, such as those defined by age, sex, race, etc., one needs to test for significance of the difference. If the p-value of the test statistic is less than the predetermined significant level α, then the null-hypothesis of no difference is rejected and one concludes that there is a difference in wait time between the groups. The probability of a Type I (α) error for a statistical test describes the probability of incorrectly rejecting the null-hypothesis and concluding there is a difference in ED visit wait time. The smaller the α, the less frequently one would reject the null hypothesis. It is common practice to set the probability of a Type I error at 5%.

The statistical models and the hypothesis testing described above are used to examine the wait time in hospital EDs among different population subgroups.

The negative binomial model applied in this research accounts for the properties of the NHAMCS data – properties such as the Poisson distribution of wait time and correlated visits to each ED, which have not been investigated before to examine ED visit wait time with NHAMCS data. Table 1 shows that collapsing wait time values into 15-minute units increased the mean minutes of wait time from 58.8 to 63 (=4.2*15) minutes. That is, collapsing wait times into 15 minute-based discrete values introduced imprecision into the data and, hence, the analysis results.

Table 2 presents results of comparisons between visit groups defined by patient race and ethnicity and groups defined by arrival mode. While the wait time difference between blacks and Hispanic whites is not significant, the ED wait time differences between non-Hispanic whites and Hispanic whites and between non-Hispanic whites and non-Hispanic blacks are both significant. Non-Hispanic whites have the shortest mean wait time compared to non-Hispanic blacks and Hispanic whites.

Table 2 also shows that the ED wait time difference between arrivals by ambulance and arrivals by non-ambulance methods is significant.

Also, from the model selection process, it cannot be concluded that patient age significantly effects wait times (not shown).

This study focuses on the development of a fitting model to examine factors associated with wait time experienced by patients in hospital EDs, while some previously well-known results are also investigated. The study analyzed publicly released micro data on ED visits from the 2009 NHAMCS, and the negative binomial model was chosen.

Previously known results that non-Hispanic black patients and Hispanic white patients waited longer than non-Hispanic white patients were independently confirmed in this analysis. It was also shown that wait time was less for patients who arrived by ambulance than for those who arrived by other means.

There are limitations to this study. First, ED wait time was not reported for about one quarter of the sample ED visits; therefore, some bias analysis is needed. Second, the main focus of this study is on the development of a fitting model that is used to examine factors associated with ED wait time. Not all relevant patient- and ED-related factors have been included in the study. Other research questions concerning ED wait time can be studied using the model derived in this study. For example, will the difference remain between whites and non-whites in ED wait time if the model adjusts for hospital location?

As discussed in this paper, the negative binomial regression model with associated clustered data methods is an appropriate statistical method for use in studying wait time for ED visits using NHAMCS data. The model reflects characteristics of ED wait time data, such as Poisson distribution of wait time and clustered data property of the visits while models used previously in literature, such as linear regression model and logistic model, did not.