Using decision trees for measuring gender equity in the timing of angiography in patients with acute coronary syndrome: a novel approach to equity analysis
© Bierman et al. 2015
Received: 27 May 2015
Accepted: 9 December 2015
Published: 23 December 2015
Methods to measure or quantify equity in health care remain scarce, if not difficult to interpret. A novel method to measure health equity is presented, applied to gender health equity, and illustrated with an example of timing of angiography in patients following a hospital admission for an acute coronary syndrome.
Linked administrative hospital discharge and survey data was used to identify a retrospective cohort of patients hospitalized with Acute Coronary Syndrome (ACS) between 2002 and 2008 who also responded to the Canadian Community Health Survey (CCHS), was analyzed using decision trees to determine whether gender impacted the delay to angiography following an ACS.
Defining a delay to angiography as 1 day or more, resulted in a non-significant difference in an equity score of 0.14 for women and 0.12 for men, where 0 and 1 represents perfect equity and inequity respectively. Using 2 and 3 day delays as a secondary outcome resulted in women and men producing scores of 0.19 and 0.17 for a 2 day delay and 0.22 and 0.23 for a 3 day delay.
A technique developed expressly for measuring equity suggests that men and women in Ontario receive equitable care in access to angiography with respect to timeliness following an ACS.
KeywordsEquity Gini coefficient Lorenz curve Decision trees
Heart disease is the leading cause of mortality for both men and women in North American [1, 2]. Advances in clinical management coupled with increased access to timely cardiac services, such as coronary angiography, have resulted in reduced cardiac mortality. Despite these advances, it is widely recognized that inequity exists in the access that various groups have to timely cardiac services, and this may impact health outcomes . In particular, previous research has shown differences in treatment patterns and health outcomes between men and women with cardiac conditions, including acute coronary syndromes [4–7], although the causes of these differences are multifactorial and may be confounded by other clinical and demographic variables .
Health policy researchers have developed conceptual frameworks to begin to quantify the impact of gender equity, [9, 10], created equity metrics [11–15] and refined indices used to objectively measure equity [16, 17] to answer these questions, yet none of this work has been able to determine the interactions of clinical and socio-demographic factors that may contribute to gender inequity.
To assess the impact of gender inequity on timely access to cardiac angiography for patients who suffered from an acute coronary syndrome (ACS), we used novel statistical techniques to create a general framework for measuring equity, and tested the model to ascertain whether women have inequitable access to coronary angiography compared with men. We hypothesize that once other demographic and clinical factors are controlled for, women’s access to angiography will be worse compared with men.
All patients admitted to an acute care hospital in the province of Ontario, Canada, between the years 2002 and 2008, diagnosed with an acute coronary syndrome (ACS) and who received a coronary angiogram were eligible for entry into this study. A complete summary of the inclusion and exclusion criteria are provided in Appendix 1.
The Discharge Abstract Database (DAD) created, by the Canadian Institute for Health Information (CIHI) providing information on admission and discharge dates, diagnostic codes, hospital identifiers, age, sex, postal code, and discharge disposition was linked at the patient level to Statistics Canada’s Canadian Community Health Survey (CCHS) [18–21]. The CCHS survey was started in 2001 and repeated every two years. It provides information on numerous demographic metrics including language, ethnicity, cultural group, age, sex, geographic region (urban versus rural), marital status, education, residence type, labor force participation, personal and household income, and a health utility index (HUI) developed at McMaster, measuring health status. Approximately 42,000 patients were surveyed from Ontario.
The primary outcome variable, delay to procedure was defined as the difference in days between date of admission to an acute care facility and date of angiography procedure. The importance of timing of angiography results from recent studies suggesting strong correlations between early invasive treatment (i.e. angiography with revascularization if indicated) and outcomes (death, myocardial infarction, stroke, or refractory ischemia) among patients with an ACS. For some types of ACS early angiography (i.e. within 24 h of admission) is recommended to optimize outcomes [22–24], while for others a more conservative approach (i.e. three or more days) may be equally as effective [25–27]. Thus rather then use a continuous measure for delay to angiography, we chose a discrete cutpoint. Subsequently the primary outcome was defined as a binary cutoff in excess of 1 day as a delay to angiography. Secondary outcomes were defined using 2 and 3 days to angiography from admission date.
Categorical variables, both clinical and socio-economic, were compared using chi-square or Fisher’s exact tests as required. Continuous variables were reported as mean ± standard error.
Decision Trees allow the integration of a variety of factors reflecting clinical properties (such as co-morbid diagnoses in men and women), other social factors (such as income, education), and of the interaction of these two types of factors. In essence, each branch of the regression tree describes coefficients reflecting the rates of access formed by such factors as income or co-morbidities. The Decision Tree algorithm generates the vector of coefficients used in calculating the Gini coefficient, a cumulative measure of inequality, via a Lorenz curve . If we rank order the groups corresponding to the coefficients so formed, and plot them, for example, against the cumulative rates of access to coronary angiography, the graph produced is the Lorenz curve. Furthermore, if we add a 45-degree line through the origin, representing equity, the departure of the Lorenz curve from this line characterizes the degree of inequity across groups . The area between the Lorenz curve and the line of identity or equity, from here on in referred to as the departure from equity, is captured in the Gini coefficient (More precisely the Gini Coefficient is twice the difference between the Lorenz curve and the 450 line of equity) whose formula can be expressed by equation 3, Appendix 2 (illustrating a more practical formulation of the Gini coefficient). The Gini coefficient can also be expressed in a more suggestive way using equation 4 [32, 33]: For purposes of inference it is much easier to work with equation 4, Appendix 2 for an alternative formulation of the Gini coefficient. The normative coefficient takes values in the range of 0 to 1, where 0 represents perfect equity and 1 represents complete inequity. By comparing the Gini coefficients (or Lorenz curves) developed around an outcome for men and women it is possible to describe the effect of gender on a health outcome. More generally, and for completeness we may generalize the Gini coefficient (Appendix 2, equation 5) by incorporating a parameter that captures the extent of aversion to gender inequitable differences [34, 35]. In the context of measuring gender equity, the algorithm is set out in the following sequence of steps:
Select a binary measure of access such as whether or not a patient had delayed access to angiography (i.e. > 1 day) following an Acute Coronary Syndrome event.
Construct the tree, using a Gini index as a splitting criterion, first forcing in any confounding or clinical factors including (age, type of admission, co-morbidities, health utility index (HUI), etc.).
Prune the tree to obtain the most parsimonious model. The strata formed by the tree yield a new set of clinical classifications .
The classifications so formed can then be ranked by increasing rates of access and compared with the cumulative rates as represented by the Lorenz curve . Thus it is the contribution of decision trees in defining complex interactions or combinations of clinical factors that enhance existing approaches to evaluating gender inequities in health.
Run the cohort of women down the appropriate branches of the tree populating the previous defined clinical classes.
Repeat the same analysis for men. Consequently, Gini coefficients can be compared in order to assess the degree of disparity between men and women with respect to the particular outcome measure, adjusting or controlling for clinical variables.
The final stage of the model-building process is to allow all remaining variables, in this case social determinants, such as education and income levels, to enter the model. Once again pruning is performed to obtain the most robust model. The terminal nodes of the tree now define a disparate set of classes formed by the interactions of a diverse collection of variables.
Following a process of pruning, the cohort of men and women, separately, are run through the model emulating the same pathways as developed in the complete tree (Clinical + Social variables).
The distribution of individuals along matching branches can then be compared again via the Gini coefficients.
The statistical significance of differences between Gini coefficients for men and women can be determined from the standard error of the Gini coefficient itself as denoted by equation 6 [38, 39] (Appendix 2) or more generally using re-sampling techniques such as the bootstrap. Having thus defined the asymptotic standard error for the Gini coefficient, testing for differences in Gini coefficients becomes a straight forward matter of examining coverage of confidence intervals using t critical values as shown in equation 7  (Appendix 2) . Furthermore, by observing the particular points on the Lorenz curve (vertical line between corresponding point for men and women) where the differences are most pronounced, we can easily isolate the particular profiles that contribute greatest towards inequity. In using t-tests we can test for statistical significance
By extension, we can incorporate into the model variables to stratify the model along regional or area axis making it possible not only to determine gender-based inequities across different outcomes but also to determine gender-based inequities across regions such as provinces. A further extension of the model allows for analysis at the group level, lending itself to embedding a hierarchical structure within the Decision Tree framework.
By the nature of the design and the way Decision Trees work, potential issues or pitfalls of confounding and effect modification have been addressed. In layering social and clinical factors, we can control for confounding. In the process of building profiles through the interactions of variables and allowing a given variable to repeatedly enter the model, effect modification is dealt with naturally.
The study was submitted through the Sunnybrook Health Sciences Centre Research Ethics Board (REB) for approval and publication. Sunnybrook Health Sciences Centre is a fully affiliated teaching hospital of the University of Toronto in Ontario, Canada.
Descriptive statistics: Clinical/Health and social determinants N (mean,standard error) for continuous predictors or N (percentage) for categorical predictors
Age in years
Health utility index (Response optional)
McMaster developed health status index ranging from −0.36 (poor) to 1(perfect health)
High blood pressure
363 (42.6 %)
286 (57.7 %)
98 (11.5 %)
70 (14.1 %)
197 (23.1 %)
127 (25.6 %)
301 (35.3 %)
159 (32.0 %
193 (22.7 %)
88 (17.7 %)
63 (7.4 %)
53 (10.7 %)
Previous heart disease
340 (39.9 %)
213 (42.9 %)
181 (21.2 %)
135 (27.2 %)
312 (36.6 %)
289 (58.2 %)
13 (2.3 %)
6 (1.8 %)
38 (6.6 %)
23 (7.0 %)
151 (26.4 %)
88 (26.9 %)
175 (30.6 %)
115 (35.2 %)
195 (34.1 %)
95 (29.1 %)
Less than secondary
278 (33.1 %)
195 (39.3 %)
136 (16.2 %)
105 (21.2 %)
58 (6.0 %)
33 (6.7 %)
Post secondary degree
377 (44.8 %)
163 (32.9 %)
Unmet healthcare needs
79 (9.3 %)
59 (11.9 %)
Born in Canada
649 (77.6 %)
389 (78.4 %
616 (72.4 %)
240 (48.3 %)
Employed in last 12 months
390 (47.0 %)
106 (21.5 %)
Barriers to health
155 (18.9 %)
106 (21.4 %)
Rating availability of heath services
Range from 1(Excellent) to 4 (poor)
657 (77.1 %)
402 (80.9 %)
799 (94.1 %)
476 (96.0 %)
155 (18.3 %)
104 (21.1 %)
145 (17.2 %)
99 (20.1 %)
283 (33.5 %)
162 (32.9 %)
Decision tree analysis
Group profiles for Angiography delays (>1 day of index event) following an ACS event
Group # (N)
Age < = 65 + (HUI* > = 0.93)
Age > 65 + no cognitive impairment + no previous heart disease
Age < = 65 + HUI* > 0.93
Age > 65 + no cognitive impairment + no pre-existing heart disease
Age > 65 + no cognitive impairment + no pre-existing heart disease
Age < = 65 + (HUI* > = 0.80, HUI* < = 0.93)
Age > 65 + cognitive impairment and/or pre-existing heart disease)
Immigration after 1962+ middle to upper income + University educated
Immigration on or prior to 1955
Full employment + income > $17,500 + poor social network
Shift work or irregular schedule
Personal income < = 42,000 + some post secondary education
Daily activities limited
< =1 Day delay to Angiography Vs > 1 day delay to Angiography following an ACS event. Results from a logistic regression model depicting social and health determinants with Odds ratios, lower and upper confidence intervals (C.I.), and P-values
High blood pressure
Less than secondary
Unmet healthcare needs
Born in Canada
Employed in last 12 months
Barriers to health
In this paper we present novel data on the impact of gender of timely access to angiography after ACS. We used a novel statistical method, along with clinical and social determinants of health to create a model to isolate the impact of gender on access to cardiac procedures, represented by coronary angiography. Our results demonstrate that when multiple clinical and socio-economic factors are controlled for, the impact of gender on time to angiography is non-significant.
The results presented in this paper using the Decision Tree analysis technique were similar to that derived from logistic regression. Why use this Decision Tree analytic technique over more traditional methods like logistic regression? Decision Trees, unlike logistic regression, present data in a visual format. For health policy makers, decision trees more readily allow greater transparency in the interpretation of the factors that results in greater or lesser health inequity. How? Simply descending the various branches of a tree reveals the interaction of socio-demographic factors that most contribute to health inequity. This is further amplified by graphically representing the results of the decision tree on a Lorenz curve stratified according to gender. Hypothetically, unlike our particular study, if a large difference occurred at a spilt represented by say, education attainment, it could be transparently depicted on the Lorenz curve. In such an instance a policy maker could focus on specific interventions for patients with low levels of educational attainment to narrow such inequities. Thus policy makers or planners could more accurately target specific subpopulations disadvantaged in their healthcare treatment, through illuminating how these clinical and social factors interact with one another.
Although, in our study, and more generally decision trees are pruned to avoid spurious findings or over fitting resulting from small sample sizes in the descending branches of the tree, they are not adversely affected by outliers as they depend on the relative values of a variable unlike traditional analytical methods including logistic regression. Moreover, the decision tree technique affirms its robustness or stability in examining the results when outcomes varied according to delay times (i.e. 1,2 or 3 days). Small changes in delay times were reflected in similar effects on the equity index scores and differences between men and women.
“Equity is the absence of avoidable or remediable differences among groups of people, whether those groups are defined socially, economically, demographically, or geographically. Health inequities therefore involve more than inequality with respect to health determinants…….”
The results of this study are consistent with recent studies that have demonstrated that age and pre-existing co-morbidities were independent predictors of coronary angiography following an ACS [42–44]. Although age, health, comorbidities such as cognitive impairment, and socio-economic determinants are important factors in inequity of timing to angiography, care should be taken in making any inferences as procedure appropriateness may highly influence these and many other inequities [45–47]. Nonetheless additional examinations may be warranted in order to investigate inequities resulting from these socio-economic determinants and develop interventions to reduce them. Furthermore, previous research has shown gender differences in outcomes of patients hospitalized with ACS, with both biological and sociological explanations for such differences. A landmark paper by Ayanian and colleagues  found women hospitalized for coronary disease in the states of Massachusetts or Maryland underwent fewer cardiac procedures than men, and more recent studies involving Medicare patients hospitalized in acute care centers across the United States have shown this same care gap, though smaller than previously reported . Within Canadian jurisdictions the picture was mixed. A study by Fransoo et al.  analyzed a cohort of patients from the province of Manitoba, and found no gender difference in angiography rates during index hospitalization after adjusting for age. More recently, research on patients hospitalized in Alberta found significant gender differences in the timing of angiography (i.e. Using a 48 h time window from admission) adjusting for income quintiles . In previous studies, women have tended to be older with more co-morbidities, which may have dissuaded clinicians from treating them as aggressively. Furthermore, social factors, such as income and education level, may confound any analysis of the impact of gender. It has also been observed that because women may manifest disease somewhat differently than men more aggressive treatment options are sometimes overlooked [51, 52]. However, once a decision is made to have patients undergo an angiogram, timing no longer differentiates men and women regardless of clinical and socio-demographic determinants, as supported by our study. Moreover once a decision is made to perform an angiography, perhaps pre-existing guidelines supersede any other factors including gender, race, education etc.
The Decision Tree modeling technique can identify and delineate cases in which biological factors have a legitimate impact on access, from cases in which social determinants (or the interaction social factors with clinical factors), have a potentially reducible impact on health inequities. This makes this statistical modeling technique ideally suited to address the complex interplay of factors that impact access to cardiac services and care. To our knowledge, this is the first study to use the Decision Tree model to assess the impact of gender inequity on access to timely angiography, and more generally in the measurement of equity itself.
The statistical methods and results of this paper have significant health policy implications. The Decision Tree technique provides guidance on the specific factors within populations that programs can target to reduce inequity and can better tease out the impact of biological factors from socio-economic ones. From a policy perspective, targeting specific populations subgroups that are underserved in their health care needs is likely to be a more cost-effective approach to spending health care dollars, and will have a greater impact on health outcomes [53, 54].
This study has significant limitations that warrant mention. The interval of time between hospitalization and response to the CCHS survey may have been as much as 1 year. However many of the socio-economic characteristics including age, co-morbidities, gender, race, ethnicity, income, labor participation are fixed, or very unlikely to have changed very much within the time window of hospitalization and survey response. For the same reasons the inequities in age and socio-economic determinants are not artifacts of these time gaps. Likewise, the administrative data component of our database provided details of the diagnosis and subsequent procedures, but little information on the extent, severity of disease (i.e. single vs. multi vessel involvement), or classification of the ACS (ST-segment elevation myocardial infarction (STEMI) and Non-STEMI). Care must also be taken in generalizing these results beyond the province of Ontario. As alluded to earlier, while the results in Manitoba agreed with those of Ontario, the Alberta study diverged in this respect. Finally, data on the admitting institution – such as the presence of an angiography laboratory was not available although we were able to access data on the procedures performed in all hospitals treating the patient during the same episode of care. With respect to the analytic method itself, a potential limitation is the requirement of significant sample sizes in order to accommodate large numbers of factors and their interactions. Yet with the growing availability of big data and linked data from multiple sources including EHR’s (electronic health records), this approach and inclusion of multiple factors will become more feasible. Despite these limitations, however, the Decision Tree modeling technique and the use of the Gini coefficient provides a novel technique to identify and delineate cases in which biological factors (e.g. co-morbidities and age) have a legitimate impact on differences on measures of access, from cases in which social determinants (or the interaction of social factors with clinical factors), have a potentially reducible impact on health inequities.
In conclusion, use of a novel statistical modeling technique has shown that timing in access to coronary angiography was not adversely affected by gender, after controlling for multiple biologic and socio-economic factors. Further research into the relationships between these factors is warranted.
The authors wish to express their gratitude to the Institute for Clinical and Evaluative Sciences (ICES) for providing access to the Canadian Community Health Survey and the Data Abstract Discharge (DAD) administrative database as well as their expertise and considerable investment of time in linking the two data sets.
Source of funding
We are indebted to both the Canadian Institutes of Health Research (CIHR) and the Ontario Ministry of Health and Long Term Care for funding this study.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
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