The analysis of multiple correlated outcomes is relevant for epidemiologic research. Subjects in epidemiologic studies are often assessed using various outcomes measures. How can multiple correlated outcomes be used to establish an overall assessment of health risk? How can such a risk assessment be related to predictors? We used item response theory (IRT) to explore these questions and to build on our prior work with the health-related quality of life (HRQOL) indicators included in the Behavioral Risk Factor Surveillance System (BRFSS) (1).

HRQOL is a latent variable or latent trait that cannot be observed directly by a single measurement. A set of indicators (outcomes) (Figure) used to measure HRQOL is included in the BRFSS (2). Many researchers have examined the relationships between specific BRFSS HRQOL indicators and various health risk factors. Most of their studies have analyzed BRFSS HRQOL indicators by using either a logistic (3-11) or linear regression model (12). They are multivariable analyses that use multiple risk factor variables to predict specific HRQOL outcomes (eg, depression, activity limitation). However, individual HRQOL indicators are correlated because each HRQOL indicator measures a certain aspect of HRQOL. We found considerable overlap in results of the multiple single outcome models we described in our prior work (1). This finding led us to seek a single model that would combine results of the multiple HRQOL models. Item response theory (IRT) provided a possible means of accomplishing this objective because it enables analysis of multiple correlated outcomes within a single model. In this study, we apply IRT to Rhode Island's 2004 BRFSS data, which include 9 HRQOL indicators, to develop a single model for HRQOL.

IRT is popular in the fields of educational measurement and psychometrics. The method uses responses to a set of discrete items (indicators) (13) to estimate latent traits or latent variables that cannot be measured directly. For example, in educational testing, students' ability (latent trait) is estimated through their answers to multiple test items (indicators) (13). Our objective in applying the IRT model was to assess the effect of each of a number of predictors on overall HRQOL (latent variable).

Overall, 14.8% had poor or fair general health; 28.8% reported lack of energy, and 23.8% reported inadequate sleep or rest (Table 1).

Table 2 highlights the performance of the 9 HRQOL indicators by displaying the values of α (indicator discrimination parameter) and β (indicator difficulty parameter) for each of the indicators. For each of the 9 indicators, α is statistically significant, meaning each indicator is able to discriminate reliably between good and poor for 1 aspect of HRQOL. The larger the value of β for each indicator, the higher the probability that the Rhode Island population has a poor HRQOL as measured by that indicator.

Table 3 displays how HRQOL (θ, latent variable) is related to the 12 predictors that are 0-1 variables, with 0 referring to the reference level. Interpreting these results is the same as if we were interpreting the results of a linear regression. Women have poor HRQOL (θ) compared with men, and the difference is significant. Poor HRQOL (θ) increased with decreasing levels of annual household income, and the differences are significant. Respondents who were unable to work or who were unemployed had significantly worse HRQOL (θ) than people in other employment categories. Homemakers/students and retired people had HRQOL (θ) similar to that of employed people. Current smokers, chronic alcohol users, or people who were physically inactive all had significantly worse HRQOL (θ) than nonsmokers, people who were not chronic users of alcohol, or who were physically active. People who had been told by a physician that they had diabetes or asthma were significantly more likely to have poor HRQOL (θ) than were people without these conditions. Obese people and disabled people were also more likely to have poor HRQOL (θ) than were nonobese or nondisabled people, and differences were significant. There were no significant differences for age or race/ethnicity groups.

IRT is a special type of structural equation model that has been applied in educational measurement with great success (24). In recent years, IRT methods have been used to develop measurement tools for health status assessment, for example, to construct instruments, score scales, or validate tests. These applications have focused on the measurement component of IRT. However, we have used IRT to integrate the analysis of multiple correlated outcomes. We focused on the structural component of the model (Figure), which characterizes the relationship between HRQOL (θ), demographics, risk factors, and health conditions.

We used an IRT model to analyze the BRFSS HRQOL data for 2 reasons. First, when we used multivariable logistic regression models to analyze the multiple correlated indicators in our previous study (1), each individual indicator (outcome) for HRQOL reflected only a specific aspect of physical health or mental health or both. The results of these multiple discrete models for HRQOL, which overlapped each another, were redundant and cumbersome to integrate into an overall evaluation. Finding a method to integrate these multiple correlated indicators into an encompassing simple indicator was our objective. IRT enabled assessment of overall HRQOL as an underlying or latent variable not amenable to direct measurement. It allowed evaluation of HRQOL (θ) in relation to demographics, health risks, and health conditions. Second, if any single indicator is used to assess HRQOL, its reliability can be compromised by the various factors that might influence an individual's response to any single indicator measure. If all indicators are considered together, the effect of this kind of variation for any single measure is reduced, improving the reliability of our assessment of HRQOL. IRT provides a solution to measuring HRQOL across multiple correlated indicators (outcomes).

Equation no. 2 represents the relationship between the latent trait and predictors, and equation no. 4 represents the relationship between indicators and predictors. In equation no. 4 for "Mentally unhealthy" in Table 2, α is 1.45; and in Table 3, the estimated coefficient for "Current smoker" is 0.27, thus OR = exp(α·c) = exp(1.45 × 0.27) = 1.5. In our previous analysis using a logistic regression model (1), the OR is also 1.5 for "mentally unhealthy" and "current smoker." Using this calculation, we can get similar results to those in our previous analysis, which was based on logistic regression models (1). This process illustrates how 1 IRT model can generate the results of 9 logistic regression models, and the results from the IRT model and the logistic regression models are similar. This also demonstrates that we can use 1 IRT model to combine results of multiple logistic regression models.

Our previous article (1) demonstrated that the prevalence of poor physical health increased with age, and the prevalence of poor mental health decreased with age. However, our IRT results indicate no significant difference in overall HRQOL (θ) between younger and older adults (Table 3). Our previous research (1) also showed that Hispanics had the highest percentage of "poor or fair" general health but did not have the highest percentage for other indicators of poor HRQOL. Research suggests that Hispanics who do not speak English fluently have lower educational achievement and lower levels of health literacy, which may make it difficult for them to respond to questions on HRQOL (30). Our IRT results show no difference in HRQOL (θ) among different racial/ethnic groups.

Results represented in Table 3 can enable health-related initiatives in Rhode Island to target specific populations at high risk for poor HRQOL (θ). Factors significantly associated with poor HRQOL (θ) were being female, having a household income less than $50,000, being unemployed or unable to work, being a smoker or chronic alcohol user, not engaging in leisure-time physical activity, having doctor-diagnosed asthma or diabetes, being obese, or having a disability.

Because IRT methods were originally developed for educational assessment with a homogeneous population (24,31), there is no guidebook that tells how to use IRT methods to evaluate health measures. There are many IRT models from which to choose, which means that finding a model that fits the available data and can estimate model parameters is difficult (24,26). IRT has the potential of being applied to other epidemiologic data with multiple correlated outcomes (32,33).

IRT methods may find increasing application in epidemiology. IRT may be a solution for modeling the multiple correlated outcomes often found in epidemiologic studies. This study provides a picture of the relation between overall HRQOL and demographics, behavioral risk factors, and health conditions. It indicates at-risk subpopulations in Rhode Island where interventions might have the most significant impact on HRQOL.