Testing whether patients with diabetes and healthy people perceive the meaning of the items in the Persian version of the SF-36 questionnaire similarly: a differential item functioning analysis

Abstract

Purpose

It has been rarely studied whether observed disparity in health-related quality-of-life (HRQoL) scores between patients with diabetes and healthy individuals is due to differential item functioning (DIF) or a true difference in the underlying construct. This study aimed to examine DIF in the SF-36 questionnaire and its effect on comparing HRQoL scores between patients with diabetes and healthy people.

Methods

The sample consisted of 230 patients with type 2 diabetes and 642 healthy individuals who filled out the Persian version of the SF-36 questionnaire. To detect DIF across patients with diabetes and healthy individuals, multiple-group multiple-indicator multiple-causes model was used. In addition, item calibration strategy was used to determine whether the effect of item-level DIF was transferred to the scale level.

Results

Nine out of thirty-six (25 %) items were detected as DIF, of which one item (11 %) was flagged as uniform and eight items (89 %) as non-uniform DIF. Most of the DIF items were detected in the mental health component which includes vitality, perceived mental health and social functioning subscales rather than in physical health component. Moreover, nonsignificant latent mean differences for general health perception and social functioning subscales became significant after DIF calibration.

Conclusion

The findings of the present study show that patients with diabetes and healthy individuals perceived some items in the SF-36 questionnaire differently. More importantly, in some subscales, the effect of item-level DIF was transferred to the scale level. Consequently, considerable caution should be taken in comparing HRQoL scores between patients with diabetes and healthy individuals.

Appendices

Appendix 1

The MIMIC model consists of two main components, namely measurement and structural components. In the measurement component, the model relates test items to the underlying constructs of interest by a vector of regression coefficients (factor loadings) by the following equation:

$$X_{ij} = \lambda_{j} \zeta_{i} + \beta_{j} Z + \delta_{i}$$

In this equation, X _ij is the response of ith individual to the jth item, λ _j is the factor loading of jth item, ζ _i is latent trait variable of ith individual (e.g., physical functioning), Z is a vector of background variables (e.g., age, gender or grouping variable), β _j is the effect from the Z variable to X _ij and δ _i is random error with mean zero and is assumed to be normally distributed and independent of Z. If β _j  = 0, for the grouping variable, then jth item is homogeneous across groups or there is no DIF in this item.

In the structural component, the underlying construct of interest and the test items are related to background variables through matrices of regression coefficients by the following equation:

$${\varvec{\upzeta}}_{{\mathbf{i}}} =\varvec{\gamma}{^\prime}{\mathbf{Z}} + {\varvec{\upvarepsilon}}_{{\mathbf{i}}} ,$$

where $\varvec{\gamma}{^\prime}$ is a vector of regression coefficient which models the relation between latent structure and background variables and ε _i is the random disturbance of the latent trait variable with mean zero and is assumed to be normally distributed and independent of Z [57]. In the current study, the latent constructs of interest or latent subscales of the SF-36 regressed to age and gender as confounding variables in order to control the effect of these variables when assessing differential item functioning across healthy individuals and patients with diabetes.

Appendix 2

The WLSMV is an asymptotically distribution-free estimation method which has been specifically designed for categorical variables (binary and ordinal). This method is a simplified version of the weighted least square (WLS) approach. In WLS, it is assumed that a continuous, normal, latent response distribution X ^* underlies an observed ordinal variable X in the population:

$${\mathbf{X}} = \, {\mathbf{m}}; \, {\mathbf{if}} \, {\varvec{\uptau}}_{{{\mathbf{m}} - {\mathbf{1}}}} < {\mathbf{X}}^{*} < {\varvec{\uptau}}_{{\mathbf{m}}} ,$$

where m (=1, 2,…, c) defines the observed value of an ordinal observed variable X and τ is the latent threshold parameter which partitions the continuous distribution of X ^* into c categories (c = 0, 1, …, C − 1). The lowest category of the threshold is predetermined to −∞ (τ ₀ ⁼−∞, i.e., c = 0) and highest one to +∞ (τ _c ⁼+∞, i.e., c = C − 1), whereas the other thresholds should be estimated from the data. In the first step of WLS technique, the thresholds and polychoric correlations are estimated using two-stage ML estimation method. Then, parameter estimates and their standard errors are obtained by the estimated asymptotic covariance matrix of the polychoric correlation and threshold estimates (denoted ${\tilde{\mathbf{V}}}$) in a weight matrix W to minimize the following weighted least squares fit function:

$${\mathbf{F}}_{{{\mathbf{WLS}}}} = \, \left[ {{\mathbf{s}} \, {-} \, {\varvec{\upsigma}}\left( {\varvec{\uptheta}} \right)} \right]{^ \prime} \cdot \, {\mathbf{W}}^{{ - {\mathbf{1}}}} \left[ {{\mathbf{s}} \, {-} \, {\varvec{\upsigma}}\left( {\varvec{\uptheta}} \right)} \right]$$

In this function, θ is the vector of model parameters, W (=${\tilde{\mathbf{V}}}$) is the weight matrix, σ(θ) is the model-implied vector including then non-redundant, vectorized elements of Σ(θ), and s is the vector of sample statistics like threshold and polychoric correlation estimates. From mathematical point of view, LSMV is simpler than WLS estimator since it only considers diagonal elements of the full weight matrix in the above fit function. In addition, the diagonal weight matrix W _D  = diag(${\tilde{\mathbf{V}}}$) which does not need not be positive definite is more flexible than the full weight matrix W = ${\tilde{\mathbf{V}}}$. Therefore, computations and encountering numerical problems in the process of parameters estimation are not as extensive as WLS [58, 59].