Comparison of intra-individual coefficients of variation on the paired sampling data when inter-individual variations are different between measures

Abstract

Background

Pain intensities of patients are repeatedly measured by Visual Analog Scale (VAS) and Pain Vision (PV) in a clinical research. Two measurements by VAS and PV are performed at the same time. In order to evaluate within patient consistency, intra-individual coefficient of variations (CVs) are compared between measures assuming that the pain status of each patient is stable during the research period. The correlated samples and different inter-individual variation due to different scales of the measures should be taken into account in statistical analysis. The adjustment of covariates will improve the estimation of population mean values of the measures.

Methods

In this paper, statistical approach to compare the intra-individual CVs is proposed. The approach consists of two steps: (1) estimating population mean values and intra-individual variances of the pain intensities by measure in a mixed effect model framework, (2) computing intra-individual CVs and comparing them between measures. The mixed effect model includes measure and some variables as fixed effects and subject by measure as a random effect. The different inter-individual variations between measures and their covariance reflect the paired sampling in the variance component. The confidence interval of the difference of intra-individual CVs is constructed using the asymptotic normality and the delta method. Bootstrap method is available if sample size is small.

Results

The proposed approach is illustrated using pain research data. Measure (VAS and PV), age and sex are included in the model as fixed effects. The confidence intervals of the difference of intra-individual CVs between measures are estimated by the asymptotic theory and by bootstrap using a subgroup resampling, respectively. Both confidence intervals are similar.

Conclusion

The proposed approach is useful to compare two intra-individual CVs taking it into account to reflect the paired sampling, different inter-individual variations between measures and some covariates. Although the inclusion of covariates did not improve the goodness-of-fit in the illustration, the proposed model with covariates will improve the accuracy and/or precision if covariates truly influence response variable. This approach can be applicable with small modification to various situations.