Estimating the reliability of repeatedly measured endpoints based on linear mixed‐effects models. A tutorial

Abstract

There are various settings in which researchers are interested in the assessment of the correlation between repeated measurements that are taken within the same subject (i.e., reliability). For example, the same rating scale may be used to assess the symptom severity of the same patients by multiple physicians, or the same outcome may be measured repeatedly over time in the same patients. Reliability can be estimated in various ways, for example, using the classical Pearson correlation or the intra-class correlation in clustered data. However, contemporary data often have a complex structure that goes well beyond the restrictive assumptions that are needed with the more conventional methods to estimate reliability. In the current paper, we propose a general and flexible modeling approach that allows for the derivation of reliability estimates, standard errors, and confidence intervals - appropriately taking hierarchies and covariates in the data into account. Our methodology is developed for continuous outcomes together with covariates of an arbitrary type. The methodology is illustrated in a case study, and a Web Appendix is provided which details the computations using the R package CorrMixed and the SAS software. Copyright © 2016 John Wiley & Sons, Ltd.

Measuring Goal Setting in School-Aged Children: Studying the Effects of Demographic Variables in Regression-Based Norms

“…Fractional polynomial (regression) models with exponents are used to achieve the best possible fit capturing complex curvilinearity in the data. The demographic variables (age, sex, LPE) and their two-way interactions are included (Van der Elst et al 2016). A restricted set of 7 exponents {− 2, − 1, − 0.5, 0, 0.5, 1, 2} is used, which is typically adequate to capture complex relationships between variables (Van der Elst et al 2016).…”

“…The demographic variables (age, sex, LPE) and their two-way interactions are included (Van der Elst et al 2016). A restricted set of 7 exponents {− 2, − 1, − 0.5, 0, 0.5, 1, 2} is used, which is typically adequate to capture complex relationships between variables (Van der Elst et al 2016). We establish which demographic variables are predictive for each of the outcome measures of the SWM, SOC, and NNAT.…”

Orphan Drugs: Getting Arms around Rare Diseases

“…Official outputs from these studies have been published and presented in different events [34][35][36][37][38][39][40][41][42][43][44][45].…”

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“…Adjusting for the possibility of multiple curves in the data resulted in choosing fractional polynomial models because the parameters for each curve can be more reliably estimated compared to multiple linear regressions (Van der Elst, Molenberghs, Hilgers, Verbeke, & Heussen, 2016). For a better fit a restricted set of 7 exponents was used {-2, -1, -0.5, 0, 0.5, 1, 2} with exponent 0 as the natural log (Van der Elst et al, 2016). Each of these values were used for the combinations of powers, while this restricted set has proven to reliably result in an optimally fitting regression model and prevents having to consider too many (multiples of hundreds) fractional polynomials (Van der Elst et al, 2016).…”

“…For a better fit a restricted set of 7 exponents was used {-2, -1, -0.5, 0, 0.5, 1, 2} with exponent 0 as the natural log (Van der Elst et al, 2016). Each of these values were used for the combinations of powers, while this restricted set has proven to reliably result in an optimally fitting regression model and prevents having to consider too many (multiples of hundreds) fractional polynomials (Van der Elst et al, 2016). The best model was selected among a proposed set of several models in the analysis based on the Akaike Information Criterion (AIC, i.e., lower indicates a better fit).…”