Response to: On item response theory models in allostatic load scoring.

Dear Editor,

We thank [1] for their interest in our work. The goal of our paper [2] was to provide researchers a practical alternative to the sum-score parameterization [3] of allostatic load (AL) that has dominated the AL field since the 1990s. As stated in the discussion section [2], our aim was not to evaluate dimensionality of AL, as this specific question has been the subject of multiple analyses (e.g., see Ref. [4] for an excellent discussion).

The AL sum-score, which appears arithmetic and model-free, is actually an uni-dimensional parallel factor model with unit-weighting of all biomarkers (see Ref. [5] for an in-depth discussion). Taken together, if a researcher has dichotomized biomarkers that they are using to calculate the AL sum-score, we encourage the researcher to also try the item response theory (IRT) scoring approach using the same data. As we have shown [2], in some situations the IRT scoring approach may be more sensitive, and able to detect effects not seen when using the sum-score parameterization of AL. Said otherwise, an IRT approach to assessing AL may allow researchers to detect associations with health outcomes that are otherwise missed using the sum-score.

In practice, there is no gold standard way to verify sufficient uni-dimensionality for IRT. Possible approaches include using multiple criteria from factor analysis [6], Stout’s Test of Essential Unidimensionality [7], among others. Importantly, simulation studies in the psychometrics literature have shown that estimates of theta – the AL burden score we are estimating in our study – are unbiased even when uni-dimensionality is violated [8]. Interested researchers may also want to explore extensions to IRT, such as multi-dimensional IRT, which would allow for a multi-dimensional conceptualization of AL. Researchers may also want to consider other IRT models, such as graded response models, which allow for ordinal data (e.g. quantiles of biomarkers rather than dichotomized biomarkers) to capture more variability in the biomarker data.

Extensions to our approach, such as using IRT to harmonize [9] measurement of AL across cohorts that used different but overlapping methods of assessment, are not trivial. As the authors of the letter have stated, these efforts require additional thoughtful study on how AL is measured in each cohort, and should indeed be the focus of further study.

The supplementary code provided [2] was not intended to be a thorough tutorial, but rather a starting point for other researchers who may want to use R software for IRT. IRT can be implemented using a variety of software, such as MPlus, SAS, Stata, and IRTPRO, among others.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.