Alternative parameterization approaches for modelling risk assessment in the presence of imbalance: An example using parotid malignancy

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Abstract In collaborative statistics, logistic regression models are commonly used with binary outcomes and reference cell coding for categorical predictors. However, despite the usefulness of reference cell coding schemes under many investigative objectives, it is not always appropriate to address research questions of interest. Investigators often consider modifying research questions to align with inference possible using reference cell coding. Alternative coding schemes can offer a more appropriate approach for the investigation. We explored application of deviation from means coding in determining how results from a diagnostic tool provide additional information on a patient's risk of disease with respect to the overall (naïve) risk at clinical presentation. We compared model parameterizations between using reference cell coding and deviation from means coding, by both unweighted and weighted approaches, for assessing risk of parotid malignancy, comparing patients with indeterminate FNAB results with the general (naïve) risk among presenting patients. Unweighted deviation from means coding estimates a 1.2‐fold increase in the odds of malignancy with an indeterminate FNAB result compared to the naïve odds of malignancy at clinical presentation (OR: 1.21 [95% CI: 1.63–2.32], p = 0.5699). The weighted approach takes into account the imbalance in the presenting population and estimates an increased risk (OR: 2.54 [95% CI: 1.52–4.26], p = 0.0004), which is more accurately representing the naïve risk at presentation and to answer the research question of interest. Using standard reference cell coding, an indeterminate result is associated with significantly higher odds than that of a negative result (OR: 5.20 [95% CI: 2.22–12.20], p = 0.0001), but this does not inform us as to the risk with respect to that inherent at clinical presentation and thus may not be useful for clinical decision making.

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