Using a depression-scale item to measure loneliness: low validity and tautological inflation of the loneliness–depression association

In several large ageing cohorts, loneliness is measured with the single "felt lonely" item of the Center for Epidemiologic Studies Depression (CES-D) scale, while the CES-D total score serves as the depression outcome, so that one item stands on both sides of the association. Using the 2018 wave of the Health and Retirement Study (HRS) leave-behind subsample (N = 5,083, survey-weighted, Rao–Wu rescaled cluster bootstrap with 1,000 replicates), two properties of this practice were quantified in the same respondents. The adjusted coefficient of the item was 3.2408 against the eight-item CES-D and 2.2408 against the same scale with the item removed; the difference was 1.0000 in every bootstrap replicate, an algebraic consequence of the item being one of the components of the total. In the main specification this definitional component accounts for 30.9% (95% confidence interval 29.3–33.0) of the contaminated coefficient, and for between 27.6% and 30.9% across twelve alternative specifications. Against the three-item University of California, Los Angeles (UCLA) loneliness scale the item had a sensitivity of 37.7% and a kappa of 0.363, missing 62.3% of respondents classified as lonely; this criterion-validity comparison independently replicates and extends the validation reported by Yu et al. (2025) in the same cohort. In a mediation specification the proportion mediated was 1.33 times its value under the clean specification, with an interval of 0.63–2.29 that includes unity. The item is neither an adequate measure of loneliness nor independent of the outcome it is used to predict.