Letter to the editor in response to the article: “Vitamin D concentrations and COVID-19 infection in UK biobank” (Hastie et al.)

UK Biobank analyses concluded that COVID-19 risk, particularly higher risk in ethnic minorities were not explained by vitamin D [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. Hastie et al. dismissed previous critiques, responding that their analyses were " … as powerful as any to date” [8]. However, the reported statistical significance and high precision are illusory; these papers used unreliable data and contained grave errors: mislabelled data, flawed models, low power and high bias.

Only 449 Covid-19 test-positive cases were available, containing just 31 Black and 19 Asian individuals; plus 1,025 test negatives [1]. The Covid-19-negative set ("controls") was artificially inflated by adding all 347,124 untested individuals [1]. At that time, only those hospitalized (∼8.2% of cases) were tested [10,11]. Therefore, the “Covid-19-negative” control set likely contained nine times as many positives as the “test-positive” set, including pre-hospitalisations, some in care homes, and milder cases [11]. Moreover, because COVID-19 risk is zero in the absence of SARS-CoV-2 exposure, the vast majority of the so-called controls was meaningless noise [12].

This data inflation led to serious errors: overfit, over-adjusted, and unnecessarily adjusted models [13,14]. Too many model variables in logistic regressions introduces bias, obscures effects and reduces precision [15,16]. Estimation efficiency deteriorates with each added covariate and reduces statistical significance, which can lead to important associations being declared insignificant [17]. Controlling for more variables does not necessarily reduce confounding; in fact, adding variables amplifies bias faster than it reduces confounding [17]. Selection criteria based on a priori theoretical or biological relationships should have been used to judiciously construct models [18].

These mistakes were compounded by using vitamin D levels and confounder variables (including self-reported subjective indexes) measured 10–14 years ago [1,9,10]. The authors claimed vitamin D levels remain stable over time, appearing to confuse the correlation coefficient, R, with explained variance, R² [1]. Indeed, studies they referenced demonstrated levels are not stable over many years, particularly among 25(OH)D-deficient individuals [1,5,19,20] - nor are blood pressure, pulse, and body mass index [19]. Biobank data explained only ∼16% of variance in 2020 vitamin D values [19].

Categorising continuous variables is inadvisable in regressions, even for precise measures; categorising unreliable data amplifies errors by up to ten times [21]. A much larger sample size could increase power [22], but inestimably large and insurmountable bias issues would remain [23,24].

The reported conclusions were unjustified and incorrect. The data set was 1,474, not 348,598; misused statistical methods led to misleading results; and the UK Biobank data are too old to be appropriate for investigating this subject. A more detailed critique is available [25].

Declaration of competing interest

The authors received no funding for this work.

The authors have no conflicts of interest to disclose.