BackgroundCluster randomised controlled trials (CRCTs) are frequently used in health service evaluation. Assuming an average cluster size, required sample sizes are readily computed for both binary and continuous outcomes, by estimating a design effect or inflation factor. However, where the number of clusters are fixed in advance, but where it is possible to increase the number of individuals within each cluster, as is frequently the case in health service evaluation, sample size formulae have been less well studied.MethodsWe systematically outline sample size formulae (including required number of randomisation units, detectable difference and power) for CRCTs with a fixed number of clusters, to provide a concise summary for both binary and continuous outcomes. Extensions to the case of unequal cluster sizes are provided.ResultsFor trials with a fixed number of equal sized clusters (k), the trial will be feasible provided the number of clusters is greater than the product of the number of individuals required under individual randomisation (nI) and the estimated intra-cluster correlation (ρ). So, a simple rule is that the number of clusters (k) will be sufficient provided:Where this is not the case, investigators can determine the maximum available power to detect the pre-specified difference, or the minimum detectable difference under the pre-specified value for power.ConclusionsDesigning a CRCT with a fixed number of clusters might mean that the study will not be feasible, leading to the notion of a minimum detectable difference (or a maximum achievable power), irrespective of how many individuals are included within each cluster.

BACKGROUND. Adrenal aldosterone excess is the most common cause of secondary hypertension and is associated with increased cardiovascular morbidity. However, adverse metabolic risk in primary aldosteronism extends beyond hypertension, with increased rates of insulin resistance, type 2 diabetes, and osteoporosis, which cannot be easily explained by aldosterone excess.METHODS. We performed mass spectrometry–based analysis of a 24-hour urine steroid metabolome in 174 newly diagnosed patients with primary aldosteronism (103 unilateral adenomas, 71 bilateral adrenal hyperplasias) in comparison to 162 healthy controls, 56 patients with endocrine inactive adrenal adenoma, 104 patients with mild subclinical, and 47 with clinically overt adrenal cortisol excess. We also analyzed the expression of cortisol-producing CYP11B1 and aldosterone-producing CYP11B2 enzymes in adenoma tissue from 57 patients with aldosterone-producing adenoma, employing immunohistochemistry with digital image analysis.RESULTS. Primary aldosteronism patients had significantly increased cortisol and total glucocorticoid metabolite excretion (all P < 0.001), only exceeded by glucocorticoid output in patients with clinically overt adrenal Cushing syndrome. Several surrogate parameters of metabolic risk correlated significantly with glucocorticoid but not mineralocorticoid output. Intratumoral CYP11B1 expression was significantly associated with the corresponding in vivo glucocorticoid excretion. Unilateral adrenalectomy resolved both mineralocorticoid and glucocorticoid excess. Postoperative evidence of adrenal insufficiency was found in 13 (29%) of 45 consecutively tested patients.CONCLUSION. Our data indicate that glucocorticoid cosecretion is frequently found in primary aldosteronism and contributes to associated metabolic risk. Mineralocorticoid receptor antagonist therapy alone may not be sufficient to counteract adverse metabolic risk in medically treated patients with primary aldosteronism.FUNDING. Medical Research Council UK, Wellcome Trust, European Commission.

BackgroundAndrogen excess is a defining feature of polycystic ovary syndrome (PCOS), which affects 10% of women and represents a lifelong metabolic disorder, with increased risk of type 2 diabetes, hypertension, and cardiovascular events. Previous studies have suggested an increased risk of nonalcoholic fatty liver disease (NAFLD) in individuals with PCOS and implicated androgen excess as a potential driver.Methods and findingsWe carried out a retrospective longitudinal cohort study utilizing a large primary care database in the United Kingdom, evaluating NAFLD rates in 63,120 women with PCOS and 121,064 age-, body mass index (BMI)-, and location-matched control women registered from January 2000 to May 2016. In 2 independent cohorts, we also determined the rate of NAFLD in women with a measurement of serum testosterone (n = 71,061) and sex hormone-binding globulin (SHBG; n = 49,625). We used multivariate Cox models to estimate the hazard ratio (HR) for NAFLD and found that women with PCOS had an increased rate of NAFLD (HR = 2.23, 95% CI 1.86–2.66, p < 0.001), also after adjusting for BMI or dysglycemia. Serum testosterone >3.0 nmol/L was associated with an increase in NAFLD (HR = 2.30, 95% CI 1.16–4.53, p = 0.017 for 3–3.49 nmol/L and HR = 2.40, 95% CI 1.24–4.66, p = 0.009 for >3.5 nmol/L). Mirroring this finding, SHBG <30 nmol/L was associated with increased NAFLD hazard (HR = 4.75, 95% CI 2.44–9.25, p < 0.001 for 20–29.99 nmol/L and HR = 4.98, 95% CI 2.45–10.11, p < 0.001 for <20 nmol/L). Limitations of this study include its retrospective nature, absence of detailed information on criteria used to diagnosis PCOS and NAFLD, and absence of data on laboratory assays used to measure serum androgens.ConclusionsWe found that women with PCOS have an increased rate of NAFLD. In addition to increased BMI and dysglycemia, androgen excess contributes to the development of NAFLD in women with PCOS. In women with PCOS-related androgen excess, systematic NAFLD screening should be considered.

Summary Background Cross-sectional imaging regularly results in incidental discovery of adrenal tumours, requiring exclusion of adrenocortical carcinoma (ACC). However, differentiation is hampered by poor specificity of imaging characteristics. We aimed to validate a urine steroid metabolomics approach, using steroid profiling as the diagnostic basis for ACC. Methods We did a prospective multicentre study in adult participants (age ≥18 years) with newly diagnosed adrenal masses. We assessed the accuracy of diagnostic imaging strategies based on maximum tumour diameter (≥4 cm vs <4 cm), imaging characteristics (positive vs negative), and urine steroid metabolomics (low, medium, or high risk of ACC), separately and in combination, using a reference standard of histopathology and follow-up investigations. With respect to imaging characteristics, we also assessed the diagnostic utility of increasing the unenhanced CT tumour attenuation threshold from the recommended 10 Hounsfield units (HU) to 20 HU. Findings Of 2169 participants recruited between Jan 17, 2011, and July 15, 2016, we included 2017 from 14 specialist centres in 11 countries in the final analysis. 98 (4·9%) had histopathologically or clinically and biochemically confirmed ACC. Tumours with diameters of 4 cm or larger were identified in 488 participants (24·2%), including 96 of the 98 with ACC (positive predictive value [PPV] 19·7%, 95% CI 16·2–23·5). For imaging characteristics, increasing the unenhanced CT tumour attenuation threshold to 20 HU from the recommended 10 HU increased specificity for ACC (80·0% [95% CI 77·9–82·0] vs 64·0% [61·4–66.4]) while maintaining sensitivity (99·0% [94·4–100·0] vs 100·0% [96·3–100·0]; PPV 19·7%, 16·3–23·5). A urine steroid metabolomics result indicating high risk of ACC had a PPV of 34·6% (95% CI 28·6–41·0). When the three tests were combined, in the order of tumour diameter, positive imaging characteristics, and urine steroid metabolomics, 106 (5·3%) participants had the result maximum tumour diameter of 4 cm or larger, positive imaging characteristics (with the 20 HU cutoff), and urine steroid metabolomics indicating high risk of ACC, for which the PPV was 76·4% (95% CI 67·2–84·1). 70 (3·5%) were classified as being at moderate risk of ACC and 1841 (91·3%) at low risk (negative predictive value 99·7%, 99·4–100·0). Interpretation An unenhanced CT tumour attenuation cutoff of 20 HU should replace that of 10 HU for exclusion of ACC. A triple test strategy of tumour diameter, imaging characteristics, and urine steroid metabolomics improves detection of ACC, which could shorten time to surgery for patients with ACC and help to avoid unnecessary surgery in patients with benign tumours. Funding European Commission, UK Medical Research Council, Wellcome Trust, and UK National ...