Diagnostic accuracy of calculated serumosmolarity to predict dehydration inolder people: adding value to pathologylaboratory reports

Lee Hooper,1 Asmaa Abdelhamid,1 Adam Ali,1 Diane K Bunn,1 Amy Jennings,1

W Garry John,2 Susan Kerry,2 Gregor Lindner,3 Carmen A Pfortmueller,4

Fredrik Sjöstrand,5 Neil P Walsh,6 Susan J Fairweather-Tait,1 John F Potter,1,2

Paul R Hunter,1,2 Lee Shepstone1

To cite: Hooper L,Abdelhamid A, Ali A, et al.Diagnostic accuracy ofcalculated serum osmolarityto predict dehydration inolder people: adding value topathology laboratory reports.BMJ Open 2015;5:e008846.doi:10.1136/bmjopen-2015-008846

▸ Prepublication history andadditional material isavailable. To view please visitthe journal (http://dx.doi.org/10.1136/bmjopen-2015-008846).

Received 20 May 2015Revised 26 August 2015Accepted 18 September 2015

For numbered affiliations seeend of article.

Correspondence toDr Lee Hooper;L.hooper@uea.ac.uk

ABSTRACTObjectives: To assess which osmolarity equation bestpredicts directly measured serum/plasma osmolalityand whether its use could add value to routine bloodtest results through screening for dehydration in olderpeople.Design: Diagnostic accuracy study.Participants: Older people (≥65 years) in 5 cohorts:Dietary Strategies for Healthy Ageing in Europe(NU-AGE, living in the community), DehydrationRecognition In our Elders (DRIE, living in residentialcare), Fortes (admitted to acute medical care),Sjöstrand (emergency room) or Pfortmueller cohorts(hospitalised with liver cirrhosis).Reference standard for hydration status: Directlymeasured serum/plasma osmolality: currentdehydration (serum osmolality >300 mOsm/kg),impending/current dehydration (≥295 mOsm/kg).Index tests: 39 osmolarity equations calculated usingserum indices from the same blood draw as directlymeasured osmolality.Results: Across 5 cohorts 595 older people wereincluded, of whom 19% were dehydrated (directlymeasured osmolality >300 mOsm/kg). Of 39 osmolarityequations, 5 showed reasonable agreement with directlymeasured osmolality and 3 had good predictive accuracyin subgroups with diabetes and poor renal function. Twoequations were characterised by narrower limits ofagreement, low levels of differential bias and gooddiagnostic accuracy in receiver operating characteristicplots (areas under the curve >0.8). The best equationwas osmolarity=1.86×(Na++ K+)+1.15×glucose+urea+14(all measured in mmol/L). It appeared useful in peopleaged ≥65 years with and without diabetes, poor renalfunction, dehydration, in men and women, with a rangeof ages, health, cognitive and functional status.Conclusions: Some commonly used osmolarityequations work poorly, and should not be used. Givencosts and prevalence of dehydration in older people wesuggest use of the best formula by pathologylaboratories using a cutpoint of 295 mOsm/L (sensitivity85%, specificity 59%), to report dehydration riskopportunistically when serum glucose, urea and

electrolytes are measured for other reasons in olderadults.Trial registration numbers: DRIE: Research Register forSocial Care, 122273; NU-AGE: ClinicalTrials.govNCT01754012.

BACKGROUNDTwenty per cent of older people living in UKresidential care are dehydrated,1 40% dehy-drated on UK hospital admission2 and >20%of free-living US older people3 4 are dehy-drated. Despite increased risks of disability,mortality and hospital admissions associatedwith water-loss dehydration (or simply dehy-dration, not to be confused with

Strengths and limitations of this study

▪ Dehydration has become a generic term – wehave clearly described dehydration type (water-loss dehydration) and used serum osmolality,the correct reference standard.

▪ Assessment of equations in five different groupsof older people including healthy free-living olderpeople, frailer people living in residential care,and older people visiting emergency care orstaying in hospital, living in several Europeancountries, and including men and women,people with and without poor renal function,people with and without diabetes, with andwithout dehydration.

▪ Careful measurement of osmolality and the com-ponents of osmolarity in hospital laboratorieswith good standardisation or under researchconditions, from community and hospitalsamples.

▪ Lack of incorporation of alcohol into the equa-tions, though we did assess the effect of mildinebriation and found it only modestly affectedresults.

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hypovolaemia, see box 1 for definitions)5–7 dehydrationis often unnoticed. Our aim was to add value to routineblood test results by using them to screen for dehydra-tion in older people.Water-loss dehydration is due to insufficient fluid

intake and is characterised by an increase in directlymeasured (by freezing point depression) serum/plasmaosmolality. Directly measured osmolality is the referencestandard for hydration status in older people becauseosmolality is central to physiological fluid control, actingas a trigger for thirst and renal fluid conservation,10 asingle measurement can diagnose dehydration (withoutprior information), and other measures do not workwell in older people.9 11 12 Serum urea/creatinine ratiois non-specific and not useful in indicating hydrationstatus when kidneys are not functioning well, commonin older adults.9 13 While low fluid intake is indicated inyoung adults by alterations in urinary parameters,14 15

actual dehydration appears to be better characterisedeven in young adults by plasma or serum osmolality,12

and in older adults urinary measures do not indicatehydration status as poor urinary concentration iscommon16 17 (L Hooper, DK Bunn, A Abdelhamid, et al.Dehydration assessed using urinary tests, how well dothey work? Diagnostic accuracy in older people. Am JClin Nutr 2015; submitted). Weight fluctuates in well-hydrated older people and dehydration may occur grad-ually rather than acutely, so sudden weight loss is not agood indicator.18 19 Physician assessment of hydrationstatus is not consistent between physicians,20 and bio-electrical impedance does not appear accurateenough.21–23 For these reasons serum and plasma osmo-lality are stated as the reference standards for diagnosingwater-loss dehydration in older adults.9 12 24 25

Monitoring directly measured serum osmolality willprovide information on hydration status, but would beinvasive, and is only partially automated in UK pathologylaboratories so is expensive–growing numbers of requestsfor directly measured serum osmolality would causesample handling problems in the clinical laboratory.Simple tests such as urine measures and skin turgorhave not shown promise in screening for dehydration inolder people16 17 (L Hooper, et al. 2015, submitted), andcalculated osmolarity is recommended in standardmedical textbooks and doctors’ websites to assess fordehydration.26–29 Components of osmolarity equations(sodium, potassium, urea and glucose) are commonlymeasured as part of routine blood tests when olderpeople visit hospitals or general practitioners. Manyosmolarity equations have been developed and are inuse, but it is not clear which are most useful. In theDehydration Recognition In our Elders (DRIE) study,which included older people living in UK residentialcare, we assessed diagnostic accuracy of different calcu-lated osmolarity formulae, compared to directly mea-sured serum osmolality and identified an osmolarityformula usefully diagnostic for dehydration.1 Calculatedosmolarity >296 mOsm/L had high sensitivity (97%)and reasonable specificity (76%), and a diagnostic ORof 99. A calculated osmolarity equation that accuratelyidentifies dehydration in the full spectrum of olderpeople (healthy older people, frailer people in residen-tial care and those needing secondary care) couldenable pathology laboratories to use routine blood teststo provide individual information on hydration status.This would enable health professionals to support olderpeople to maintain or increase their fluid intake. Weassessed which osmolarity equation best predicts directlymeasured serum/plasma osmolality (and dehydration)in five cohorts of older people, and whether it could beused to add value to routine blood test results throughscreening for dehydration in older people.

METHODSDatasetsWe assessed osmolarity equations in five data sets, each ofwhich assessed directly measured osmolality, sodium,potassium, glucose and urea from a single blood draw foreach participant. For each data set we removed partici-pants aged <65 years, those missing any of serum/plasmaosmolality, serum sodium, potassium, urea or glucosemeasurements or who presented values resulting fromartefact or physiological extremes (potassium >8 mmol/L,sodium <80 mmol/L, osmolality >340 mOsm/kg).Estimated-glomerular filtration rate (eGFR) was calculatedwith the Modification of Diet in Renal Disease formula,30

truncated at 90 to reflect clinical practice. The referencestandard was directly measured serum/plasma osmolalitycategorised as hydrated (275 to <295 mOsm/kg), impend-ing dehydration (295–300 mOsm/kg) or current dehydra-tion (>300 mOsm/kg).9 19

Box 1 Key concepts and definitions

Dehydration: water-loss dehydration, the result of insufficient fluidintake, which leads to elevation of directly measured serumosmolality.Directly measured serum osmolality: the osmotic concentration ofblood serum, expressed as the number of milliosmoles of soluteper kilogram of serum water.8 Directly measured serum osmolal-ity is assessed by degree of freezing point depression. Normalvalues for directly measured serum osmolality, indicating euhy-dration, are 275 to ≤295 mOsm/kg, while 295 to 300 mOsm/kg isclassified as impending dehydration, and >300 mOsm/kg ascurrent dehydration.9

Directly measured plasma osmolality: the osmotic concentrationof blood plasma, expressed as the number of milliosmoles ofsolute per kilogram of plasma water. Directly measured plasmaosmolality is assessed by degree of freezing point depression.Thought to be equivalent to directly measured serum osmolality.Calculated serum osmolarity: is an estimation of the osmolar con-centration of serum and is proportional to the number of particlesper litre of solution; it is expressed as mOsm/L. This is what isused when a calculated value is derived (for further details seeDeardorff8).

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The Dietary Strategies for Healthy Ageing in Europe(NU-AGE) study was a randomised controlled multicen-tre trial of healthy, independent older people (withoutfrailty, heart failure or serious chronic illness) respon-sible for their own shopping/cooking/meal choice andpreparation aged 65–79 years (http://www.nu-age.eu).The NU-AGE project aimed to assess effects of a 1 yeardietary intervention on markers of inflammation andhealth.11 31 32 We used cross-sectional baseline data from271 Norfolk (UK) participants recruited betweenSeptember 2012 and January 2014, of whom 238 hadmeasured serum osmolality. Two were excluded (onepotassium >8 mmol/L, one missing serum glucose), so236 were included in analyses. Participants were asked toavoid alcohol for 24 h before phlebotomy, but this wasnot verified. Venepuncture was in the morning after≥8 h fasting (though participants were encouraged todrink water). Whole blood was processed (using clotactivator tubes) to give serum samples, and stored at−80°C until analyses. Samples were analysed in theDepartment of Clinical Biochemistry, Norfolk andNorwich University Hospital (NNUH, Norfolk, UK).The laboratory is fully accredited (Clinical PathologyAccreditation), performs daily calibration, internalquality control and participates in External QualityAssessment. Serum osmolality was measured by depres-sion of freezing point (Advanced model 2020 multisam-ple osmometer; Advance Instruments, repeatability of±3 mOsm/kg, SD 1, in the 0–400 mOsm/kg region,coefficient of variance (CV) as for DRIE samples, 0.6%),frozen samples defrosted at room temperature on aroller mixer. When sufficient blood was available we alsoassessed serum sodium and potassium (indirect ion-selective electrode, ISE; Abbott Architect), urea (usingurease; Abbott Architect), creatinine (enzymaticmethod; Abbott Architect), haemoglobin (Sysmex XN)and glucose (hexokinase/glucose 6-phosphate dehydro-genase; Abbott Architect). It is not known whetherlaboratory staff analysing directly measured serum osmo-lality were aware of other blood measurements or viceversa.The DRIE cohort were aged ≥65 years (range 65–105)

living in residential care in Norfolk and Suffolk (UK),with a variety of cognitive and/or functional impair-ments. Those with heart failure, end-stage renal failureor terminal illness were excluded.1 33 Recruitmentoccurred between April 2012 and August 2013, and thisanalysis used baseline (cross-sectional) data. Full detailsof recruitment criteria, consent and the study flow havebeen published previously.1 Participants had low levelsof self-reported alcohol intake, and none appeared ineb-riated on interview. During the interview non-fastingvenous blood samples were collected from an antecubi-tal vein or back of hand using needle and syringe afterparticipants had rested sitting (occasionally lying)≥5 min. Samples were immediately transferred to SSTvacutainers, stored at room temperature, delivered tothe Department of Clinical Biochemistry (NNUH)

within 4 h and analysed immediately for serum osmolal-ity. Serum analyses for DRIE were as for NU-AGE (samelaboratory, personnel, accuracy and equipment). Wesent 19 hidden duplicate samples for serum osmolalityanalysis to the NNUH laboratory between June 2014 andJanuary 2015 (samples taken from the same blood draw,but in separate tubes labelled with different samplenumbers) to assess CV. The laboratory mean CV forthese 19 duplicates was 0.6%. Of 201 people living inresidential care recruited and interviewed, 198 had dir-ectly measured serum osmolality, of whom 26 weremissing serum glucose, so 172 were included in thisanalysis.Fortes included people aged ≥60 years admitted to

Welsh acute medical care or emergency departmentswith any primary diagnosis and capacity to consent May–November 2011.17 Those too unwell, who had begunmedical treatment or rehydration were excluded. Bloodwas collected from antecubital or dorsal metacarpalveins without venestasis into one lithium heparin coatedvacutainer (Becton Dickinson, Oxford, UK) and centri-fuged immediately (1500g, 10 min, 4°C). Plasma wasaspirated and directly measured plasma osmolalityassessed (freezing point depression osmometer, Model330 MO; Advanced Instruments, Norwood,Massachusetts, USA) in duplicate. Where the differencewas <3 mOsm/kg the mean was used, otherwise furtherrepeats were carried out until the mean was clear. Themean CV for the 2–8 duplications for each sample(mean 2.8 duplications) was 0.7%. Standard solutions(290 mOsm/kg) were run daily to ensure±2 mOsm/kgprecision. Serum sodium, potassium, urea and glucosewere analysed in the hospital clinical biochemistrydepartment (indirect ISE, Olympus AU 2700 automatedchemistry immuno-analyser; Beckman Coulter, Brea,California, USA), so analysis of osmolarity componentswas blind to directly measured osmolality and vice versa.Participants were not asked about recent alcohol intake,but those clearly inebriated could not give informedconsent. Of 180 participants recruited, one did not haveplasma osmolality measured, 10 lacked sodium, 62glucose and 10 were <65 years, leaving 97 analysed.Sjöstrand recruited older adults (≥75 years) able to

provide informed consent and not critically ill whoattended the emergency room of a Swedish tertiary carecentre in spring-summer 2010. Those taking ACE inhibi-tors, >40 mg/day diuretics or >50 mg/d β-blockers wereexcluded, as were those with heart failure or under theinfluence of alcohol (assessed by study nurse, not dis-cussed or tested). Main study results on fluid dynamicsover several hours are not published, but some aspectshave been reported.16 34 This analysis used baseline dir-ectly measured serum osmolality and serum measures.Serum samples were analysed immediately at theKarolinska ISO-certified laboratory, osmolality measuredusing freezing point depression (Osmometer Advanced2020, Advanced Instruments Inc, USA, CV unclear),serum sodium, potassium, urea, creatinine and glucose

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assessed (by indirect ISE, glucose assessment was dupli-cated and mean recorded, Hitachi 917, Naka, Japan). Theosmometer was automated, so assessment of serum osmo-lality was independent of other blood measures. Of 41older adults recruited, 5 were excluded (one had serumosmolality >340 mOsm/kg, two were missing potassiumvalues and two urea), so 36 were included here.Pfortmueller included adults admitted to a Swiss

emergency department with primary diagnosis ofdecompensated liver cirrhosis, January 2002 toDecember 2012.35 Pfortmueller’s retrospective analysisaimed to assess the association of glucose disturbanceswith outcome, and the select group included a highproportion with very low or raised non-fasting glucose.Patients were identified via computerised patient data-base (Qualicare Office, Medical Database Software;Qualidoc AG, Bern). Directly measured serum osmo-lality (Advanced 3900 osmometer, assessment of freez-ing point depression, CV <1%) and electrolytes, ureaand glucose (indirect ISE, Roche Modular 800 System)were measured by the Department of ClinicalChemistry, Bern University Hospital. Thirty-one partici-pants were alcoholic, but recent alcohol intake was notrecorded. It is unclear whether laboratory staff analys-ing directly measured serum osmolality were aware ofother blood measures or vice versa. Of 312 partici-pants in the data set, 58 were ≥65 years, of whom weexcluded four (one with osmolality >340 mOsm/kg,three potassium >8 mmol/L), therefore 54 wereincluded in analyses.

Osmolarity equationsFazekas et al36 collected 36 equations to calculate osmolar-ity. Since sodium, potassium, glucose and urea are regu-larly measured in older people undergoing blood tests, wefocused on the 33 equations that only included thesefactors (omitting 3 equations including ionised calcium orlactate)37 38 (VA Nelson, R A Scheidt. Personal communi-cation to Fazekas et al 2013, 1969). Fazekas multipliedresults of several equations by 0.985 (as they were reportedin mOsm/L39–41); however, as this may not have been theoriginal authors’ intention we ran these equations withand without this multiplication (adding equations 25a and27a). We also evaluated equations we have observed localphysicians using including the Wikipedia equation,26 USNational Health and Nutrition Examination Survey,42

MDcalc and Joint British Diabetes Societies equations27 29

and tonicity (associated with adverse outcomes6) (seeonline supplementary table S1). We assessed equivalenceof each of the 39 calculated osmolarity equations to thereference standard.

Terminology and unitsDirectly measured osmolality was assessed in molal units(mOsm/kg) and calculated osmolarity produced molarunits (mOsm/L) making terminology comparing the twomeasurements complex. For clarity we have written allequations using SI units, referred to as calculated

osmolarity, and expressed in mOsm/L. Directly measuredosmolality was measured and reported in mOsm/kg, whileserum sodium, potassium, urea and glucose measure-ments were in mmol/L. Since we were aiming for equiva-lence between osmolarity and osmolality, units for theosmolar gap, the difference between directly measuredosmolality and calculated osmolarity, were labelledmOsm.43

Statistical analysisWe used descriptive statistics to summarise each cohort,and Pearson’s correlation to assess associations betweendirectly measured osmolality and serum sodium, potas-sium, urea, creatinine and glucose. Osmolarity was calcu-lated using each of the 39 formulae for each participantand compared against directly measured osmolality (dif-ference in mOsm, measured osmolality in mOsm/kgminus calculated osmolarity in mOsm/L), then averagedfor each equation in each cohort. We were interested inosmolarity equations which approximated directly mea-sured osmolality, so we identified equations where:1. Mean difference was −1 to+1 mOsm;2. There was no statistically significant difference

between osmolarity equation results and directly mea-sured osmolality (p value for the paired t test ≥0.01,set at 0.01 due to multiple testing and aiming not tolose potentially useful equations at the beginning ofthe selection process).We were interested in equations where ≥3 of the 5

cohorts fulfilled either of these criteria.Having chosen the five most useful equations this way,

remaining analyses used only these equations. We assessedpercentage of participants whose osmolarity equationresults fell within 2% of directly measured osmolality foreach cohort and used a weighted mean to assess equationsacross all cohorts and for specific subgroups.Bland-Altman plots compared each osmolarity equationwith directly measured osmolality, plotting the differenceagainst the mean of osmolality and osmolarity. To assessdifferential bias, Pearson’s correlation assessed the associ-ation of the difference with osmolality, biochemical para-meters (haemoglobin, sodium, potassium, glucose, ureaand eGFR), age and measures of nutritional, cognitiveand functional status. We created receiver operating char-acteristic (ROC) plots to compare the ability of each of thefive equations to diagnose current dehydration (serum/plasma osmolality >300 mOsm/kg). Sensitivity and specifi-city, positive and negative likelihood ratios were calculatedfor each equation compared to current dehydration, asses-sing specificity where sensitivity was ≥75%, ≥80%, ≥85%and ≥90%, and assessing the sensitivity and specificity ofan appropriate whole-number cutpoint. A decision thresh-old was determined using the method of Zweig andCampbell,44 calculating a slope m=(false-positive cost/false-negative cost)×(1-dehydration prevalence)/(dehydra-tion prevalence). The best decision threshold was thepoint on the ROC curve where the line with this slope wastangent. All statistical analyses were carried out in excel or

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in STATA (IC 11.2), and statistical significance set atp<0.05 unless otherwise stated. This paper conforms toSTARD reporting standards for diagnostic studies.45

RESULTSParticipants’ are characterised by cohort in table 1.Briefly, NU-AGE participants (mean age 70 years) hadgood cognitive and functional status, and few partici-pants had raised sodium, potassium, glucose or loweGFR. DRIE care home residents were older (mean86 years), with lower cognitive and functional status,>40% had poor renal function (eGFR<60), 20% raisedglucose. Pfortmueller participants were relatively young(mean 69 years, similar to NU-AGE), with high propor-tions of hyperglycaemia and hyperkalaemia, whileSjöstrand emergency department participants wereolder (mean 84 years, similar to DRIE) with high levelsof dehydration and hypernatraemia. Fortes participants(mean 79 years) had the lowest levels of dehydration,but 36% had poor renal function. Current dehydration(directly measured serum/plasma osmolality>300 mOsm/kg) varied from 8% of participants (Fortes)to 44% (Sjöstrand).Adverse events associated with blood draws include

bruising, but no cohorts recorded bruising or notedother adverse effects of participation.In all cohorts apart from Pfortmueller, sodium concen-

trations were strongly, statistically significantly correlatedwith serum/plasma osmolality (see online supplementarytable S2). Pfortmueller data showed no statistically signifi-cant relationships between sodium, potassium, urea, cre-atinine or glucose and directly measured osmolality. Ureawas less strongly but significantly correlated with directlymeasured osmolality. Potassium and creatinine wereweakly and significantly or borderline significantly corre-lated with directly measured osmolality in NU-AGE,DRIE and Fortes, but not Sjöstrand or Pfortmueller.Glucose was weakly and significantly correlated with dir-ectly measured serum osmolality in DRIE, but not signifi-cantly in other cohorts. This suggested that usefulosmolarity equations would probably include sodium,urea or creatinine and probably potassium and glucose.Participants with raised serum sodium, potassium, ureaand glucose were classified by hydration status in onlinesupplementary table S3.

Absolute biasThe difference (directly measured osmolality, mOsm/kg,minus calculated osmolarity, mOsm/L) varied from−37.6 mOsm (Fortes equation 27) to 31.8 mOsm(NU-AGE equation 1). The p values (paired t test) com-paring osmolarity and osmolality are displayed in onlinesupplementary table S4. We were interested in equationswhere for ≥3 of 5 cohorts the mean difference was −1 to+1or the p value was ≥0.01. Equations which fulfilled the firstcriterion were 10, 24, 32 and 33, while equations 10, 24, 26,32 and 33 fulfilled the second and were examined further.

Predictive accuracyFor these five equations we calculated percentage of par-ticipants whose osmolarity equation results fell within2% of directly measured osmolality (see online supple-mentary figure S1). Percentages were 70–90% for mostequations for NU-AGE, DRIE and Sjöstrand, but lowerin Fortes (40–50%) and Pfortmueller (30–50%). Wecreated a weighted mean percentage for each equationacross all five cohorts, which confirmed equation 32 asconsistently useful and returning a greater proportion ofparticipants within 2% of directly measured osmolality.Predictive accuracy was assessed for specific subgroups:

people with and without diagnosed diabetes mellitus;with good or poor (eGFR <60) renal function; withnormal hydration, impending or current dehydration;men and women; low-alcohol and high-alcohol intake(figure 1). Equations 10 (which did not includeglucose) and 26 performed less well than other equa-tions where participants were diabetic or had currentdehydration. Equation 32 returned a higher proportionof participants within 2% of directly measured osmolalitythan the other equations for all subgroups, except ofthose who were without diabetes, well hydrated and cur-rently dehydrated (when it was second most predictive).

Bland-Altman analysisBland-Altman plots compared the five osmolarity equa-tions with directly measured osmolality,46 with 95%limits of agreement (see online supplementary figureS2). Narrower limits imply better agreement, andsmaller mean difference suggests near equality of osmo-lality and osmolarity. The narrowest limits were providedby formula 32 for NU-AGE, DRIE and Fortes, andformula 32 was a close second to formula 33 forSjöstrand, though not good for Pfortmueller. Equation10 did not show the narrowest limits for any data set,equation 24 was joint equal for NU-AGE only, and equa-tion 26 was narrowest for Pfortmueller.

Differential biasFor all five equations in all data sets the difference waspositively associated with directly measured osmolality,although correlations were less strong for equations 32and 33 (see online supplementary table S5). There wasa tendency for the difference in equations 10, 24 and 26to be significantly associated with sodium, potassium,urea, creatinine, glucose and eGFR values in several datasets (DRIE and Fortes in particular) while equations 32and 33 appeared to be less related. No equations wereconsistently associated with age, body mass index,haemoglobin, cognitive or functional status.

Diagnostic accuracyROC plots compared ability of each equation to diag-nose current dehydration (serum/plasma osmolality>300 mOsm/kg) (figure 2, see online supplementarytable S6). Diagnostic accuracy is represented by areaunder the curve (AUC, greater AUC equating to greater

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diagnostic accuracy, maximum 1.0). Equation 32 showedgreatest ROCAUC in DRIE, Fortes and Sjöstrand, equa-tion 24 was more useful in NU-AGE and 33 inPfortmueller. In the combined data set (595 partici-pants) equations 32 and 33 had similar diagnostic accur-acy (ROCAUC 0.821 and 0.820, respectively). In thecombined data sets omitting Pfortmueller, which couldbe said to be atypical, had little effect on diagnosticaccuracy and equations 32 and 33 were still preferable(ROCAUC 0.831 and 0.828, respectively, data not shown).Ensuring sensitivity ≥75% specificity was 71% for equa-tion 32 and 73% for equation 33. Raising sensitivity to≥80% produced specificity of 67% for both equations(see online supplementary table S7). At a cutpoint of

≥296 for equation 32, sensitivity for current dehydrationwas 80% and specificity 66%, positive likelihood ratio2.36, and negative likelihood ratio 0.30. At a cutpoint of≥297 for equation 33, sensitivity for current dehydrationwas 78% and specificity 69%, positive likelihood ratio2.54 and negative likelihood ratio 0.31.

Overall diagnostic accuracyTable 2 summarises the performance of the five equa-tions across the characteristics we tested. Equations 32and 33 performed well across all assessments, but equa-tion 32 was consistently most useful.Using the ROC plot for equation 32 (figure 2, com-

bined, see yellow line) we chose a decision threshold for

Table 1 Descriptive characteristics of participants of the five cohorts

Type of older

participants

NU-AGE

(n=236)

DRIE

(n=172) Fortes (n=97)

Sjöstrand ED

(n=36)

Pfortmueller

(n=54)

Free-living,

healthy

Residential

care, frailer

Admitted to medical

care /emergency

department

Awaiting

emergency room

treatment

Decompensated

liver cirrhosis

Age, years (all

≥65 years)

70.1 (4.1) 86.0 (7.9) 78.6 (7.5) 83.8 (5.9) 69.3 (4.3)

Sex, n (%) female 147 (62%) 111 (65%) 50 (52%) 20 (56%) 13 (24%)

Weight, kg 74.3 (13.8) 69.5 (17.3) ND 68.4 (13.4) ND

Height, cm 166.0 (8.8) 163.6 (10.6) ND 169.7 (9.1) ND

BMI, kg/m2 26.9 (4.1) 25.9 (5.6) ND 24.0 (4.4) ND

MMSE 28.4 (1.5) 22.2 (5.6) ND ND ND

Functional status* IADL

6.8 (1.5)

BI

67.3 (26.4)

ND ND ND

Serum osmolality,

mOsm/kg

296.0 (7.0) 291.9 (9.5) 286.7 (14.4) 299.7 (7.0) 290.9 (8.6)

Osmolality, n (%)

>300 mOsm/kg

53 (22%) 33 (19%) 8 (8%) 16 (44%) 6 (11%)

Sodium, mmol/L 140.7 (2.2) 137.4 (3.9) 136.6 (5.2) 142.6 (2.3) 135.6 (4.4)

Sodium, n (%)

>145 mmol/L

1 (<1%) 1 (1%) 2 (2%) 3 (8%) 1 (2%)

Potassium, mmol/L 4.3 (0.3) 4.2 (0.4) 4.4 (0.6) 3.9 (0.4) 4.3 (0.9)

Potassium, n (%)

>5.0 mmol/L

2 (1%) 6 (3%) 10 (10%) 0 (0%) 9 (17%)

Urea, mmol/L 5.4 (1.2) 7.0 (2.7) 8.8 (6.1) 8.2 (2.8) 9.7 (6.2)

Creatinine, µmol/L 79.6 (15.7) 90.2 (36.3) 118.9 (76.4) 84.0 (28.8) 123.0 (91.6)

Glucose, mmol/L 5.2 (0.7) 6.9 (3.2) 7.1 (2.6) 5.7 (1.2) 6.7 (4.0)

Glucose, n (%)

>7.8 mmol/L

2 (1%) 34 (20%) 25 (26%) 1 (3%) 19 (35%)

Diabetes diagnosed 6 (3%) 32 (19%) 19 (20%) ND 27 (50%)

eGFR, mL/min† 75.0 (10.9) 63.7 (19.1) 57.2 (19.3) 71.5 (17.3) 63.9 (24.4)

Poor renal function,

n (%) eGFR 30 to

<60

23 (10%) 65 (38%) 36 (37%) 13 (36%) 14 (26%)

eGFR <30, n (%) 0 (0%) 7 (4%) 11 (11%) 0 (0%) 6 (11%)

Haemoglobin, g/dL 13.9 (1.0)

n=231

12.4 (1.5) 12.4 (2.2) 13.0 (1.5) ND

All numbers are mean (SD) except where otherwise labelled.*IADL (Instrumental Activities of Daily Living) and BI (Barthel Index) assess functional status. IADL scores from 0 to 8 and 8 is fullyfunctioning, while the BI scores from 0 to 100, with 100 being fully functioning.†For creatinine in µmol/L the following equation was used, and truncated at 90 (top measure)30:

eGFR ¼ 32788� SerumCreatinine�1:154 � Age�0:203 � [1:210 if Black]� [0:742 if Female]

BMI, body mass index; eGFR, estimated-glomerular filtration rate; MMSE, Mini-Mental State Examination; ND, no data (not measured).

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dehydration as assessed by equation 32.44 The meanprevalence of dehydration across all five cohorts was 0.19,and we estimated that the cost of a false-negative finding(missing that a person is dehydrated, with its health

consequences) has five-times the cost of a false-positivefinding (labelling a person as dehydrated when they arenot, resulting in a further blood test to directly measureosmolality or simply encouraging them to drink more).

Figure 1 Percentages of individuals whose calculated osmolarity fell within 2% of measured osmolality, by equation and by

specific conditions*. DM: diabetes mellitus. *In assessing by alcohol intake we had limited information on recent alcohol intake in

any cohort, but Dehydration Recognition In our Elders (DRIE) participants reported very low alcohol intake, and the Dietary

Strategies for Healthy Ageing in Europe (NU-AGE) participants had usual alcohol intake assessments so we separated out those

who drank ≥21 g alcohol/week (intake mean plus one SD). For Pfortmueller we separated out alcoholics, other cohorts were not

represented.

Figure 2 ROC plots for each equation for each data set and for all data sets combined. DRIE, Dehydration Recognition In our

Elders; NU-AGE, the Dietary Strategies for Healthy Ageing in Europe; ROC, receiver operating characteristic.

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This gave a slope of 0.2×0.81/0.19=0.85. A line with aslope of 0.85, is tangent to the equation 32 ROC curve atthe cutpoint of 295 mOsm/L giving sensitivity of 84.5%and specificity of 58.9% (with a positive likelihood ratioof 2.05 and a negative likelihood ratio of 0.26).

DISCUSSIONWe report the most comprehensive assessment of therelationship between calculated osmolarity and directlymeasured osmolality in older people to-date. One osmo-larity equation (equation 32, by Khajuria and Krahn47)estimated directly measured serum/plasma osmolalitywell across healthy and frail older people, those in andout of hospital, with and without diabetes, with andwithout poor renal function, at all levels of directly mea-sured serum osmolality (or dehydration) and in menand women. This equation (osmolarity=1.86×(Na++K+)+1.15×glucose+urea+14) had ROCAUC 0.82 (95% CI 0.78to 0.86). Using an osmolarity cutpoint of >295 mOsm/Lgives sensitivity of 85% accompanied by specificity of59% over the full range of older participants. Of theother, widely used, osmolarity equations (includingequations suggested by standard medical sources) manywere poor at predicting directly measured serum/plasma osmolality, the reference standard for water-lossdehydration in older people. This suggests that someequations should not be used to estimate directly mea-sured osmolality.Study strengths include careful measurement of osmo-

lality and the components of osmolarity in hospitallaboratories with good standardisation or under researchconditions (regular external standard, duplicating ana-lyses of every sample).A potential weakness was lack of incorporation of

alcohol into the equations. Alcohol depresses serum/plasma freezing point, increasing directly measuredosmolality, with minimal impact on electrolytes, ureaand glucose (increasing the difference between directlymeasured osmolality and osmolarity equations, the

osmolar gap). The full Khajuria and Krahn47 equationincorporates blood alcohol:

Calculated osmolarity ¼ 1:86� (Naþ K)þ 1:15

� glucoseþ ureaþ 1:2

� ethanolþ 14

(all components inmmol=L)

No participants in any cohort were noticeably ineb-riated, so we estimated effects on calculated osmolarityof drinking 0.5 or 1 bottle of wine 2 or 8 h before phle-botomy (assuming 70 kg body weight). Blood alcoholwas negligible to 2.8 mmol/Li, highest in those drinkinga bottle of wine 2 h before phlebotomy which increasedcalculated osmolarity by 3.4 mOsm/L. This alters therelationship between osmolarity and directly measuredosmolality by only a small amount. Our analyses sug-gested that equations’ performance were slightly poorerin people more likely to have taken recent alcohol(figure 1), but this effect was not dramatic (and categor-ies poorly defined). Despite likely alcohol intake insome participants osmolarity equations were good atscreening for dehydration.A further potential weakness was that we assumed that

plasma osmolality (directly measured in Fortes) andserum osmolality (directly measured in the othercohorts) were equivalent. However, a high-quality studycomparing lithium heparin plasma (as used in Fortes)with serum samples found equivalent directly measuredosmolality.48 They also confirm that directly measuredserum osmolality of fresh and frozen serum samples(stored at −78°C and thawed rapidly) were equivalent(although not when stored at higher temperatures).48 49

On this basis we believe it is appropriate to use directlymeasured heparinised plasma osmolality and serumosmolality, as well as the osmolality of fresh and frozensamples (NU-AGE samples were the only frozen samplesand were stored at −80°C), interchangeably. Previousstudies have suggested a rise of 1–2 mOsm/kg in directlymeasured serum osmolality of samples stored at roomtemperature for up to 4 h before serum separation (asoccurred in DRIE, and is standard practice for samplestaken in primary care and transported to hospitallaboratories for analysis).50

In all of our cohorts sodium and potassium concentra-tions were determined by indirect ISE (typically used inthe large chemistry analysers in clinical laboratories,indirect ISE measures sodium on a plasma or serumsample that has been diluted with a large volume ofdiluent while direct ISE measures the electrolyte activityin the plasma water using a non-diluted whole-blood,plasma or serum sample and is typically used inpoint-of-care analysers).51 Indirect ISE (unlike directISE) is affected by the volume of non-aqueous cell com-ponents, lipids and proteins. While samples with high

Table 2 Summary of results of analyses by equation

Test Eq10 Eq24 Eq26 Eq32 Eq33

Percentage of

participants with

osmolarity within 2%

of osmolality

X – X ☼ –

Bland-Altman

analyses

X − − ☼ −

Differential bias X X X ☼ ☼ROC plots X − X ☼ ☼Sensitivity and

specificity

X − − ☼ ☼

X, indicates that a test is not useful; –, indicates a test whichsometimes appears useful, but not consistently; ☼, that it doeswell and appears particularly useful.ROC, receiver operating characteristic. ihttp://www.csgnetwork.com/bloodalcolevelcalc.html

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levels of lipid or protein are routinely re-analysed usingdirect ISE, low protein concentrations, common in olderadults, may lead to higher sodium and potassium read-ings (compared to direct ISE),52 affecting 25% of inten-sive care unit samples and 8% of general hospitalsamples. While this may be reflected in some impreci-sion in the matching of osmolarity formulae to directlymeasured osmolality our results suggest that despite useof indirect ISE the Khajuria and Krahn equation isuseful in screening for dehydration in older people.The Khajuria and Krahn equation is generalisable

across healthy free-living older people, frailer peopleliving in residential care, and older people visiting emer-gency care or staying in hospital. It worked well in thosewith and without good renal function, with and withoutdiabetes, with and without dehydration, with andwithout a tendency to drink alcohol and in men andwomen. It even worked well in patients with decompen-sated liver cirrhosis (who experience difficulty withsodium and water balance due to abnormalities in anti-diuretic hormone and aldosterone, reflected in lowmean sodium). It works well using standard hospitalequipment for analysis of sodium, potassium, urea andglucose, in plasma and serum samples, in fresh andfrozen samples.Classical thought is that hypernatraemia principally

explains raised osmolality when fluids are restricted,53 andthe correlations in online supplementary table S2 werehighest between serum osmolality and sodium, but therewere also significant correlations with potassium, urea, cre-atinine and glucose in some cohorts, suggesting that thesealso contribute. The statistical significance of correlationsin different cohorts may partially relate to cohortcharacteristics—we are more likely to see weak but statistic-ally significant relationships in the larger cohorts(NU-AGE and DRIE). In NU-AGE there was no correl-ation between glucose and serum osmolality, but only 1%of NU-AGE participants had raised serum glucose, whilein DRIE, where 20% of participants had raised serumglucose, the relationship with osmolality was weak but stat-istically significant. Raised serum sodium was not equiva-lent to raised serum osmolality in these cohorts of olderpeople (only 4% had serum sodium >145 mmol/L, while19% had serum osmolality >300 mOsm/kg, see onlinesupplementary table S3). This reflects data in young fitarmy volunteers dehydrated by walking and fluid restric-tion in a hot environment, where only one of 36 volun-teers who were clearly dehydrated (fluid loss assessed byweight loss) had raised serum sodium—plasma osmolality,with a threshold of 301 mOsm/kg, reflected hydrationstatus much better than serum sodium.25 It appears that toassess hydration status plasma or serum osmolality is key,and to estimate serum osmolality well in cohorts with avariety of characteristics the contribution of sodium, potas-sium, glucose and urea are all crucial.The finding that the Khajuria and Krahn47 equation

(equation 32) was most useful in older people is consist-ent with our findings in DRIE data alone,1 but the

equation may also be useful in younger populations.Heavens et al54 recently assessed a similar set of osmolar-ity equations against directly measured plasma osmolalityin 60 young volunteers (aged 19–46 years), and foundthat five equations were useful, including Khajuria andKrahn’s.47 The suggestion that this formula may beuseful in young fit adults as well as in older adults addsweight to its utility.Pathology laboratories could use this equation to

report calculated osmolarity and hydration status ofolder people when analysing any blood sample includ-ing sodium, potassium, urea and glucose. For suchroutine screening for dehydration we could choose acutpoint of ≥295 mOsm/L to provide sensitivity of 85%and specificity of 59%, where a positive finding could befollowed up by directly measured serum osmolality toconfirm diagnosis and rule out false positives (suggestedproforma in figure 3). A finding of dehydration wouldbe followed by consideration of glucose—if glucose israised then treatment would address serum glucose(across our populations 16% of those with raised directlymeasured serum osmolality had raised glucose). Whereglucose is not raised treatment would focus on increas-ing fluid intake. This screening would allow for earlyidentification of dehydration (but not hypovolaemia) inolder people, at little additional cost to the NationalHealth Service. The alternative would be to assess fordehydration by directly measuring serum osmolalityacross the older population, but the cost of this, inlaboratory time, resource and expense would be prohibi-tive without additional resources.Using routine blood tests in older people to screen

for dehydration using the Khajuria and Krahn formulafor serum osmolarity would enable healthcare profes-sionals and carers to provide appropriate support inolder people by increasing fluid intake and improvingand maintaining good hydration and thereby preventassociated poor health. This information could be pro-vided automatically on the reports from pathologylaboratories where serum sodium, potassium, urea and

Figure 3 Suggested proforma for opportunistic assessment

of hydration status by health laboratories.

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glucose have been measured, although to improve sen-sitivity (though increasing costs) positive results fromthis screening could be followed by assessment of dir-ectly measured serum osmolality. To assess the cost-effectiveness of these different screening models weneed detailed data on the costs of dehydration and ofserum osmolality analysis.

Author affiliations1Norwich Medical School, University of East Anglia, Norwich, UK2Norfolk and Norwich University Hospitals NHS Foundation Trust, Norwich, UK3Department of General Internal Medicine, Inselspital, University Hospital Bern,Bern, Switzerland4Department of General Anesthesiology, Intensive Care and Pain Management,Medical University of Vienna, Vienna, Austria5Department of Emergency Medicine, Södersjukhuset AB, Stockholm, Sweden6College of Health and Behavioural Sciences, Bangor University, Bangor, UK

Acknowledgements The authors would like to thank and acknowledge theparticipants of the DRIE and NU-AGE, Fortes, Sjöstrand and Pfortmuellerstudies, and DRIE advisory and steering group members, for their help, time,enthusiasm, support, ideas and participation with this work.

Contributors The DRIE study was conceived by LH, and developed by LH,DKB, JP, PRH and LS. NU-AGE was conceived by SJF-T and developed by AJand SJF-T. The Fortes study was overseen by NPW, Sjöstrand by FS,Pfortmueller by CAP and GL. This analysis was conceived by LH, carried outby LH and AA2 and developed by all authors. Data collection was carried outby LH, DKB, AJ, CAP, FS and LS. WGJ and SK oversaw analysis of samplesfor DRIE and NU-AGE and discussed laboratory implications. LH, AA1 andDKB wrote the first draft of the manuscript, all authors revised it critically forimportant intellectual content and agreed the final draft. All authors declarethemselves to be accountable for all aspects of the work in ensuring thatquestions related to the accuracy or integrity of any part of the work areappropriately investigated and resolved.

Funding This paper summarises independent research funded in part by NHSEngland, in part by the National Institute of Health Research Fellowshipprogramme (DRIE data, NIHR-CDF-2011-04-025), the European Union’s SeventhFramework Programme under grant agreement no. 266486 (‘NU-AGE: Newdietary strategies addressing the specific needs of the elderly population forhealthy ageing in Europe’), HydraDx Inc. (Fortes data), and a regional agreementon medical training and clinical research (ALF) between Stockholm CountyCouncil and Karolinska Institutet and an unrestricted grant by Masimo Inc,Irvine, CA (Sjöstrand data). The views expressed are those of the authorsand not necessarily those of the NHS, the NIHR, the Department of Health orother body.

Competing interests All authors have completed the Unified CompetingInterests form at http://www.icmje.org/coi_disclosure.pdf (available on requestfrom LH) and declare that LH, AA1, AA2, DKB, AJ, WGJ, SK, GL, CAP, FS,NPW, SF-T, JP, PRH, LS have had no relationships with any companies thatmight have an interest in the submitted work in the previous 3 years; theirspouses, partners and children have no financial relationships that may berelevant to the submitted work; and have no non-financial interests that maybe relevant to the submitted work. The exceptions are that.

▸ The European Hydration Institute (EHI) supplied plane tickets and paid fortwo nights hotel accommodation for LH to give a talk on dehydration in olderpeople at the EHI’s symposium at the International Congress of Nutrition,Granada, Spain 16–18 September 2013;

▸ The Sjöstrand study was funded by a regional agreement on medicaltraining and clinical research (ALF) between Stockholm County Council andKarolinska Institutet and an unrestricted grant by Masimo Inc, Irvine,California, USA;

▸ The Fortes study was funded by HydraDx Inc.

Ethics approval The NU-AGE study protocol was approved by the NationalResearch Ethics Committee—East of England (12/EE/0109):

▸ DRIE was approved by the UK National Research Ethics Service CommitteeLondon–East Research Ethics committee (11/LO/1997).

▸ Fortes study approval was from North West Wales Research EthicsCommittee (11/WA/0023).

▸ Sjöstrand study approval was from Ethical Board of Stockholm County,Sweden (2009/669-31/3).

▸ Pfortmueller study approval was from the Ethics Committee of the Cantonof Bern, Switzerland (14-02-13).

Study procedures for all studies were in accordance with the ethical standardsof the Helsinki Declaration. All NU-AGE, Fortes and Sjöstrand participantsgave informed consent before participating. DRIE included participants whogave their own informed consent, and also some who were unable to giveinformed consent (the process of inclusion of these participants wasapproved by our ethics committee and is explained within this manuscript).

Provenance and peer review Not commissioned; externally peer reviewed.

Data sharing statement No additional data are available.

Open Access This is an Open Access article distributed in accordance withthe terms of the Creative Commons Attribution (CC BY 4.0) license, whichpermits others to distribute, remix, adapt and build upon this work, forcommercial use, provided the original work is properly cited. See: http://creativecommons.org/licenses/by/4.0/

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