Toxicol Rev 2004; 23 (3): 189-202 1176-2551/04/0003-0189/$31.00/0

REVIEW ARTICLE

© 2004 Adis Data Information BV. All rights reserved.

The Use of the Osmole Gap as a Screening Test for the Presence of Exogenous Substances Roy A. Purssell,1 Larry D. Lynd2,3 and Yoshikata Koga4 1 2 3 4

Division of Emergency Medicine, University of British Columbia, Vancouver, British Columbia, Canada Faculty of Pharmaceutical Sciences, University of British Columbia, Vancouver, British Columbia, Canada Centre for Clinical Epidemiology and Evaluation, Vancouver Coastal Health Research Institute, Vancouver General Hospital, Vancouver, British Columbia, Canada Department of Chemistry, University of British Columbia, Vancouver, British Columbia, Canada

Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 1.1 Physical Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 1.2 Principles for the Evaluation of Diagnostic/Screening Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 1.3 Evaluating the Osmole Gap (OG) as a Screening or Diagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 2. Review of the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 2.1 Summary of Endogenous Osmotically Active Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 2.2 The Relationship Between Calculated Serum Molarity and Measured Serum Osmolality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 2.3 Evaluation of the Ability of the OG to Estimate Serum Ethanol Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 2.4 The Utility of the OG for the Evaluation of Methanol and Ethylene Glycol Poisoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 3. Situations in Which Osmometry May Produce Erroneous Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 4. Limitations of Current Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

Abstract

The rapid and accurate diagnosis of toxic alcohol poisoning due to methanol (methyl alcohol) [MeOH] and ethylene glycol (EG), is paramount in preventing serious adverse outcomes. The quantitative measurement of specific serum levels of these substances using gas chromatography is expensive, time consuming and generally only available at major tertiary-care facilities. Therefore, because these toxic substances are osmotically active and the measurement of serum osmolality is easily performed and more readily available, the presence of an osmole gap (OG) has been adopted as an alternative screening test. By definition, the OG is the difference between the measured serum osmolality determined using the freezing point depression (Osmm) and the calculated serum molarity (Mc), which is estimated from the known and readily measurable osmotically active substances in the serum, in particular sodium, urea, glucose, and potassium and ethanol (alcohol). Thus, the OG = Osmm – Mc, and an OG above a specific threshold (the threshold of positivity) suggests the presence of unmeasured osmotically active substances, which could be indicative of a toxic exposure. The objectives of this study were to review the principles of evaluating screening tests, the theory behind the OG as a screening test and the literature upon which the adoption of the OG as a screening test has been based. This review revealed that there have been numerous equations derived and proposed for the estimation of the Mc, with the objective of developing empirical evidence of the best equation for the determination of the OG and ultimately the utility of OG as a screening test. However, the methods and statistical analysis employed have generally been inconsistent with recommended guidelines for screening test evaluation and although many equations have been derived, they have not been appropriately validated.

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Specific evidence of the clinical utility of the OG requires that a threshold of positivity be definitively established, and the sensitivity and specificity of the OG in patients exposed to either EG or MeOH be measured. However, the majority of studies to date have only evaluated the relationship between the Osmm (mmol/kg H2O) and the Mc (mmol/L) in patients that have not been exposed to either MeOH or EG. While some studies have evaluated the relationship between the OG and serum ethanol concentration, these findings cannot be extrapolated to the use of the OG to screen for toxic alcohol exposure. This review shows that there has not been an appropriately designed empirical evaluation of the diagnostic utility of the OG and that its clinical utility remains hypothetical, having been theoretically extrapolated from the non-poisoned population.

1. Background The osmole gap (OG) is commonly used in the clinical setting for estimation of the concentration of several osmotically active substances and to determine if a patient has been exposed to a potentially toxic, osmotically active substance. Because obtaining specific levels of potentially toxic substances is expensive, labour intensive and generally only available in tertiary-care centres, the OG has become an alternative clinical screening method. It is less expensive, readily determined and often more available. Although its use has become widespread, the validity of the OG as a diagnostic or screening test has not been systematically evaluated. 1.1 Physical Chemistry

It is clear that the literature on serum osmometry includes some misinterpretation of principles of physical chemistry, the most important being the erroneous assumption that serum behaves as a dilute ‘ideal’ solution and that the osmotic activity of a substance depends solely on the number of particles in solution. The degree of variance of serum containing exogenous substance from ideal behaviour is indicated by the value of the osmotic coefficient. For instance, the osmotic coefficient for serum containing ethanol (alcohol) [EtOH] has been found to deviate from unity by as much as 16%.[1] Unless corrections in the testing procedures are made, it can be expected that the results of serum osmolality testing will vary from an accurate result by a similar factor. Therefore, it is important that the osmotic coefficient for serum containing low molecular weight substances such as methanol (methyl alcohol) [MeOH], isopropyl alcohol and ethylene glycol (EG) also be determined. Considering the basic principles of physical chemistry and the relationship between molarity and molality, we will demonstrate that the currently applied method of determining the OG is fundamentally flawed. The OG is defined as the difference between the serum osmolality, measured with an osmometer (measured osmolality [Osmm]) and the estimated total molarity of solute in serum, determined by directly measuring the concentration of the princi© 2004 Adis Data Information BV. All rights reserved.

ple osmotically active endogenous substances (i.e. sodium, glucose and blood urea nitrogen), and then substituting these measured values into a formula (calculated molarity [Mc]) [table I]. Some authors call this sum the calculated or estimated ‘osmolarity’, but because the concentrations are measured directly and not with an osmometer, the term calculated ‘molarity’ is more appropriate. Thus, the OG = Osmm – Mc. However, the units of osmolality (Osmm) are mmol/kg of water and the units of molarity (Mc) are mmol/L. Therefore, the practice of subtracting calculated serum molarity from measured serum osmolality is technically invalid and is an oversimplification for ease of application. Serum osmolality can be easily converted to molarity provided the weight percentage and the density of the solution are known. Thus, the measured serum osmolality should be converted to serum molarity before the OG is calculated. Mc = Osmm (d[Pw/100]) where: Mc = calculated molarity (mmol/L), Osmm = measured osmolality (mmol/L), d = density of solution (serum – 1.026 kg/L), Pw = percentage weight (wt%) of H2O in solution = (weight of H2O in solution/total weight of solution) × 100 (serum – 91%). With substitution: Mc = 0.933 Osm. Once the units are consistent, the ‘osmolar’ (as opposed to ‘osmole’) gap can be calculated, a standard value and reference range for the osmolar gap could be determined in an adequate number of patient populations and in a variety of clinical settings, and its utility as a screening test for low molecular weight substances can then be meaningfully evaluated. However, a detailed discussion of the physical chemical principles underlying the practice of osmometry and the OG are extremely complex and outside the scope of this review. We have provided an in-depth review of the relevant physical chemical principles in the accompanying article.[1] 1.2 Principles for the Evaluation of Diagnostic/ Screening Tests

The OG is often used as a screening test for the possible diagnosis of MeOH or EG poisoning. Thus, the presence of an OG Toxicol Rev 2004; 23 (3)

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Table I. Equations for calculation of serum molarity Equation no.

Study

Year

Units

Equation

1

Edelman et al.[2]

1958

Standard

Mc (mmol/L) = 1.75 Na (mEq/L) + BUN (mg/dL)/2.8 + glucose (mg/dL)/18 + 10.1

SI

Mc (mmol/L) = 1.75 Na (mEq/L) + BUN (mmol/L) + glucose (mmol/L) + 10.1

2

Dorwart and Chalmers[3]

1975

Standard

Mc (mmol/L) = 1.86 Na (mEq/L) + BUN (mg/dL)/2.8 + glucose (mg/dL)/18 + 9

SI

Mc (mmol/L) = 1.86 Na (mEq/L) + BUN (mmol/L) + glucose (mmol/L) + 9

3

Gennari[4]

1984

Standard

Mc (mmol/L) = 2 Na (mEq/L) + BUN (mg/dL)/2.8 + glucose (mg/dL)/18

Smithline and Gardner[5]

1976

SI

Mc (mmol/L) = 2 Na (mEq/L) + BUN (mmol/L) + glucose (mmol/L)

4

Glasser et al.[6]

1973

Standard

Mc (mmol/L) = 1.86 Na (mEq/L) + BUN (mg/dL)/2.8 + glucose (mg/dL)/18

SI

Mc (mmol/L) = 1.86 Na (mEq/L) + BUN (mmol/L) + glucose (mmol/L)

5

Bhagat et al.[7]

1984

Standard

Mc (mmol/L) = 1.89 Na (mEq/L) + 1.38 K (mEq/L) + BUN (mg/dL)/2.9 + glucose (mg/dL)/19.4 + 7.45

SI

Mc (mmol/L) = 1.89 Na (mEq/L) + 1.38 K (mEq/L) + 1.03 urea (mmol/L) + 1.08 glucose (mmol/L) + 7.45

Standard

Mc (mmol/L) = 1.86 {Na (mEq/L) + K (mEq/L)} + BUN (mg/dL)/2.8 + glucose (mg/dL)/18 + 10

SI

Mc (mmol/L) = 1.86 {Na (mEq/L) + K (mEq/L)} + BUN (mmol/L) + glucose (mmol/L) + 10

Standard

Mc (mmol/L) = 2 {Na (mEq/L) + K (mEq/L)} + BUN (mg/dL)/2.8 + glucose (mg/dL)/18

6

Bhagat et al.[7]

1984

7

Worthley et al.[8]

1987

SI

Mc (mmol/L) = 2 {Na (mEq/L) + K (mEq/L)} + BUN (mmol/L) + glucose (mmol/L)

8

Hoffman et al.[9]

1993

Standard

Mc (mmol/L) = 2 Na (mEq/L) + BUN (mg/dL)/2.8 + glucose (mg/dL)/18 + EtOH/4.6 (mg/dL)

SI

Mc (mmol/L) = 2 Na (mEq/L) + BUN (mmol/L) + glucose (mmol/L) + EtOH (mg/dL)

9

Osypiw et al.[10]

1997

Standard

Mc (mmol/L) = 2 Na (mEq/L) + K (mEq/L) + BUN (mg/dL)/2.8 + glucose (mg/dL)/18

SI

Mc (mmol/L) = 2 Na (mEq/L) + K (mEq/L) + BUN (mmol/L) + glucose (mmol/L)

BUN = blood urea nitrogen; EtOH = ethanol (alcohol); Mc = calculated molarity.

above a specific threshold suggests the presence of unmeasured osmotically active substances that could be indicative of a toxic exposure. The OG is often used to ‘screen’ for EG and MeOH exposure. Screening for toxic alcohols by determining the OG is inexpensive, readily available and easy to perform relative to using gas chromatography to measure specific serum EG and MeOH concentrations. The latter determinations are expensive, complex to perform and generally only available in tertiary-care hospitals in urban centres, often not on a 24-hour basis.[11] Candidate diseases appropriate for screening are those with latent periods and those for which early diagnosis and initiation of treatment prior to the development of symptoms improves prognosis.[12,13] MeOH and EG poisoning fit these criteria in that a patient with a potential exposure may present in a preclinical phase of toxicity but go on to © 2004 Adis Data Information BV. All rights reserved.

subsequently develop life-threatening symptoms if left untreated. Although the preclinical phase is generally defined as the point at which the pathological process is first present, in the case of toxic alcohol poisoning it can be defined as the presence of toxin prior to its metabolism to toxic metabolites and, therefore, prior to the development of toxic effects. Alternatively, patients poisoned by these substances may present acutely ill at a later stage. In this case it is important to screen for possible toxic alcohol poisoning to determine whether therapy such as inhibition of alcohol dehydrogenase or haemodialysis should be initiated. When evaluating the clinical utility of a screening test, one must consider: (i) whether the test has been compared with a valid gold standard for diagnosis; (ii) if it has been evaluated in a patient sample that included an appropriate spectrum of patients with mild to severe disease, and in individuals with different but commonly Toxicol Rev 2004; 23 (3)

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confused disorders; (iii) whether the test precision and observer variation or bias has been adequately measured and evaluated; (iv) if an abnormal test has been adequately defined; (v) if the exact method of applying the test has been sufficiently described to permit exact replication; and (vi) if the overall utility of the test relative to existing tests has been substantiated.[14] The validity of the OG as a screening test must, therefore, be measured by its ability to correctly classify persons who have been exposed to EG or MeOH as test-positive and those who have not as test-negative. The sensitivity (the probability of testing positive if exposed) and specificity (the probability of testing negative if unexposed) are measures of the validity of a test. A highly sensitive test is unlikely to falsely diagnose a patient as unexposed, and a highly specific test will rarely be positive in the absence of the disease or exposure. Although ideally it is desirable that the screening test be both highly sensitive and highly specific, this is generally not possible. When screening for toxic alcohols, a false-negative test will result in potentially greater patient morbidity than a falsepositive test and, therefore, the sensitivity of any test that is to be applied in this clinical scenario is of primary importance. Both the sensitivity and specificity of the test will be influenced by the established ‘criterion of positivity’ (i.e. the threshold at which a patient is considered test-positive). Therefore, the ‘normal’ value of the test must be defined either prior to, or during the evaluation of any screening test. The probability of an erroneous diagnosis will be directly related to this threshold. Setting a low threshold will result in a higher rate of false-positive tests, whereas a high threshold will result in false-negative tests, a situation that is obviously undesirable in screening assays. 1.3 Evaluating the Osmole Gap (OG) as a Screening or Diagnostic Test

Appropriately designed studies of diagnostic accuracy compare the results from one or more tests to those obtained using a reference standard (gold standard test), both of which are measured in subjects suspected as having the condition or exposure of interest. The reference standard should be the best available method for establishing the presence or absence of the condition or exposure. A survey of studies of diagnostic accuracy published in four major medical journals between 1978 and 1993 revealed their methodological quality to be mediocre at best.[15] Lijmer et al.[16] found that studies of lower methodological quality, particularly those including non-representative patients and those that applied different reference standards, tended to overestimate the diagnostic performance of the test. Following the identification of the inherently poor methodological quality of studies evaluating diagnostic accuracy, a group of © 2004 Adis Data Information BV. All rights reserved.

investigators and editors developed the Standards for Reporting Diagnostic Accuracy (STARD) statement. This statement consists of 25 criteria and a flow diagram that authors should use when evaluating diagnostic accuracy, compiled with the objective of improving the quality of the reporting of these studies.[17] We were unable to identify any studies that evaluated the performance of the OG in both exposed and unexposed subjects covering a clinically relevant range of exposures. The majority of the literature on the OG has focused on evaluating the relationship between serum osmolality (mmol/kg H2O) and calculated serum molarity (mmol/ L) in patients that have not been exposed to MeOH, EG, or other low molecular weight substances known to produce an OG. A number of authors have also evaluated the ability of the OG to estimate serum EtOH concentrations. Therefore, the balance of this review is intended to provide an overview of the theoretical underpinnings of the clinical utility of the OG as a screening test for MeOH or EG poisoning, and to summarise and critique the literature and methodological approaches that have contributed to the adoption of the OG as a screening test for these poisonings. 2. Review of the Literature 2.1 Summary of Endogenous Osmotically Active Substances

Exposure to a variety of substances is associated with an increase in OG. Most substances produce clinical effects and toxicity at serum concentrations that would not produce detectable changes in the OG. However, there are some substances that require higher levels for toxic symptoms to manifest clinically and have been shown to produce a measurable increase in serum osmolality (table II). These substances may, therefore, theoretically be detected using the OG. However, the sensitivity and specificity of the OG for the detection of each of these substances must be determined in various patient populations, in various settings and in an adequate number of exposed and unexposed subjects before it can be advocated as a screening test for any of the substances. MeOH ingestion typically produces gastrointestinal symptoms and mild central nervous system depression initially, then after a latent period of 6–12 hours, metabolic acidosis and characteristic visual disturbances occur. Treatment guidelines recommend antidotal therapy for patients with serum MeOH concentrations >6 mmol/L (20 mg/dL) and haemodialysis if serum MeOH levels are >15 mmol/L (50 mg/dL).[18] Similarly, EG produces gastrointestinal symptoms and central nervous system depression initially, followed by renal and myocardial dysfunction, and metabolic disturbances after a similar latent period. Treatment guidelines recommend antidotal therapy for patients with a serum EG conToxicol Rev 2004; 23 (3)

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Table II. Summary of exogenous substances that can increase the osmole gap Substance

Reference

Methanol (methyl alcohol)

18

Ethylene glycol

18

Ethanol (alcohol)

6,9,19,20

Isopropyl alcohol

6

Acetone

6

Propylene glycol

21-23

Mannitol

24-26

Glycerol

24-26

Sorbitol

27

Glycine

27

Sodium diatrizoate

28

Dimethyl sulfoxide

29

Methyl ethyl ketone

30

Lacquer thinner (methyl ethyl ketone, toluene, xylene)

31

centration of >3 mmol/L (20 mg/dL), and haemodialysis if serum EG concentrations are >8 mmol/L (50 mg/dL).[32] EtOH produces significant increases in the OG at levels commonly seen clinically.[6,9,19,20] In many jurisdictions it is illegal to drive with a serum EtOH concentration >17 mmol/L (80 mg/dL), which would produce a detectable change in the serum osmolality. Isopropyl alcohol, and its metabolic byproduct acetone, can produce a significant increase in the OG at serum levels commonly seen clinically.[6] Propylene glycol is a common vehicle for numerous medications. Although an elevated OG has been reported in patients receiving infusions of lorazepam,[21] etomidate[22] and in patients treated for large burns with massive topical administration of silver sulfadiazine,[23] iatrogenic or accidental overdose with propylene glycol is uncommon. Methyl ethyl ketone (MEK), toluene and xylene have been shown to produce clinically detectable increases in the OG following purposeful ingestions. Price et al.[30] reported a case in which a patient ingested both MeOH and MEK and they estimated that MEK and its metabolite, 2-butanol, contributed 20 to an observed OG of 99. Brubacher et al.[31] reported a case of a patient who ingested 250mL of lacquer thinner in whom the OG increased from 15 to 31 over an 8-hour period following ingestion, a change that was attributed to the MEK component of the solvent. Browning and Curry[33] evaluated the effect of glycol ethers on plasma osmolality in vitro and concluded that these agents produced a linear increase in plasma osmolality with increasing plasma concentration. However, the change in osmolality © 2004 Adis Data Information BV. All rights reserved.

may be too small to be clinically useful at concentrations expected in cases of human glycol ether poisoning. Many osmotically active substances are administered clinically and can produce clinically significant and detectable increases in the OG. Mannitol and glycerol are administered for the management of intracranial hypertension and increases in intracranial pressure during which it has been recommended that the serum osmolality be monitored and infusions stopped if the serum osmolality exceeds 320 mOsm/kg.[24-26] Mannitol, sorbitol and glycine are used as irrigating solutions during transurethral prostatic resection and have produced a measurable increase in the OG.[27] Sodium amidotrizoate and dimethyl sulfoxide have also produced clinically detectable increases in the OG.[28,29] Although these substance can produce detectable increases in the OG following their administration, it is unlikely that they would be ingested purposefully or accidentally in quantities sufficient to produce toxicity and thus are not a necessary consideration in the evaluation of the OG as a screening test. Without any empirical evidence, Glasser et al.[6] stated that the following list of substances would contribute greater than 1 mmol/kg to the serum osmolality at a serum level reported to be lethal: EtOH, ethyl ether, isopropyl alcohol, MeOH, acetone, trichoroethane, paraldehyde, EG, chloroform, salicylate, chloral hydrate and ethchlorvyrol. The first five agents in this list would contribute >10 mOsm/kg. These data show that there are many substances capable of producing clinically important and detectable increases in the OG, but only some are of importance in terms of the clinical utility of the OG as a screening tool. This evaluation of the clinical utility of the OG therefore focuses on screening for those substances most likely to produce significant toxicity: EtOH, EG and MeOH.

2.2 The Relationship Between Calculated Serum Molarity and Measured Serum Osmolality

To date, the primary focus of studies of the OG has been on the evaluation of the relationship between the Osmm and the Mc in patients who have not been exposed to low molecular weight substances. More then four decades ago, Edelman et al.[2] published the initial study that illustrated the relationship between serum sodium and serum osmolality (r = 0.81, p < 0.001) but concluded based on a large sample standard deviation from regression (SD 17.4 mOsm/L) that other substances must be contributing to the total serum osmolarity. They concluded that there was a linear dependence of serum osmolarity on serum sodium concentration when corrections are made for the osmotic contributions of non-protein nitrogen (i.e. urea) and serum glucose, and that total serum osmolarity could be estimated using equation 1: Toxicol Rev 2004; 23 (3)

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Mc (mmol/L) = 1.75 Na (mEq/L) + BUN (mg/dL)/2.8 + glucose (mg/dL)/18 + 10.1

(Eq. 1) where BUN = blood urea nitrogen. Use of this equation resulted in a correlation of r = 0.98 between the Osmm and the Mc, and sample standard deviation of 5.6 mOsm/L. Since the initial study of Edelman et al.,[2] numerous stud[3,6-8,10,34] ies and clinical reviews[4,5,35,36] have addressed the question of whether the Osmm can be predicted from the Mc, and if it can, which formula provides the best estimation. Dorwart and Chalmers[3] used simple linear regression to compare the Mc, calculated using 13 equations (only three of which were derived using empirical data) to the Osmm in a convenience sample of 715 sera. The origin of the equations is discussed by Weisberg.[37] Although they do not explicitly outline their statistical methods, their comparisons between the Mc and the Osmm consisted of calculating the correlation coefficient (assumed to be Pearson’s) and the means and standard deviations of the differences. Despite their calculation of mean differences, the authors elected to focus their evaluation of the ‘calculation methods that yielded the best results’ based on the correlation coefficient and the SD of the difference. Unfortunately, neither of these measurements provides any information on the ‘agreement’ between the two methods given that an equation with a high correlation and SD ~6 could be systematically over- or underestimating the Osmm. Additionally, their analytic approach does not provide any information regarding potential systematic differences of prediction over the range of the measurement. Bearing in mind these methodological shortcomings, they concluded that equation 2 most accurately estimated serum osmolality. Mc (mmol/L) = 1.86 Na (mEq/L) + BUN (mg/dL)/2.8 + glucose (mg/dL)/18 + 9

(Eq. 2) Without presenting any empirical evidence, Smithline and Gardner[5] condone the use of equation 3 for the calculation of serum molarity, but suggest that it can be further simplified by rounding off the denominators of the BUN and glucose to 3 and 20, respectively; however, they do not provide any data to support their recommendations or conclusions. Mc (mmol/L) = 2 Na (mEq/L) + BUN (mg/dL)/2.8 + glucose (mg/dL)/18 (Eq. 3) If the BUN and glucose terms are expressed in SI units (mmol/ L) in this or similar equations, they can be further simplified by excluding the denominators. Glasser et al.[6] studied 56 normal subjects and 54 patients admitted to an emergency department to determine the applicabili© 2004 Adis Data Information BV. All rights reserved.

ty of the serum osmolality in cases of intoxication with drugs or other substances using equation 4 to calculate serum molarity. Mc (mmol/L) = 1.86 Na (mEq/L) + BUN (mg/dL)/2.8 + glucose (mg/dL)/18 (Eq. 4) Although 21 patients had measurable serum EtOH concentrations, no study subject had been exposed to either EG or MeOH. Applying this formula to the 56 healthy volunteers resulted in OGs ranging from –9 mOsm/L to +5 mOsm/L. As hypothesised, there was a strong correlation between the OG and the Osmm (correlation coefficient = 0.9939) in the 21 subjects with a detectable serum EtOH concentration. Despite the high correlation, the estimated serum EtOH values were consistently higher than the measured values. Using least squares regression, they determined the relationship between the measured serum EtOH concentration (EtOH)m and estimated EtOH serum concentration based on the OG to be EtOHm (mg/dL) = 3.09 + 0.9083 (mg/dL). This was the first study to suggest that 1 mmol/L of EtOH did not result in a 1 mmol/kg H2O increase in serum osmolarity, i.e. that the relationship was not 1 : 1. In a review article, Gennari[4] stated that the Smithline and Gardner[5] formula (or minor variations thereof) [equation 3] has been shown empirically to predict Osmm within 5–10 mOsm/L. Although this is one of the formulae evaluated by Dorwart and Chalmers,[3] it was not one of the two formulae that was the most predictive using their data. Although Gennari[4] argues that serum osmolality as a screen for low molecular weight toxins “has been reviewed in detail by Glasser and his associates”, in fact, Glasser et al.[6] did not present any empirical evidence from patients exposed to MeOH or EG but merely stated that serum osmolality could theoretically be used for this clinical application. Further, Glasser et al.[6] explicitly state that in their opinion the OG is unlikely to be a useful screening test for EG. It appears that the source of the currently applied upper limit of normal for the OG of 10 are the statements published by Smithline and Gardner,[5] and Gennari,[4] neither of which present any empirical evidence to support this, but rather refer to Glasser et al.[6] who did not include any patients exposed to MeOH or EG.[4,5] In an attempt to establish further empiric evidence supporting the OG, Bhagat et al.[7] analysed 100 plasma samples from hospitalised patients with the objective of deriving the most accurate formula for estimating the serum molarity. They evaluated the Dorwart-Chalmers formula (equation 2), a modified DorwartChalmers formula that included a term for potassium, and derived their own formula from their data. In their sample, the DorwartChalmers formula resulted in a mean difference between Osmm and Mc of 9.08 (SD 9.8) not accounting for potassium, and 1.67 Toxicol Rev 2004; 23 (3)

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(SD 3.7) after including a term for potassium in the equation. Their derivation of a formula using their data resulted in equation 5, which yielded a mean difference of zero (SD 3.2) between the Mc and Osmm. Mc (mmol/L) = 1.89 Na (mEq/L) + 1.38 K (mEq/L) + BUN (mg/dL)/2.9 + glucose (mg/dL)/19.4 + 7.45 (Eq. 5) Unfortunately, they did not validate their formula in a different patient sample. Bhagat et al.[7] conclude that because the DorwartChalmers equation (equation 2) appears to consistently underestimate the measured osmolality, it should no longer be used, and that equation 5, derived from their data is preferable. In a validation study, Worthley et al.[8] evaluated five different formulae in 100 normal, 100 general hospital and 100 intensive care unit (ICU) patients. Again, their sample did not include any patients exposed to MeOH or EG and explicitly excluded any patient that had received mannitol or had a measurable serum EtOH concentration. Because they used a Student’s t-test for between group comparisons, there is concern for statistically significant results to be an artifact of multiple comparisons. No correction for multiple comparisons was reported. They also report the correlation between the Osmm and Mc for all sub-groups, but neglected to specify in their methods whether this was planned or what method was used. Worthley et al.[8] report a greater variance in all measured parameters in both the ICU and general hospital groups relative to normal subjects, which is expected as it is known that critically ill patients commonly have elevations of serum osmolality.[38,39] They state in their results that equation 3 showed a significant difference between the Osmm and Mc in both the ICU and general hospitalised patients only, which is contrary to what is presented in their summary table. It appears that this is an editorial error and, in fact, that the table of results is correct. However, similar discrepancies occur in their discussion where they state that the Dorwart and Chalmers formula (equation 2) yielded the lowest standard deviation of the mean difference (3.68) in normal subjects, whereas it was the modified Dorwart-Chalmers formula proposed by Bhagat et al.[7] (equation 6) that resulted in the least variance of the difference (SD = 3.66). They also state that equations 2 and 6 yielded the smallest standard deviation in both ICU (4.49 and 4.33, respectively) and hospitalised patients (4.67 and 4.37, respectively). However, equation 7 actually resulted in the smallest standard deviation in both ICU (4.19) and general hospital (4.16) patients: Mc (mmol/L) = 1.86 {Na (mEq/L) + K (mEq/L)} + BUN (mg/dL)/2.8 + glucose (mg/dL)/18 + 10 (Eq. 6) © 2004 Adis Data Information BV. All rights reserved.

Mc (mmol/L) = 2 {Na (mEq/L) + K (mEq/L)} + BUN (mg/dL)/2.8 + glucose (mg/dL)/18 (Eq. 7) Equation 3, the simplest formula, produced the ‘smallest’ OG. In their discussion, Worthley et al.[8] state that in the acutely ill patient there is often a need to accurately calculate the OG in order to screen for unmeasured osmotically active substances as potential aetiologies of poisoning, thereby implying that their results will contribute to determining the utility of OG for the diagnosis of poisoning. In order for this to be the case, appropriate methods should have included the identification and presentation of outliers in the ICU and general hospital groups, excluding those subjects with other identified causes of the ‘abnormal’ OG, and then recalculating their results after having excluded these individuals. Although the poisoned patient is more likely to come from a population that is otherwise normal, the presentation of their results in the pooled sample would provide more evidence of the generalisability of OG as a screening test. Aabakken et al.[34] attempted to “establish a reference range for the OG and anion gap (AG) in an unselected population” of 184 Norwegian subjects using equation 8 that Hoffman et al.[9] found yielded the mean closest to zero and an SD of 6. Mc (mmol/L) = 2 Na (mEq/L) + BUN (mg/dL)/2.8 + glucose (mg/dL)/18 + EtOH/4.6 (mg/dL) (Eq. 8) but adjusted it for the aqueous fraction of serum (0.93). This modified equation 8 yielded a mean OG of 5.2 with an SD of 7. Thus, it appears that the variation in the OG is consistent across studies, but the mean differences vary considerably, once again raising the question of “what is a normal OG”. If one accepts that 2 standard deviations of the mean should be considered ‘normal’, then from this study the normal OG would be 5 ± 15 or –10 to +20, the upper bound differing substantially from +10 that is often applied clinically. An upper limit of normal of +20 suggests the test is essentially of no clinical benefit considering that an individual with a normal OG of –3 could ingest a toxin, which results in a serum concentration of 17 mmol/L and the potential for serious toxicity, but which would only increase the OG to 14 and thus be considered normal and thereby produce a false-negative result. In their discussion, Abakken et al.[34] raise the valid argument that “the high sensitivity of the combination of increased OG and AG (for diagnosing MeOH or EG poisoning) has been demonstrated in several reports”. Although this is correct, the primary clinical question is not “what is the sensitivity of an ‘elevated’ OG and AG”, but rather, what is the sensitivity of the OG (with or without Toxicol Rev 2004; 23 (3)

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the AG) for the screening and diagnosis of toxic alcohol poisoning. Their results provide evidence of the high positive predictive value (PPV; probability of being exposed given a positive test) of the OG for the presence of MeOH or EG, but does not address the potential for false-negative findings (normal OG and AG in the presence of a toxic alcohol), which is a necessary consideration in the determination of the overall clinical utility of the OG as a screening test. The authors also aptly point out that a necessary component in the determination of the overall sensitivity of the OG is the establishment of the definition of ‘elevated OG’. In this regard, they suggest that the reference range for the OG (and AG) should be calculated for each institution, depending on the variability of their laboratory equipment. Kruse and Cadnapaphornchai[35] published an eloquent review of serum osmolality, for the most part reiterating what had been published previously, but including clinical and toxicological applications. They list 20 formulae that have been proposed for the calculation of Mc and provide a summary of studies that have evaluated the OG in various clinical scenarios. Ironically, this does not include its use to screen for MeOH or EG poisoning; however, they do correctly suggest that in the appropriate setting the finding of an increased AG and OG is sufficient evidence to make a presumptive diagnosis of MeOH or EG poisoning and, therefore, to initiate treatment. This conclusion is based on a high PPV of the OG, but unfortunately once again, does not provide any evidence of the overall clinical utility (i.e. the sensitivity) of the OG as a screening test. Osypiw et al.[10] evaluated the ‘utility’ of six commonly used formulae when applied to data obtained from 212 patients presenting to a surgical outpatient department or an intensive therapy unit by comparing the confidence intervals around the mean error (bias) and root mean square error compared with a naive standard, i.e. the mean serum osmolality of the measured osmolalities. They used 50 consecutive specimens to evaluate each formula and the remaining 162 to validate the chosen formula. They found that equation 9 resulted in the best predictive performance based on the mean error and root mean square of the error; their iterative linear regression did not produce a better alternative formula. Mc (mmol/L) = 2 Na (mEq/L) + K (mEq/L) + BUN (mg/dL)/2.8 + glucose (mg/dL)/18 (Eq. 9) Thus, after five decades of research, the relationship between the Mc and the Osmm has not been clearly established. Multiple formulae have been proposed (table I) but none have been adequately validated in different clinical settings or patient populations. © 2004 Adis Data Information BV. All rights reserved.

2.3 Evaluation of the Ability of the OG to Estimate Serum Ethanol Concentration

Several studies have specifically evaluated the contribution of EtOH to the OG, or conversely, the ability to estimate the serum EtOH concentration using the OG. Hoffman et al.[9] evaluated the OG in patients whose serum EtOH concentrations were known. They derived a new formula for the calculating the Mc from this data, as well as evaluating four previously proposed formulae. Because the goal of the study was to establish the ‘normal’ OG including EtOH in the calculation, any patient with a measurable serum concentration of MeOH, EG, isopropyl alcohol or acetone were excluded. Their findings showed that all equations provided a very high correlation between the Osmm and the Mc (0.989) and similar variation around the mean differences (SD 5.5–6.1). However, there was a wide variation in the estimates of the OG, ranging from –5 to +15 and two of the four formulae tested yielded mean OGs >10 in a population without any patients with a potential MeOH or EG exposure. Osterloh et al.[19] used a convenience sample of 79 serum specimens drawn specifically for the detection of EtOH to estimate unexplained OGs during EtOH ingestion and to evaluate unexplained OGs following EtOH ingestion after accounting for EtOH concentrations. In this study, calculated osmolalities were determined using both the Smithline and Gardner (equation 3), and the Dorwart and Chalmers (equation 2) equations, and regression analyses were used to evaluate the associations between measured and calculated serum EtOH concentrations, and serum osmolality. Both equations 2 and 3 resulted in a strong correlation between measured and calculated serum EtOH concentrations (r > 0.97 and slope = 1.06 in both cases); however, they concluded that the Smithline and Gardner equation (equation 3) was superior in its predictive ability, resulting in an intercept of –3.9 (SD 6.6) mg/dL versus 45.2 (SD 6.4) with the Dorwart and Chalmers equation (equation 2). The analysis of the relationship between the Osmm and Mc resulted in similar findings, yielding mean OGs of 1.4 (SD 8.5) and 12.3 (SD 8.3), respectively. Although the OG predicted by the Smithline and Gardner equation (equation 3) was similar to that reported by Hoffman et al.,[9] the variance provided by this equation in this sample was greater than previously reported by both Hoffman et al.[9] and Dorwart and Chalmers (SD ~6).[3,9] Galvan and Watts[40] suggest an approach of developing a nomogram for each individual laboratory upon which the OG can be plotted as a function of the measured serum EtOH concentration to determine if the patients’ results are inconsistent with what are considered normal values for that specific institution. They suggest that each laboratory could develop a nomogram for their institution that would control for the inter-laboratory biases and Toxicol Rev 2004; 23 (3)

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the differential choices of formula. In their evaluation of this proposed approach, they applied the simplest formula (equation 3) for practical reasons of having the greatest bedside utility. Their evaluation of this equation in a pilot study of 40 alcohol-negative subjects revealed an average difference between the (Osmm) and Mc of 1.9 (SD 6.6). Using a simple spreadsheet software package and simple linear regression with measured serum EtOH concentration as the explanatory variable and calculated EtOH as the dependent variable, they calculated the expected serum omolalilty as: osmolality (including EtOH) = osmolality (excluding EtOH) + ([{slope × EtOHmeasured (mg/dL)} + intercept]/4.61) Using a technique for the determination of normal ranges for laboratory data, the final nomogram was derived. This approach resulted in an intercept of 2 and 95% confidence intervals for the residual osmolalities of –14 to +12. They then argue that because these values are close to the +10 cut-off point for the OG that they use these cut-off points in their nomogram, which by rounding down the interval would result in an increase in sensitivity. An excess OG is then defined as abnormal if it falls >10 above the regression line (i.e. above the upper diagonal line on the nomogram) after accounting for the different intercept and the relationship between measured and estimated EtOH concentrations, which has been demonstrated as not being 1 : 1 as historically assumed. Although sound analytical techniques are applied and their proposal is theoretically attractive, clearly there are significant logistical difficulties in the widespread utilisation of any test where a unique formula must be derived, validated and implemented in every institution where the test is performed. In all, at least ten studies have evaluated the relationship between the OG and the EtOH concentration in various patient populations.[9,19,20,40-45] All investigators have found that the relationship between serum osmolality and serum EtOH concentration is not 1 : 1 which, based on the physical chemistry of serum, is not unexpected. This is related to the fact that serum containing EtOH is not a dilute ‘ideal’ solution and the osmotic coefficient for serum containing EtOH is not 1. This concept is discussed in detail in the accompanying article,[1] but in general this illustrates the complexity of the physical chemistry of serum osmolality and how the present practice is likely to lead to erroneous findings. 2.4 The Utility of the OG for the Evaluation of Methanol and Ethylene Glycol Poisoning

Despite the widespread clinical application of the OG for screening for toxic alcohol exposure, there is a paucity of data on its validity and clinical utility in this clinical situation. Kjonnoy et al.[46] report their experiences from a cluster of MeOH exposures © 2004 Adis Data Information BV. All rights reserved.

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in a rural area of Norway, using these data to evaluate the AG and OG as diagnostic tools in patients presenting with metabolic acidosis of unknown origin. All patients in this cluster were mainly admitted to hospitals without facilities to measure MeOH levels on a 24-hour basis which, therefore, necessitated the use of other diagnostic modalities. In the acute setting, triage and treatment decisions were mainly based upon the values of the OG and AG. However, each subject had subsequent serum MeOH concentrations measured thereby facilitating the comparison of the OG and AG results with those of the gold standard. The method of serum MeOH determination was not provided in the abstract. Analysis of the laboratory parameters identified a correlation (r = 0.943) between the OGs and serum MeOH concentrations. Fitting a regression between these parameters using simple linear regression resulted in a slope of 1.041 and an intercept of 10.3. Unfortunately, the specific equation used to calculate the serum osmolality and thus provide the estimate of the OGs and the serum MeOH concentrations was not provided. They also report that six patients had normal OGs as a result of low serum MeOH concentrations but elevated AG due to formate accumulation, the combination of which is likely attributable to late presentation. One patient with concomitant EtOH ingestion had an elevated OG and a normal AG, as expected. Although the authors only present data pertaining to the ‘agreement’ between measured and calculated OGs and AGs, they conclude that their data illustrate that these robust laboratory parameters were useful in the diagnosis and triage of MeOHpoisoned patients, and that confounders were low MeOH and concomitant EtOH ingestion. However, they provide no evidence as to the sensitivity or specificity, or the positive predictive value of the OG and/or AG in making their diagnosis. Furthermore, the utility of any screening test is directly related to the pre-test probability of the disease (i.e. exposure) being present. The clinical utility, or the change in the probability of a disease being present based on the result of the test in the situation of an outbreak, epidemic, or cluster, decreases over time as the clinician becomes aware of the outbreak. In this example, the OG and/or AG may have been very useful in modifying the probability of exposure to MeOH upwards for the initial patients, but once the clinicians learned of the potential for more patients, the pre-test probability of exposure increased and the magnitude of the difference between the pre- and post-test probabilities of exposure based on the results of the test would be minimal. Thus, although an interesting case series, it does not provide sufficient data to lend unequivocal support to the OG and AG as diagnostic tools for this poisoning. Based on a review of published cases, Kostic and Dart[47] recommend a re-evaluation of the threshold definition of a ‘toxic’ Toxicol Rev 2004; 23 (3)

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exposure for MeOH exposure in the non-acidotic patient. Following a rigorous systematic review of the international literature to identify human cases with a known time of a known isolated exposure to MeOH, they found that the majority of reported cases of MeOH poisoning involved acidotic patients presenting to emergency many hours after the exposure. In the 22 patients that arrived within 6 hours of ingestion, 87.8 mg/dL (27.4 mmol/L) was the lowest early blood MeOH concentration that resulted in acidosis. From this, they concluded that current data are inadequate to support 6 mmol/L (20 mg/dL) or even 15 mmol/L (50 mg/ dL) as the treatment threshold in the non-acidotic patient arriving early for care. These findings have significant implications for the sensitivity and specificity of the OG for screening for MeOH, as it is possible that the threshold necessary for detection might be increased, which is of even greater importance if the same arguments hold for EG. The OG is commonly used as a screening test for MeOH and EG exposure. If the OG is being used in this fashion and possesses a poor sensitivity for detection of exposures to MeOH and EG capable of producing toxicity then there would be a number of reports of patients who had low OGs when tested, and then developed toxicity. In fact, case reports of this type are uncommon. We found only six reported cases of EG poisoning and one case of MeOH poisoning where the OG was <10. However, all of these cases had either an elevated anion gap or a metabolic acidosis.[48-53] There are numerous possible explanations for the paucity of published case reports in which the OG has failed as a screening test. Foremost is the publication bias in that the cases may just not be written up by clinicians. It is also possible that physicians rarely use the OG as a screening test or if they do, the invariably obtain confirmatory testing in a timely fashion, or use other information from the history, physical examination and laboratory testing to make the diagnosis and may, therefore, disregard a negative screening result. However, it is plausible that patients may tolerate MeOH or EG levels that are higher than those listed in current guidelines as necessitating treatment.[18,32] If this is the case, the OG may possess adequate sensitivity to consistently detect patients with a high enough level to develop toxicity. 3. Situations in Which Osmometry May Produce Erroneous Results There are a variety of circumstances in which osmometry will produce erroneous results and must not be used (table III). The OG must not be used when the concentration of unmeasured osmotically active substances cannot be accurately estimated. Although it is possible to measure the concentration of ‘all’ osmotically active © 2004 Adis Data Information BV. All rights reserved.

Table III. Clinical scenarios in which osmometry can produce erroneous results Clinical Scenarios

References

Critically ill patients

38,39,54-56

Circulatory shock

54,55,57

Very low birth-weight infants

58

Diabetic ketoacidosis

59,60

Hyperosmolar non-ketotic coma

61,62

Alcoholic acidosis

63-65

Chronic renal failure

66,67

Elevation of serum lipids

68

Elevation of serum protein

69

Use of anticoagulants in collection tube (if plasma tested)

19,35

Laboratory tests not taken simultaneously

35

Delay in analysing laboratory tests

70,71

Vapour pressure osmometry (if volatile solutes present)

3,37,72-75

substances in blood, this is neither practical, nor necessary. The estimation of serum osmolarity most often accounts for only the concentrations of sodium, glucose and urea, making the assumption that the contribution of all other osmotically active substances to the OG is relatively minor and constant; this is a reasonable assumption in most patients. However, there are specific clinical situations when this assumption is violated, and thus, the OG gap should not be used. Critically ill patients with multi-system failure can have significant increases in the their serum osmolality by as much as 100 mmol/kg H2O, although increases in the range of 30 mmol/kg H2O are more typical.[38,39,54-56] This increase has been found to be related to increased cellular membrane permeability with leakage of amino acids and other cellular products into the serum.[38,39] The presence of an elevated OG in this clinical setting is associated with a poor prognosis.[3,38,39,54,55,57,63,76,77] Increased serum osmolality also occurs in adults in circulatory shock[54,55,57] and in very low birth-weight neonates with and without shock.[58] An elevated OG has been found in patients with diabetic ketoacidosis due to an increase in acetone levels, small increases in amino acids and glycerol levels, and a decrease in plasma water.[59,60] An increase in the OG has also been observed in patients with hyperosmolal nonketotic coma,[61,62] alcoholic ketoacidosis[63-65] and chronic renal failure.[66,67] It is important to ensure that blood for all tests required for the calculation of the OG be drawn concurrently given that the values of sodium, urea, glucose and osmolarity can change quickly in critically ill patients or patients receiving dialysis. If the samples Toxicol Rev 2004; 23 (3)

The Osmole Gap as a Screening Test

are not drawn at the same time this will result in erroneous values.[35] If there is a long delay between the time that the blood is collected and analysed this will result in a spurious increase in osmolality. In vitro anaerobic metabolism will occur in erythrocytes and leucocytes concerning glucose and producing lactate. Each molecule of glucose that is consumed will be converted in two molecules of lactate thereby increasing the osmolality.[70,71] Freezing point and vapour pressure osmolality testing will produce discordant values if lipemic serum is tested. Mercier found that the readings with the vapour-pressure method were 7.5 mmol/kg H2O higher than the freezing point method.[68] However, it is unclear which method yields more accurate result in this situation.[35] In cases of pseudohyponatraemia associated with high serum proteins or lipids the serum sodium level will be spuriously low and consequently a spurious OG will occur. This will occur when the sodium concentration is measured using the standard techniques of indirect ion selective electrodes or flame photometry. Accurate readings for sodium can be obtained by using direct ion reaching ion selective electrodes.[69] Serum is the preferred medium for osmolality testing. However, on occasion the test is also performed on plasma or whole blood. If plasma or whole blood is used, an anticoagulant must also be used. All commonly used anticoagulants (heparin, oxalate, ethylenediaminetetraacetic acid [EDTA] and citrate) will increase the serum osmolality. Small amounts of heparin are acceptable and will result in a minimal increase in osmolality. Na F-K oxalate and EDTA are not acceptable as the addition of small amounts of these compounds will result in a dramatic increase in the osmolality.[35] Vapour pressure methodology will produce erroneous results in the presence of volatile solutes such as MeOH and EtOH. When a non-volatile solute is added to solvent this will lower the vapour pressure. However, if the solute is volatile the solute itself also contributes to the vapour pressure. This will counteract the decreasing vapour pressure and there will be a very small change in the total vapour of the solution. The testing equipment will produce an erroneously low value.[3,72-75] Although EtOH interferes with serum sodium determinations by ion selective electrode, the effect is very small and causes no clinically significant errors.[78] 4. Limitations of Current Knowledge Despite the fact that the OG has never been properly derived or validated for use as a screening test for toxic alcohol poisoning, it is commonly applied in this clinical situation. The bulk of the research has focused on evaluating the relationship between the measured serum osmolality and calculated serum osmolarity in individuals not exposed to either MeOH or EG. The implied © 2004 Adis Data Information BV. All rights reserved.

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assumption is that if the OG can be accurately determined in unexposed patients, then an elevated OG should be diagnostic of an exposure. However, no studies have been done in accordance with guidelines for evaluating the clinical utility of a diagnostic test in that the evaluation must be performed in a sample of patients that includes an appropriate spectrum of exposed and unexposed patients, with exposed patients representing all potential levels of exposures.[14] Therefore, as there has not been an empirical evaluation of the diagnostic performance of the OG, its clinical utility remains entirely hypothetical, having been theoretically extrapolated from the non-poisoned population. Clinical rules must be developed in one group of patients and validated in samples of similar patients to ensure the rule is generalisable. Although numerous equations for the calculation or estimation of the OG have been derived, few have been validated. Not surprisingly, each study that has derived a formula and compared it with other previously derived formulae has concluded that the newly derived formula predicts either the measured osmolality or serum EtOH concentration better. This is expected, given that the formula is derived from that data and is only reflective of the internal validity of the formula. An appropriate method of formula derivation and validation using one sample would be to split the sample and develop a screening model in half the sample, then evaluate the predictive ability of the model in the remainder of the sample. However, no equation has been validated in enough patients in various clinical settings to ensure its general applicability. Not only has the OG not been adequately evaluated in MeOH or EG poisoned patients, there remains insufficient evidence supporting the currently applied thresholds for the OG in the poisoned patient (e.g. >10) and for both the initiation of treatment and performance of haemodialysis in MeOH and EG poisoning.[47] If the current thresholds are too conservative, merely due to a lack of empirical evidence, the clinical utility of the OG will be underestimated and will ultimately be better than will be predicted using the current clinically applied thresholds. Related to this is the necessity of defining the threshold of positivity, which will be dependent upon the established treatment thresholds. There is a striking similarity between the analyses that have been undertaken in this area to date. The common approach is to use linear regression techniques to derive the slope of line representing the association between Osmm and Mc and/or serum EtOH concentrations from available data,[6,7,9,20,40] and to evaluate the ‘agreement’ between Osmm and Mc or serum EtOH levels using different predictive equations that have been previously proposed.[3,8,9,19] The methods employed to measure ‘agreement’ are similar, most often entailing a comparison of mean differences and their associated variances between the Osmm and the Mc and/or Toxicol Rev 2004; 23 (3)

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serum EtOH concentrations, or measuring the correlation between these parameters. Unfortunately, there are significant limitations to using these techniques for measuring agreement. The use of linear regression is done under the premise that the relationship between the measured and calculated values (either serum EtOH or serum osmolality) is not 1 : 1 and thus the slope of the line representing the relationship is not equal to 1. Furthermore, although not stated explicitly in any published study, using linear regression also implies that slope of the line (i.e. the association) is constant across all levels of serum EtOH or serum osmolality. Only Edelman et al.[2] explicitly stated that they assumed the relationship between serum sodium and serum osmolality was linear, implying that the relationship could be contrary to that assumption. There are published data that appear to support a hypothesis of a non-linear relationship, but this hypothesis has yet to be explicitly tested.[6,19,20,40] In the accompanying paper,[1] we explain how the osmotic coefficient of serum containing EtOH varies with the EtOH concentration, which is the likely explanation of this phenomenon. Using the mean of the differences between measured and calculated values and their SDs or standard errors of the mean (SEM) to characterise agreement is a fundamentally sound approach, but requires development beyond a comparison of the overall sample mean.[79,80] Comparing only the sample or population means makes an assumption that the differences and the variances of the differences are consistent across all levels of either the dependent or explanatory variable. Purssell et al.[20] did address this as a potential issue by plotting the regression standardised residuals against the OG obtained from their data. Although they concluded that there was no evidence of heteroskedasticity (i.e. an association between the OG and the variance), visual analysis of their plot indicates that the relationship may not only be heterskedastic given that the range of residuals up to an OG (excluding EtOH) of 75 fall within SD 2 of the value predicted by the regression, and all those falling outside SD 2 (the 95% CI) occur at OGs >75 mmol/kg. This plot may also provide some evidence of non-linearity, at least at the extremes of the OG. Above an OG (excluding EtOH) of approximately 100, eight of eleven residuals are positive with one lying just below zero. Despite the fact that numerous studies have used the correlation coefficient to measure agreement, this is an erroneous application of this statistical test;[3,6,9,19,40] the correlation coefficient does not measure agreement. This has been explained in detail previously by Bland and Altman,[79] but in summary, correlation only measures the strength of the association, not the agreement between two methods of measurement. Perfect agreement constitutes all points lying along a line representing equality, whereas perfect correlation occurs when all points lie upon any straight line. The © 2004 Adis Data Information BV. All rights reserved.

Purssell et al.

correlation between two methods of measurement is also dependent upon the range of values, with wider ranges resulting in higher correlations. In general, data with poor agreement can provide very high correlations. Although many studies have been done with the objective of evaluating the agreement between the Mc and both the Osmm and serum EtOH concentrations, the methods employed do not adequately address the question in two respects. First, regarding the clinical utility of the OG for the screening and conditional diagnosis of MeOH or EG poisoning, a formula that provides a OG of –15 may provide a less biased estimate than a formula that provides a mean OG of –2 if the magnitude of the bias is consistent across all levels of the variables of interest. The bias can, therefore, be easily accounted for. Thus, what needs to be assessed is not only the magnitude of the bias, but the consistency. Bland and Altman[79] have proposed a methodology to evaluate this, by moving beyond regression, sample means and correlation coefficients to evaluating the differences relative to the means within individual subjects.[79] 5. Conclusions For the OG to be valid, both the measured and calculated serum osmolality must be well defined, have limited variability in the normal population and change predictably in the presence of low molecular weight toxins. Although the first two components of this question have been addressed repeatedly, the latter remains to be adequately evaluated. The stage is set for a developing some empirical evidence of the clinical utility of the OG for the screening and diagnosis of toxic alcohol in a study that conforms to the recommended guidelines for the evaluation and reporting of a diagnostic tests.[14,17] Acknowledgements None of the authors received any funding to assist in the preparation of the manuscript. None of the authors have any potential conflicts of interest.

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Correspondence and offprints: Dr Roy A. Purssell, Department of Emergency Medicine, Vancouver Hospital, 855 West 12th Avenue, Vancouver, BC V5Z 1M9, Canada. E-mail: [email protected]

Toxicol Rev 2004; 23 (3)