On the Meaning of "Sensitivity": A Rejoinder

Department of Molecular Endocrinology, University College London Medical School London W1 N 8AA, UK
^a Author for correspondence. Fax 44 171 580 2737; e-mail r.ekins{at}ucl.ac.uk.

To the Editor:

Although reluctant to monopolize debate on the meaning of "sensitivity", we feel compelled to respond to Dr. Pardue's critique (1), which reveals certain misunderstandings and misrepresents our arguments (2).

Pardue claims that the "formal definition of sensitivity" is associated with the response/stimulus ratio. But formal definitions have differed, certain authorities defining sensitivity in terms of the detection limit. Elimination of the contradictions underlying the scientific use of the word has been our objective in raising this issue.

Contrary to Pardue's belief (1), we do not argue that the "slope interpretation conflicts with the formal definition". We comprehend the equivalence of the "slope" and "response/stimulus" definitions, but object to both on the grounds that they conflict with the fundamental meaning of sensitivity. We maintain, in short, that neither is a valid indicator of the ability of an instrument to sense small changes "in that to which it is designed to respond", and hence of its sensitivity in the generally accepted sense.

We nevertheless agree that the response curve slope may be "an invaluable descriptor of one of the most important characteristics of any analytical method" (1), albeit only when combined with estimates of the statistical uncertainty in response measurements. Lacking these, it is impossible to determine whether an observed change in the response constitutes a random fluctuation or reflects a real difference in the measured quantity. In short, the response curve slope is simply a property of the curve (as plotted), not a meaningful indicator of the analytical performance of a system.

Pardue claims that "proper use of the slope definition yields much more information than is available in the 'detection limit' interpretation" (1). However, his view of "proper use" entails combining the slope with "the uncertainty in the measurement response" (termed _r). This yields the "quantitative resolution" (QR)–commonly known as the (im)precision of the "variable of interest") or measured quantity (e.g., analyte concentration). [Footnote: Of the few examples of the use of this term we have found in the scientific literature, we infer that quantitative resolution refers to the general ability of a method to estimate the components of a mixture or compound. We are unfamiliar with the use of this term as a substitute for (im)precision.] This is clearly a legitimate method of determining assay precision; however, Pardue offers no evidence to support the claim that knowledge of the response curve slope in isolation is useful.

To summarize, we agree with Pardue regarding the relationship between the entities he terms the "inseparable triad", i.e., the response curve slope, the uncertainty in the response measurement, and the statistical error in the measured quantity. Indeed this relationship is generally (but not necessarily) relied on in the calculation of the "precision profile" of a system (2). Moreover, we have emphasized (2) that "an instrument's ability to reveal small amounts or slight changes in that to which it is designed to respond is determined by the quotient [error in response]/[response curve slope]" or–using Pardue's terminology–_r/S (Eq. 2 in (1)). This relationship likewise underlies the "index of precision" (), long used to describe bioassay performance, for example (3). Pardue's critique (1) thus largely elaborates concepts that we do not dispute, and on which our own papers relating to immunoassay design, for example, have been based for more than 35 years (4)(5).

We thus differ from Pardue only in our view of the terminology that most logically and unambiguously describes the performance of an analytical system, contending that IUPAC's identification of sensitivity with response curve slope contradicts the fundamental meaning of the word, leads to absurdities and to linguistic inconsistencies, and gives rise to incorrect approaches to assay design.

In justifying these claims, we have relied, inter alia, on the Oxford English Dictionary, which states that a sensitive instrument is one "indicating readily slight changes of condition, easily moved or affected by the external forces which it is constructed to detect or record", illustrating the meaning of the adjective with several 19th century examples. Writing in 1873, James Clerk Maxwell (6) states "When the instrument is intended to indicate the existence of a feeble [electric] current, it is called a Sensitive Galvanometer" (distinguished by Maxwell from a "Standard Galvanometer"). Likewise in 1872 Yeats (7) writes: "balances are made sensitive to the fraction of a grain", implying that the sensitivity of a balance is indicated by the minimum mass it can determine. Such examples demonstrate (a) that sensitive was then seen as applicable to, and descriptive of a property of, an instrument and (b) that this property was the ability of the instrument to measure a small amount of "that to which it is designed to respond" (e.g., a feeble current or small mass). Thus, although Pardue speculates on "when the detection limit interpretation of sensitivity began to emerge", it evidently underlay the use of the word long before the slope definition was introduced.

In view of this background, it is tempting to ask not only when, but why, the slope definition of sensitivity emerged? We are prepared to accept Pardue's claim (albeit the point is arguable) that the use of the word in this sense dates from the early 20th century. [Footnote: Pardue cites a 1912 reference in this context (9), based on the translation of a German student textbook (Kurzes Lehrbuch der analytischen Chemie). In the edition (the 9th) we have examined, the translator uses "sensibility" and "sensitiveness" to describe the angle by which a balance pointer rotates when a defined load (usually 1 mg) is placed on the pan. The author subsequently claims "it is customary to regard the sensitiveness or sensibility as the number of scale divisions that the zero point (of the pointer) is displaced by a load of 1 mg". These differing definitions imply the possibility of contradictory conclusions regarding the relative sensibilities of two balances (as indicated in (2)). Later the author writes: "In analyzing ores for precious metals, it is customary to weigh out a large sample on a 'pulp balance' which need not be sensitive to 1 mg. The analysis is finished by weighing a very small fragment of metal on a "button balance" sensitive to 1/100 mg" (our emphasis). Such a publication constitutes an insecure basis for defining scientific terminology; however, the word sensitive is clearly used in relation to the smallest load that a balance can detect or reliably determine.] But we would suggest that this development stemmed from an erroneous supposition–exemplified in, e.g., Berson and Yalow's publications (8), but also (implicitly) in (9)–that an increase in response curve slope (or in response/stimulus ratio) implies a concomitant increase in the ability of an instrument to indicate a "slight change of condition". That this is often not the case is recognized–indeed emphasized–by Pardue. Nevertheless, this assumption has remained unchallenged by (among others) many immunoassay practitioners, and underlies much of the mythology relating to assay design that has arisen in this field.

In short, Pardue's suggestion that we have "crashed his party", i.e., that the representation of the sensitivity of an instrument by the least change of condition or quantity it can detect is of recent origin, and that we have contradicted the original meaning of the term, has no basis. On the contrary, the slope definition appears to have arisen in consequence of past failures to perceive that two factors determine the ability of a system to register a slight change in the measured quantity. That certain authors–albeit distinguished in their fields–have made this error does not invalidate our thesis.

Putting aside these historical considerations, we turn to other implications of the slope definition to which Pardue alludes. For example, he states it is "obviously not possible to make meaningful comparisons between sensitivities for different devices such as analytical balances, galvanometers, and photographic emulsions because they all represent different responses to different stimuli". But this misrepresents our criticism. This is that the slope definition precludes comparison of the sensitivities of different measuring systems with respect to the same "stimulus" (e.g., analyte in a sample (2)). Indeed the slope definition necessarily prohibits the use of the adjective sensitive to describe any measuring system, since–as previously indicated (2)–a change in assay (or instrument) design may result in either an increase or a decrease in response curve slope (or response/stimulus ratio), depending on the response and dose variables selected and the manner in which the curve is plotted (despite a reliance on the same experimental observations). Clearly it is nonsensical to suggest that an assay has been rendered both more and less sensitive in consequence of the change in its design. [Footnote: We naturally agree with Pardue that compensating changes in the "error envelope" surrounding the response curve imply that neither the calculated detection limit nor the precision of measurement of any specified "dose" is affected by the choice of response variable, as we have previously emphasized (2).]

In other words, the IUPAC definition implies an abandonment of the long-established usage of the words sensitive and sensitivity to describe a characteristic of living things or measuring systems per se. Thus, while providing unnecessary terms to describe a property of the dose–response curve, it deprives the English language of the only words descriptive of the ability of a system to detect a small stimulus or change in condition. This can hardly be dismissed as a "minor inconvenience"; it is a sure recipe for semantic and conceptual chaos.

Dr. Pardue disregards these implications in stating (see "Linear dynamic range" in Quantitative Description of Sensitivity in (1)) that: "If one knows the sensitivity of a method (our emphasis), and the values of the signal or other measurement objective corresponding to the lower and upper ranges of sensitivity... ". Given that the slope definition of sensitivity renders such phraseology ambiguous and meaningless, it is unsurprising that this sentence (and the entire paragraph) are almost unintelligible.

Dr. Pardue has, unfortunately, misinterpreted our observations regarding "people who are or wish to remain oblivious of the internal workings of their instruments", and we feel that his remarks are unjustly censorious. In this context, we cited (as an example) an analytical balance, which provides a direct numerical readout of the mass of an object (2). We are uncertain how the sensitivity (as defined by IUPAC or the American Chemical Society (9)) of such an instrument can be determined. Should a user expose the mechanism and determine the angular rotation of a beam caused by a defined mass? Such information would be irrelevant to, and unlikely to be sought by, the majority of users, but they should not therefore be dismissed as falling "within the lowest common denominator" amongst their professional peers. It would nevertheless be good practice to determine the precision of mass measurements (including that of measurements of zero mass), aspects of the performance of a balance that the user could establish without detailed knowledge of its internal construction.

We are also surprised by Pardue's comments regarding the "imprecision and detection limit interpretations of sensitivity" and his suggestion that each merely "conveys minimal, albeit important, information about analytical methods". We regard the precision with which a system measures "that to which it is designed to respond" (including the precision with which it measures zero) as perhaps the most important aspect of its performance. In other words, knowledge of the precision profile (putting aside other performance characteristics such as bias and measurement time) of a measuring system is both necessary and sufficient to permit assessment of the analytical capabilities of the system. In contrast, a response curve devoid of any error information is virtually meaningless.

To conclude, we hope that participants in this debate will not feel intimidated by the teachings of "some of the most highly regarded analytical chemists of our time", and will make an independent assessment of the validity of the arguments advanced. We also hope that readers will recognize that analytical chemistry is doomed to everlasting confusion if sensitivity is formally defined in such a bizarre and contradictory manner as to imply that the less sensitive of two measuring systems may be capable of detecting smaller amounts of that which both are designed to determine.

References

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