Measuring Things That Are Not Themselves Directly Observable

Much of science concerns concepts not material entities. We talk easily and glibly about wealth, satisfaction, liberal democracy and metropolitan elites. But in science we need to quantify these types of thing. To paraphrase Galileo; if something is not measurable make it so!

The ARC WM Director was made very aware of definitional and measurement issues while attending the African Research Collaboration on Sepsis research meeting in Dar Es Salaam. The Collaboration is funded by an NIHR Global Health Group grant awarded to Jamie Rylance at Malawi Liverpool Wellcome Research Centre. The meeting covered many fascinating topics. One recurring theme was how to define sepsis. Since 1991, three international conferences have been held to “define sepsis” – the most recent consensus statement (2016) was published in JAMA.[1] 

Right off the bat in reading the literature there is a problem, as the challenge of the measurement task is often referred to as that of finding an operational definition or worse simply “a definition”.  This is a problem because referring to the measurement task as “defining sepsis” can obscure the fact that there is currently a well specified and seemingly widely accepted conceptual definition of sepsis from Sepsis-3, namely “Sepsis should be defined as life-threatening organ dysfunction caused by a dysregulated host response to infection.”[1]  But as noted in the same publication, “There are, as yet, no simple and unambiguous clinical criteria or biological, imaging, or laboratory features that uniquely identify a septic patient.”  So, to be clear, virtually all of the arguments and difficulties that have arisen after each consensus conference establishing a conceptual definition are in how to design a measurement procedure, including the selection of a population, a set of observable variables and the mathematical model that combines them. So this got us thinking about measurements of scientific constructs.

A clearly defined conceptual entity that is not directly observable is often referred to as a latent construct or variable.  Building on Bollen and Bauldry,[2] and Hand,[3] three scenarios are possible when defining a measurement procedure for a latent construct, such as ‘sepsis’:

  1. Where a measurable reference category or gold-standard for a latent construct exists, such as the molecular classification of intersex or the chemical classification of endocrine disorders. The reference category is then held to be the observable representation of the construct. Other potentially more easily measured observable features can be assessed directly as to how accurately and precisely they represent the construct through their relationship to the reference category.  
  1. Where theory is “poorly formulated” with regard to how the latent construct exerts its effects, some observable features can be combined in what Hand called a “pragmatic measurement”[3] procedure to produce a measurement that is useful not because you understand what is going on but only to the extent that the pragmatic measures have some ability to predict an outcome of interest, as is the case with the concept of socioeconomic status, the histological grading of tumours, or the APACHE score of acute illness severity. In the absence of a model causally relating the construct to the observed features, the combination of the features into an index can only be said to summarise the observable features rather than represent the underlying construct.  In turn, the index is actionable only because of its ability to predict.  Finally, as the index is only a summary of observable features, the components of such an index cannot be changed or left out with changing the nature of what is being measured.
  1. Where there is a well-specified formal conceptual definition the task is to identify a pool of exchangeable and observable features that theory would suggest are caused by the construct. By use of a statistical model that includes those observable features the latent variable that causes them can then be identified. Yet, the hypothesised causal relationship between the underlying construct and the observed effects requires a continuing effort to collect evidence supporting the argument that the observed effects are a valid representation of the underlying construct. The example here would be schizophrenia, where the American College of Psychiatrists definition has allowed the science to proceed. A latent social construct (‘this is a schizophrenic’) is hypothesised to predict the observed clinical manifestations that can be measured. This measurement model is itself a theory that remains open to revision or being abandoned entirely, but which still can be employed as a useful tool.

In our opinion the latter ‘third way’ is appropriate for ‘sepsis’. The conceptual definition is not, cannot be, perfect but it is based on broad consensus. Once the conceptual definition has crystallised, science can proceed to develop one or more measurement procedures.  These measurement procedures may well need to be refined or changed in different settings of care. The research may one day yield a reference standard reflecting basic mechanisms; possibly this point is within reach in the case of schizophrenia, where genome-wide association studies have yielded stunning findings.[4] We think this is the approach the sepsis field should follow. It is more profitable than devoting endless effort to attempting to find the holy grail of a reference standard for sepsis. It seems reasonable to accept the JAMA proposal for an operational measurement of the construct. While using it, continue to collect evidence that supports or refutes the theory represented in the measurement model.

Richard Lilford, ARC WM Director; Timothy Hofer, Professor of General Medicine


  1. Singer M, Deutschman CS, Seymour CW, et al. The Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3). JAMA. 2016; 315(8): 801-10.
  2. Bollen KA, & Bauldry S. Three Cs in Measurement Models: Causal Indicators, Composite Indicators, and Covariates. Psychol Methods. 2011; 16(3): 265-84.
  3. Hand DJ. Measurement theory and practice: the world through quantification. London: Wiley-Blackwell; 2004.
  4. Lilford RJ. Psychiatry Comes of Age. NIHR CLAHRC West Midlands News Blog. 11 March 2016.

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