A diagnostic algorithm for carpal tunnel syndrome based on Bayes's theorem

D. O'Gradaigh and P. Merry

Department of Rheumatology, Norfolk and Norwich Hospital, Brunswick Road, Norwich NR1 3SR, UK


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Objective. To construct a diagnostic algorithm based on Bayes's theorem and using simple clinical tests to allow accurate diagnosis without resort to nerve conduction studies.

Method. A cohort of patients being referred with possible carpal tunnel syndrome had clinical and electrophysiological testing, from which the simple calculations for sensitivity, specificity and prevalence were made and subsequently used in the formula of Bayes's theorem. The algorithm was then tested prospectively in a further cohort of similarly referred patients.

Results. The algorithm proved to be reliable when tested prospectively, and was similar to nerve conduction studies in diagnostic accuracy.

Conclusion. A simple algorithm of clinical tests can identify patients without resort to nerve conduction studies, facilitating early treatment.

When reaching a diagnosis, most doctors are blissfully unaware of the underlying logical process, preferring to ‘imagine...some mystical process...making of them an elite priesthood’ [1]. Nonetheless, we owe much to Thomas Bayes, whose theorem underpins the sequential application of observations, historical findings and clinical examination that leads to the (most probable) diagnosis. The probability of a particular diagnosis can be calculated from the prior probability of having that condition (before a test) and the likelihoods of positive tests in those with or without that diagnosis. The result is called the posterior probability. This value may then be used as the prior probability for a further diagnostic test, allowing one to combine mathematically a sequence of tests. In particular, the posterior probability calculated in this way takes account of all sensitivities and specificities in a single value, and is therefore superior to a single test with high sensitivity but usually poor specificity, or vice versa. This process is explained in detail elsewhere [1].

The role of nerve conduction studies (NCS) in carpal tunnel syndrome (CTS) continues to stimulate debate [2, 3] and waiting lists of patients with the condition are long. Clinicians need a sufficiently powerful clinical test that obviates the need for NCS before steroid injection except in the most atypical situations or preoperatively. The commonly used clinical tests do not allow such accuracy [4]. We set out to examine their predictive power when used in series, as supported by Bayes's theorem.

Inclusion of patients required a suspicion of CTS by the referring clinician on any grounds. Patients previously treated for CTS or with recognized associated conditions were excluded. Patients (n = 105) first completed a hand diagram (HD), on which they outlined the symptomatic area [4]. Katz et al. [4] included those with ‘classical’, ‘probable’ or ‘possible’ distributions on the diagram as positive when determining sensitivity. Only those with classical or probable distributions were considered positive in this study, in order to optimize the likelihood ratio. One examiner carried out Phalen's test (PT) and Tinel's test (TT) in the standard way. NCS were then carried out on all patients. Sensitivity and specificity for each test were calculated using NCS as the definitive test (sensory amplitude <10 µV or motor latency >3.7 ms).

The prevalence of CTS (by NCS) was 0.71 (75/105). Sensitivities (and number of true positives) for HD, TT and PT were 0.92 (69), 0.55 (41) and 0.72 (54), respectively, and specificities were 0.4, 0.72 and 0.53, similar to values reported previously [4]. Bayes's theorem was then applied to calculate the probability of having CTS with each combination of results (Table 1Go).


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TABLE 1. Probability of having positive nerve conduction test

 
With a classical or probable distribution of symptoms, and positive TT and PT, the probability of having CTS was 0.92. Conversely, the probability of still having CTS, despite negative HD, TT and PT, was 0.14. These values closely match the sensitivity (0.92) and false negative rate (0.08) in a study [5] which found normal NCS in 8% of those whose symptoms were improved by surgical decompression. However, sensitivity is a property of a test independent of the study population, while Bayesian probability is significantly influenced by the prevalence in the study population. In this study, prevalence was higher than in unselected populations. However, inclusion required only suspected CTS (typically based on history), a simple selection that would ordinarily occur in practice. The algorithm was tested prospectively in 42 patients in the recruitment phase of a treatment study (Table 2Go). The proportion of those with all three tests positive who subsequently had positive nerve conduction studies was 0.87. One in five of those with three negative tests had positive NCS (0.2), and each of the other test combinations also closely matched the probability defined by the algorithm.


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TABLE 2. Prospective evaluation: proportions of patients in each clinical test combination subsequently having positive NCS

 
We recommend that patients in whom CTS is suspected complete a hand diagram and the TT and PT are then assessed. Those with three positive tests do not need NCS before they are offered steroid injection. We suggest that patients with probability >0.7 could also be treated before considering NCS, which should be reserved for those with atypical clinical signs, and for preoperative assessment. As steroid injection is effective in about 70% of patients (66% overall in our study; in preparation), the recommended approach would therefore have reduced the number having NCS by 41%, while offering patients ‘accurate and parsimonious’ diagnosis [1] and early treatment.


    Notes
 
Correspondence to: D. O'Gradaigh, Department of Rheumatology, Addenbrooke's Hospital, Cambridge CB2 2QQ, UK. Back


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  1. Macartney FJ. Diagnostic logic. Br Med J1987;295:1325–31.[ISI][Medline]
  2. Pal B, Morris J, Keenan J, Mangion P. Management of idiopathic carpal tunnel syndrome: a survey of rheumatologists' practice and proposed guidelines. Br J Rheumatol1997;36:1328–30.[ISI][Medline]
  3. Sheehan NJ. Re: management of idiopathic carpal tunnel syndrome [letter]. Br J Rheumatol1998;37:1139–40.[ISI][Medline]
  4. Katz JN, Stirrat CR, Larson MG, Fossel AH, Eaton HM, Liang MH. A self administered hand symptom diagram for the diagnosis and epidemiological study of carpal tunnel syndrome. J Rheumatol1990;17:1495–8.[ISI][Medline]
  5. Grundberg AB. Carpal tunnel decompression in spite of normal electromyography. J Hand Surg1983;8:348–9.[ISI]
Submitted 28 October 1999; revised version accepted 24 February 2000.