Issues with dichotomisation

Given that the true sensitivity and specificity of a test can be estimated, the Rogan-Gladen approach (and associated methods) described in the previous chapter

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can reduce some of the limitations associated with dichotomisation. However, several potential drawbacks remain – one of which is interpretation of an individual test result. Although the Rogan-Gladen adjustment may allow a reasonable estimate of the population prevalence to be made, it does not operate at the individual animal level, which could result in difficulties when reporting individual results to stakeholders or for risk factor studies which rely on individual-level interpretation. One method of accounting for this issue is through the use of positive and negative predictive values (𝑃𝑃𝑉 and 𝑁𝑃𝑉) (Altman and Bland, 1994b). These estimates are influenced by the test sensitivity (𝑆𝑒) and specificity (𝑆𝑝) as well as the prior probability of infection in the individual (often estimated as the true prevalence of infection in the population, 𝑝):

𝑃𝑃𝑉 = (𝑆𝑒 × 𝑝)

(𝑆𝑒 × 𝑝) + ((1 − 𝑆𝑒) × (1 − 𝑝))

This approach clearly has use for dissemination of information back to stakeholders, and methods of incorporation of 𝑃𝑃𝑉 and 𝑁𝑃𝑉 into a regression model (within a Bayesian context) have also been described (Lewis et al., 2012).

Another issue resulting from dichotomisation is the loss of potentially useful information regarding the probability of infection (Choi et al., 2006b), or even in some cases the level of infection. For example, for a continually measured diagnostic test result for which higher values indicate infection, an animal with a very high test result would be more likely to be infected than an animal with a test result just above the cut-off. However, these two animals would both just be classified as ‘positive’ under a dichotomous interpretation. Similarly, in situations where levels of infection are not homogenously distributed amongst infected individuals, as is seen with overdispersed macroparasitic infections (Crofton, 1971a; Anderson and May, 1978), the test result may offer some insight into the level of infection (for example, animals with higher parasite burdens may tend to have higher test results, as is seen with the coproantigen ELISA (Deplazes et al., 1992; Allan et al., 1992)). In these cases, dichotomisation could result in the loss of information with potential implications for the risk of pathogen

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transmission (an animal with a higher parasite burden may pose a greater risk of transmission than one with lower burdens).

In the case of the former of these two issues, a method of interpretation of test results at the individual level through the use of likelihood ratios has been suggested (Deeks and Altman, 2004). The ‘likelihood ratio’ of a positive test result (𝐿𝑅+_{) can be} calculated as the ratio of the conditional probability of a positive test result (𝑇+_{) given} the individual is infected (𝐷+_{) (the sensitivity, in the case of a dichotomous result) to} the conditional probability of a positive test result given that the individual is not infected (𝐷−_{) (which is (1 − 𝑆𝑝), in the case of a dichotomous interpretation):}

𝐿𝑅+ ₌ 𝑝(𝑇+| 𝐷+) 𝑝(𝑇+_{| 𝐷}−₎=

𝑆𝑒 (1 − 𝑆𝑝)

Through the use of Bayes’ theorem, an estimate of the post-test odds of disease can then can be estimated by multiplying the 𝐿𝑅+ _{by the pre-test odds of disease, which} can then be converted to a probability if desired. The ‘raw’ test result (without dichotomisation) can also be used to estimate a likelihood ratio, using the same principles as described above. Another method, termed probability diagnostic assignment (PDA), has been developed which incorporates test results from known infected and uninfected individuals in order to estimate the individual-level probability of infection and the population-level prevalence of infection using a frequentist application of Bayes’ theorem (Thurmond et al., 2002). This approach has been developed into a fully Bayesian framework, which is computationally easier and which may be less dependent on the availability of data of known status (given there is reasonable separation in the distribution of test results between infected and uninfected individuals) (Choi et al., 2006b).

As can be seen from the equations above, these approaches require clear estimates of the sensitivity and specificity of the test (and in the case of predictive values, also an estimate of the prevalence of infection in the community). As described above, there is evidence that the sensitivity of the Echinococcus coproantigen ELISA test is correlated with the worm burden, with lower sensitivities in the case of low burdens (Allan and

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Craig, 2006). As the burden of Echinococcus in the definitive host is commonly highly overdispersed (Jenkins and Morris, 1991; Torgerson and Heath, 2003; Budke et al., 2005a), it would be expected that the majority of infected individuals would have low burdens, and as such would be less likely to be identified using a dichotomous interpretation than those with higher burdens. The overall test performance would therefore be expected to depend upon the distribution of worm burdens in the population of interest.

Another challenge when attempting to estimate the sensitivity and specificity of any test for canine echinococcosis is the lack of a readily available gold standard test (i.e. a test with perfect sensitivity and specificity). As described in previous chapters, the gold standard test for canine echinococcosis is necropsy of dogs and examination of intestines using the sedimentation and counting technique (WHO/OIE, 2001d; Torgerson and Deplazes, 2009). This is rarely possible in the field situation as it is logistically challenging, potentially biohazardous, and requires culling of dogs. Alternative strategies of estimating test performance based upon application of Bayesian modelling strategies and latent class analysis to multiple imperfect test results have been described (Ziadinov et al., 2008; Hartnack et al., 2013).