Original ArticleThree methods to construct predictive models using logistic regression and likelihood ratios to facilitate adjustment for pretest probability give similar results
Section snippets
Background
Evaluation of the diagnostic value of clinical history, examination, and subsequent tests relies on the ability to combine multiple items of diagnostic information. It is through combining several items that good predictive accuracy is achieved. Application to individual patients requires tailoring results according to pretest probabilities of disease [1].
Studies that evaluate combinations of items usually create a diagnostic rule, scoring system or predictive model, which can be used to rate
Illustrative example
The Clinical Assessment of the Reliability of the Examination-Chronic Obstructive Airway Disease (CARE-COAD) study group designed a series of multinational studies to obtain reliable information on the accuracy of the history and physical examination in diagnosing obstructive airways disease (OAD) [12]. The CARE-COAD1 study [13] recruited 309 consecutive patients and noted four items from the history (age, sex, chronic OAD history, smoking history) and two from the clinical examination (wheeze,
Methods
For illustration, we demonstrate the models using only two binary tests of OAD history and age group (Table 2). We first apply the independence Bayes' approach, and then the conventional and alternative logistic regression approaches.
Results for full illustrative example
Parameter estimates for analyses of the COAD1 data sets including all four tests are shown in Table 3, for the independence Bayes, conventional and Albert's logistic regression models, and the SKJ approach. Likelihood ratios are only estimable from the independence Bayes and SKJ models, and are converted into odds ratios (by computing ratios of likelihood ratios) solely for comparison with the logistic regression models.
Likelihood ratios adjusted for dependence using the SKJ approach are all
Discussion
Predictive models are frequently published in the medical literature, both for diagnostic and prognostic applications. Although some models are constructed using Bayesian reasoning, logistic regression is frequently used to take account of dependence between tests. Logistic regression estimates a log odds ratio for each test, simultaneously taking account of other tests included in the model [19]. Although the log odds ratio provides a measure of test performance, it is difficult for clinicians
Acknowledgments
We are grateful to Sharon Straus for providing the CARE-COAD data sets. The work was supported by the National Health and Medical Research Council (NHMRC) grants Grants No. 211205 and No. 402764 to the Screening and Test Evaluation Program. Jon Deeks is supported by a UK Department of Health NCCRCD Senior Research Scientist in Evidence Synthesis award. This work was undertaken as a Master's thesis by the first author.
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2012, Journal of Clinical EpidemiologyCitation Excerpt :There is a more sophisticated method for updating the pretest probabilities that accounts for the assessment order of the clinical information [16]. This more sophisticated method may yield different LR estimates but similar posterior probabilities in general compared with more straightforward approaches [17]. In a sequential risk model with interactions, the diagnostic value, that is, the LR, of a risk factor may depend on other risk factors already ascertained.
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2009, Journal of Clinical EpidemiologyCitation Excerpt :When important correlation between tests is found, likelihood ratios should be reported for all combinations of the test results [4]. Alternatively, one could avoid biased estimates from correlated tests with valid prediction rules or statistical methods for calculating likelihood ratios that are independent of other test results [6,7]. Knowing the correlation between tests will facilitate the utilization of such prediction rules, because they could be approximated with the substitution of a particular, unavailable component with an available, highly correlated test result [13,14].