Comparing diagnostic tests with missing data

Abstract

When missing data occur in studies designed to compare the accuracy of diagnostic tests, a common, though naive, practice is to base the comparison of sensitivity, specificity, as well as of positive and negative predictive values on some subset of the data that fits into methods implemented in standard statistical packages. Such methods are usually valid only under the strong missing completely at random (MCAR) assumption and may generate biased and less precise estimates. We review some models that use the dependence structure of the completely observed cases to incorporate the information of the partially categorized observations into the analysis and show how they may be fitted via a two-stage hybrid process involving maximum likelihood in the first stage and weighted least squares in the second. We indicate how computational subroutines written in R may be used to fit the proposed models and illustrate the different analysis strategies with observational data collected to compare the accuracy of three distinct non-invasive diagnostic methods for endometriosis. The results indicate that even when the MCAR assumption is plausible, the naive partial analyses should be avoided.

Keywords:

• missing categorical data
• negative predictive value
• positive predictive value
• sensitivity
• specificity

Acknowledgements

This research received financial support from Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil, Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil, and Fundação para a Ciência e Tecnologia (FCT) through the research centres CEMAT-IST and CEAUL-FCUL, Portugal. The authors are grateful to Dr Manoel Gonçalves and Dr Maurício Simões Abrão for providing the data.