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On the estimation and validation of biomarker-index’ accuracy
Book - Dissertation
Alzheimer’s Disease (AD) is an enormous burden on society and future perspectives foresee this burden only to increase. The need for a treatment for AD is growing but at the same time advances in AD research are hindered by issues related to the diagnosis of the disease. The currently used clinical diagnosis of AD is known to be imperfect while the perfect post-mortem diagnosis is expensive and useless from a diagnostic point of view. Therefore, the need for easily measurable biomarkers is high but many fail to show statistically adequate diagnostic accuracy. One of the reasons may be biased estimation of biomarker accuracy due to the use of the imperfect clinical diagnosis as a reference test without acknowledging this. The main goal of this dissertation was the development of methods facilitating the development of biomarker-based diagnostic tests for AD. The first research question focuses on how to efficiently estimate the accuracy of a diagnostic biomarker-index. Because of the lack of a gold-standard reference-test, currently available methods making use of the true disease labels would lead to biased accuracy estimates. Therefore, we propose the use of a Bayesian latent-class mixture model in Chapter 3. The model allows to include the information from an imperfect reference-test while accounting for its imperfectness. Care has to be taken with respect to the inclusion of prior information since a combination of uninformative priors may lead to an extremely informative prior for the parameter of interest. Therefore, an alternative parametrisation is proposed to allow the inclusion of prior information directly on the accuracy of the diagnostic-biomarker index. We show that, when appropriate priors are chosen, this model provides unbiased estimates of the diagnostic biomarker-index’ accuracy. Moreover, the results suggest that the reports indicating disappointing results of diagnostic performance of the AD CSF-biomarkers might by due in part to the fact that the clinical diagnosis was treated as a GS reference-test. The assumption that the considered biomarkers are independent of the reference test, conditionally on the true disease status, is untestable and only heuristically enforceable. Therefore, the proposed Bayesian latent-class model is extended in Chapter 4. By considering that the imperfect reference-test is a dichotomized version of an underlying continuous latent-tolerance variable, conditional dependence between the biomarkers and the reference test are modelled directly. Assuming that the continuous tolerance variable and the biomarkers are jointly normally distributed, their correlation can be estimated. Therefore, the estimated accuracy of the diagnostic biomarker-index is corrected for any possible conditional dependence between the biomarkers and reference test without the need for any untestable heuristic argumentation. In terms of the AD application, it is shown that, although statistically significant conditional dependence is observed, it has no significant impact on the accuracy estimate of the diagnostic biomarker-index. The focus of the second research question is on the validation of a developed diagnostic biomarker-index. Because of the need for large sample sizes or expensive data to reach adequate power of the validation study together with the lack of an effi- cient statistical framework, validation is rarely performed. In Chapter 5 we propose a Bayesian framework allowing efficient validation of a diagnostic biomarker-index. By making use of the exchangeability assumption of the parameters of the development and validation studies, accuracy information obtained in the development study can be included into the validation study. In particular, an approximation to the posterior distribution of the accuracy parameter from the development study, is carried over to the validation study. Validation is defined as an hypothesis test, testing whether a particular validation criterion value can be rejected. Before comparing the proposed analysis to a ’traditional’ analysis in which the development-study information is ignored, significance levels of the hypothesis test are adjusted to obtain comparable type-I error probabilities. We show that, although the information from the development study is discarded by doubling its standard deviation, a large reduction of the required sample size is possible. In particular, the considered settings shows a reduction to about 20% of the required sample size compared to a validation study ignoring the development-study accuracy information to reach a power of approximately 0.53. The development and validation of a diagnostic AD CSF-biomarker cut-off for a particular commercially available assay does not imply the applicability of the cut off on other assays, measuring the same biomarker. This would imply setting up time-consuming and expensive studies. Therefore, the third research question investigates the transfer of the cut-off value of an AD CSF-biomarker from a currently used assay to a new one, without having to conduct new development and validation studies. The validity and the effect of the currently applied linear-regression transfer-method on the clinical performance of the biomarker measured with a new assay, have never been investigated. In Chapter 6 we establish that if the underlying assumptions of the linear-regression-based transfer-method are violated the results are biased. This entails that the diagnostic biomarker has different operating characteristics depending on the assay on which it is measured. Therefore, we propose a novel two-stage Bayesian approach which leads to unbiased and more precise estimates than the linear-regression-based transfer-method. The approach first estimates the distributional characteristics of the diagnostic-biomarker on the current assay based on the results of a GS reference-test. Next, the posterior information is introduced in the second stage as prior information. In the second stage, the cut-off of the new-assay is estimated by considering data measured on both assays side-byside. Because of the introduction of the information on the current assay in the first stage, no GS information is required to end up with unbiased estimates. The proposed Bayesian approach provides more precise cut-off estimates than the linear regression-based transfer-method. Though, with the limited sample size of currently considered development and validation studies, only imprecise cut-off estimates are available. This means that the currently used cut-offs have large uncertainty in terms of operating characteristics, which is rarely acknowledged.
Number of pages: 179