Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Lutz Mattner, Frauke Mattner
Universität Trier, Kliniken der Stadt Köln
On the statistical comparison of diagnostic tests using joint test results
We consider the common problem of estimating or comparing sensitivities or specificities of (dichotomous)
diagnostic tests, with the available data consisting of joint test results from the whole population, without
true state determinations. Assuming the plausible latent class model of Gart and Buck (1966), it is well
known that interesting inferences are possible only under not always plausible additional assumptions,
most notoriously the one of conditional independence of results of different tests given the true state,
as discussed and criticized in, for example, the book of Pepe (2003). We suggest to impose additional
assumptions only if they are plausible in a given application, even if this leads to nonidentifiability of the
parameters of interest and hence to, say, only upper confidence bounds instead of two-sided confidence
intervals.
A detailed example in the talk will be the case of two diagnostic tests with the second at least as
specific as the first. An application where this specificity assumption seems plausible is the comparison
of two competing tests for diagnosing toxigenic Clostridium difficile from stool samples, applying an
enzyme-immuno-assay either directly or after culturing (possibly nontoxigenic) Clostridium difficile. We
derive confidence bounds good enough to refute the direct test.
The talk will be aimed at mathematicians without prior knowledge of diagnostic tests.
Dietmar Pfeifer
Karl von Ossietzky Universität Oldenburg
Bernstein-Copulas: wie man den ’Fluch der Dimension’ umgeht
Der Modellierung und Simulation von stochastischen Abhängigkeiten versicherungstechnischer Risiken
kommt insbesondere im Licht von Solvency II eine wachsende Bedeutung zu. Für die Konzeption
und Implementierung interner Risikomodelle ist sie praktisch unverzichtbar. In dem Vortrag wird eine
Möglichkeit auf der Basis von Bernstein- und anderen konstruktiven Copula-Ansätzen vorgestellt, die
insbesondere das Problem des ’Fluchs der Dimension’ umgehen. In dem Vortrag wird auch ein konkretes
Anwendungsbeispiel vorgestellt.
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