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Exploring Selection Bias by Causal Frailty Models: The Magnitude Matters

Stensrud, Mats Julius; Valberg, Morten; Røysland, Kjetil; Aalen, Odd O.

doi: 10.1097/EDE.0000000000000621

Counter-intuitive associations appear frequently in epidemiology, and these results are often debated. In particular, several scenarios are characterized by a general risk factor that appears protective in particular subpopulations, for example, individuals suffering from a specific disease. However, the associations are not necessarily representing causal effects. Selection bias due to conditioning on a collider may often be involved, and causal graphs are widely used to highlight such biases. These graphs, however, are qualitative, and they do not provide information on the real life relevance of a spurious association. Quantitative estimates of such associations can be obtained from simple statistical models. In this study, we present several paradoxical associations that occur in epidemiology, and we explore these associations in a causal, frailty framework. By using frailty models, we are able to put numbers on spurious effects that often are neglected in epidemiology. We discuss several counter-intuitive findings that have been reported in real life analyses, and we present calculations that may expand the understanding of these associations. In particular, we derive novel expressions to explain the magnitude of bias in index-event studies.

From the aDepartment of Biostatistics, Institute of Basic Medical Sciences, University of Oslo, Oslo, Norway; and bDiakonhjemmet Hospital, Oslo, Norway.

Submitted 9 January 2016; accepted 11 January 2017.

This study was partially supported by a grant from the Norwegian Research Council (191460/V50), and by the Norwegian Cancer Society, Project/Grant Number 171851 and 4493570.

The authors report no conflicts of interest.

The computer code can be found in

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Correspondence: Mats Julius Stensrud, Domus Medica, Postboks 1122 Blindern, 0317 Oslo, Norway. E-mail:

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