Impact of Selection Bias on Estimation of Subsequent Event Risk
Authors: Hu Yi-Juan , Schmidt Amand F. , Dudbridge Frank , Holmes Michael V. , Brophy James M. , Tragante Vinicius , Li Ziyi , Liao Peizhou , Quyyumi Arshed A. , McCubrey Raymond O. , Horne Benjamin D. , Hingorani Aroon D. , Asselbergs Folkert W. , Patel Riyaz S. , Long Qi , Åkerblom Axel , Algra Ale , Allayee Hooman , Almgren Peter , Anderson Jeffrey L. , Andreassi Maria G. , Anselmi Chiara V. , Ardissino Diego , Arsenault Benoit J. , Ballantyne Christie M. , Baranova Ekaterina V. , Behloui Hassan , Bergmeijer Thomas O. , Bezzina Connie R. , Bjornsson Eythor , Body Simon C. , Boeckx Bram , Boersma Eric (H.) , Boerwinkle Eric , Bogaty Peter , Braund Peter S. , Breitling Lutz P. , Brenner Hermann , Briguori Carlo , Brugts Jasper J. , Burkhardt Ralph , Cameron Vicky A. , Carlquist John F. , Carpeggiani Clara , Carruthers Kathryn F. , Casu Gavino , Condorelli Gianluigi , Cresci Sharon , Danchin Nicolas , de Faire Ulf , Deanfield John , Delgado Graciela , Deloukas Panos , Direk Kenan , Doughty Robert N. , Drexel Heinz , Duarte Nubia E. , Dubé Marie-Pierre , Dufresne Line , Engert James C. , Eriksson Niclas , Fitzpatrick Natalie , Foco Luisa , Ford Ian , Fox Keith A.A. , Gigante Bruna , Gijsberts Crystel M. , Girelli Domenico , Gong Yan , Gudbjartsson Daniel F. , Hagström Emil , Hartiala Jaana , Hazen Stanley L. , Held Claes , Helgadottir Anna , Hemingway Harry , Heydarpour Mahyar , Hoefer Imo E. , Hovingh Kees , Hubacek Jaroslav A. , James Stefan , Johnson Julie A. , Wouter Jukema J. , Kaczor Marcin P. , Kaminski Karol A. , Kettner Jiri , Kiliszek Marek , Kleber Marcus , Klungel Olaf H. , Kofink Daniel , Kohonen Mika , Kotti Salma , Kuukasjärvi Pekka , Lagerqvist Bo , Lambrechts Diether , Lang Chim C. , Laurikka Jari O. , Leander Karin , Lee Vei-Vei , Lehtimäki Terho , Leiherer Andreas , Lenzini Petra A. , Levin Daniel , Lindholm Daniel , Lokki Marja-Liisa , Lotufo Paulo A. , Lyytikäinen Leo-Pekka , Khan Mahmoodi B. , Maitland-van der Zee Anke H. , Martinelli Nicola , März Winfried , Marziliano Nicola , McPherson Ruth , Melander Olle , Mons Ute , Muehlschlegel Jochen D. , Muhlestein Joseph B. , Nelson Cristopher P. , Newton Cheh Chris , Olivieri Oliviero , Opolski Grzegorz , Palmer Colin N. , Pare Guillaume , Pasterkamp Gerard , Pepine Carl J. , Pepinski Witold , Pereira Alexandre C. , Pilbrow Anna P. , Pilote Louise , Pitha Jan , Ploski Rafal , Mark Richards A. , Saely Christoph H. , Samani Nilesh J. , Samman-Tahhan Ayman , Sanak Marek , Sandesara Pratik B. , Sattar Naveed , Scholz Markus , Siegbahn Agneta , Simon Tabassome , Sinisalo Juha , Gustav Smith J. , Spertus John A. , Stefansson Kari , Stewart Alexandre F.R. , Stott David J. , Szczeklik Wojciech , Szpakowicz Anna , Tanck Michael W.T. , Tang Wilson H. , Tardif Jean-Claude , ten Berg Jur M. , Teren Andrej , Thanassoulis George , Thiery Joachim , Thorgeirsson Gudmundur , Thorleifsson Gudmar , Thorsteinsdottir Unnur , Timmis Adam , Trompet Stella , van de Werf Frans , van der Graaf Yolanda , van der Haarst Pim , van der Laan Sander W. , Vilmundarson Ragnar O. , Virani Salim S. , Visseren Frank L.J. , Vlachopoulou Efthymia , Wallentin Lars , Waltenberger Johannes , Wauters Els , Wilde Arthur A.M. 
Published: October 2017

Background—
Studies of recurrent or subsequent disease events may be susceptible to bias caused by selection of subjects who both experience and survive the primary indexing event. Currently, the magnitude of any selection bias, particularly for subsequent time-to-event analysis in genetic association studies, is unknown.

Methods and Results—
We used empirically inspired simulation studies to explore the impact of selection bias on the marginal hazard ratio for risk of subsequent events among those with established coronary heart disease. The extent of selection bias was determined by the magnitudes of genetic and nongenetic effects on the indexing (first) coronary heart disease event. Unless the genetic hazard ratio was unrealistically large (>1.6 per allele) and assuming the sum of all nongenetic hazard ratios was <10, bias was usually <10% (downward toward the null). Despite the low bias, the probability that a confidence interval included the true effect decreased (undercoverage) with increasing sample size because of increasing precision. Importantly, false-positive rates were not affected by selection bias.

Conclusions—
In most empirical settings, selection bias is expected to have a limited impact on genetic effect estimates of subsequent event risk. Nevertheless, because of undercoverage increasing with sample size, most confidence intervals will be over precise (not wide enough). When there is no effect modification by history of coronary heart disease, the false-positive rates of association tests will be close to nominal.