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Chapter 3.1<br />

138<br />

U i = Time to failure (HCC) for subject i if never exposed to glycyrrhizin (=counterfactual<br />

failure time)<br />

Glycyrrhizini (t) = The treatment status of subject i at timepoint t.<br />

The model that relates the observed data Ti and Glycyrrhizini (Ti) to the counterfactual<br />

failure time Ui is assumed to be:<br />

Ti Ui (ψ) = ∫ exp (ψ Glycyrrhizini (t)) dt<br />

0<br />

The model of U as a function of ψ describes the relation between the counterfactual<br />

failure time, the observed failure time and the use of glycyrrhizin over time.<br />

Acknowledgements<br />

The following Japanese investigators contributed to the study by sharing individual<br />

patient data:<br />

N. Izumi1 , J. Toyota2 , T. Aikawa3 , S. Fujiyama4 , K. Yasuda5 , A. Shibuya6 , Y. Hirose7 , H.<br />

Harada8 , S. Hige9 , G. Yamada10 , E. Tanaka11 , N. Ohno12 .<br />

1Musashino Red Cross Hospital, Tokyo; 2Sapporo Kousei General Hospital, Hokkaido;<br />

3Aikawa Internal Hospital, Ibaraki; 4Kumamoto University Hospital, Kumamoto; 5Kiyo kawa Hospital, Tokyo; 6Kitasato University East Hospital, Kanagawa; 7Yamanashi Central<br />

Prefectural Hospital, Yamanashi; 8National Tokyo Hospital, Tokyo; 9Hokkaido University<br />

School of Medicine, Hokkaido; 10Kawasaki Medical School, Okayama; 11Shinsu University<br />

School of Medicine, Nagano; 12Ohno Internal & Gastroenterology Clinic, Ehime.<br />

We thank mr. N. Yamamoto for his important contribution in the data collection.<br />

We thank the following experts for their highly valuable advice on study design and<br />

statistical methods: 1M.A. Hernán, T. Poynard2 , T. Stijnen3 , S. Iino4 and N. Hayashi5 .<br />

1 Department of Epidemiology, School of Public Health, Harvard University, Boston MA,<br />

USA. 2Service d’Hépato- Gastroenterologie, Groupe Hospitalier Pitié Salpétrière, Paris,<br />

France. 3Department of Epidemiology and Biostatistics, <strong>Erasmus</strong> Medical Center <strong>Rotterdam</strong>,<br />

<strong>Rotterdam</strong>, The Netherlands. 4Department of Medicine, St. Marianna University<br />

School of Medicine, Kawasaki, Kanagawa, Japan. 5Department of Gastroenterology and<br />

Hepatology, Osaka University Hospital, Osaka, Japan.<br />

This study was supported by an unrestricted grant from Minophagen Pharmaceutical Co<br />

Ltd., Japan.

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