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Optimal Adaptive Designs and Adaptive Randomization Techniques for Clinical Trials

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Optimal Adaptive Designs and Adaptive Randomization Techniques for Clinical Trials UPPSALA DISSERTATIONS IN MATHEMATICS 113 Optimal adaptive designs and adaptive randomization techniques for clinical trials Yevgen Ryeznik Department of Mathematics Uppsala University UPPSALA 2019 Dissertation presented at Uppsala University to be publicly examined in Ång 4101, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Friday, 26 April 2019 at 09:00 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Associate Professor Franz König (Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna). Abstract Ryeznik, Y. 2019. Optimal adaptive designs and adaptive randomization techniques for clinical trials. Uppsala Dissertations in Mathematics 113. 94 pp. Uppsala: Department of Mathematics. ISBN 978-91-506-2748-0. In this Ph.D. thesis, we investigate how to optimize the design of clinical trials by constructing optimal adaptive designs, and how to implement the design by adaptive randomization. The results of the thesis are summarized by four research papers preceded by three chapters: an introduction, a short summary of the results obtained, and possible topics for future work. In Paper I, we investigate the structure of a D-optimal design for dose-finding studies with censored time-to-event outcomes. We show that the D-optimal design can be much more efficient than uniform allocation design for the parameter estimation. The D-optimal design obtained depends on true parameters of the dose-response model, so it is a locally D-optimal design. We construct two-stage and multi-stage adaptive designs as approximations of the D-optimal design when prior information about model parameters is not available. Adaptive designs provide very good approximations to the locally D-optimal design, and can potentially reduce total sample size in a study with a pre-specified stopping criterion. In Paper II, we investigate statistical properties of several restricted randomization procedures which target unequal allocation proportions in a multi-arm trial. We compare procedures in terms of their operational characteristics such as balance, randomness, type I error/ power, and allocation ratio preserving (ARP) property. We conclude that there is no single “best” randomization procedure for all the target allocation proportions, but the choice of randomization can be done through computer-intensive simulations for a particular target allocation. In Paper III, we combine the results from the papers I and II to implement optimal designs in practice when the sample size is small. The simulation study done in the paper shows that the choice of randomization procedure has an impact on the quality of dose-response estimation. An adaptive design with a small cohort size should be implemented with a procedure that ensures a “well-balanced” allocation according to the D-optimal design at each stage. In Paper IV, we obtain an optimal design for a comparative study with unequal treatment costs and investigate its properties. We demonstrate that unequal allocation may decrease the total study cost while having the same power as traditional equal allocation. However, a larger sample size may be required. We suggest a strategy on how to choose a suitable randomization procedure which provides a good trade-off between balance and randomness to implement optimal allocation. If there is a strong linear trend in observations, then the ARP property is important to maintain the type I error and power at a certain level. Otherwise, a randomization- based inference can be a good alternative for non-ARP procedures. Keywords: optimal designs, optimal adaptive designs, randomization in clinical trials, restricted randomization, adaptive randomization, unequal cost, allocation ratio preserving randomization procedures, heterogeneous costs, multi-arm clinical trials, randomization-based inference, unequal allocation Yevgen Ryeznik, Department of Mathematics, Box 480, Uppsala University, SE-75106 Uppsala, Sweden. © Yevgen Ryeznik 2019 ISSN 1401-2049 ISBN 978-91-506-2748-0 urn:nbn:se:uu:diva-377552 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-377552) 'HGLFDWHG WR P\ IDPLO\ DQG P\ WHDFKHUV /LVW RI SDSHUV 7KLV WKHVLV LV EDVHG RQ WKH IROORZLQJ SDSHUV ZKLFK DUH UHIHUUHG WR LQ WKH WH[W E\ WKHLU 5RPDQ QXPHUDOV , <HYJHQ 5\H]QLN 2OHNVDQGU 6YHUGORY DQG $QGUHZ & +RRNHU ³$GDSWLYH 2SWLPDO 'HVLJQV IRU 'RVH)LQGLQJ 6WXGLHV ZLWK 7LPHWR(YHQW 2XWFRPHV´ 7KH $$36 -RXUQDO ,, <HYJHQ 5\H]QLN DQG 2OHNVDQGU 6YHUGORY ³$ &RPSDUDWLYH 6WXG\ RI 5HVWULFWHG 5DQGRPL]DWLRQ 3URFHGXUHV IRU 0XOWLDUP 7ULDOV ZLWK (TXDO RU 8QHTXDO 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