A Bayesian Adaptive Design in Cancer Phase I Trials Using Dose Combinations in the Presence of a Baseline Covariate

<table class="fixed-width table-group" id="tab3"><tr><td><table class="table"><colgroup><col style="width:4.33em"/><col style="width:7.26em"/><col style="width:7.04em"/><col style="width:18.70em"/></colgroup><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Design </td><td class="align_center" colspan="3">Average % DLTs (% Trials: DLT rate <span class="nowrap"><svg height="9.92533pt" id="M300" style="vertical-align:-0.6370001pt" version="1.1" viewbox="-0.0498162 -9.28833 46.8619 9.92533" width="46.8619pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M512 -3V55L134 254V256L512 456V514L75 281V230L512 -3Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.263,0)"><path d="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.644,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,31.18,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,37.42,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,40.384,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g></svg>;</span> % Trials: DLT rate <svg height="9.92533pt" id="M301" style="vertical-align:-0.6370001pt" version="1.1" viewbox="-0.0498162 -9.28833 46.8619 9.92533" width="46.8619pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.263,0)"><path d="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.644,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,31.18,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,37.42,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,40.384,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g></svg>)</td></tr><tr class="thead"><td class="align_center">Overall</td><td class="align_center">Z = 0</td><td class="align_center">Z = 1</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">WC</td><td class="align_center">25.9 (31.9; 2.0)</td><td class="align_center">17.3 (78.5; 3.0)</td><td class="align_center">34.5 (7.2; 17.4)</td></tr><tr><td class="align_left">IC</td><td class="align_center">24.4 (48.0; 0.0)</td><td class="align_center">14.2 (85.6; 0.0)</td><td class="align_center">34.6 (7.7; 17.5)</td></tr><tr><td class="align_left">PT</td><td class="align_center">-</td><td class="align_center">15.0 (91.1; 0.0)</td><td class="align_center">28.1 (24.0; 5.0)</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Operating characteristics summarizing trial safety for designs using a covariate (WC), ignoring the covariate (IC), and parallel trials (PT) considering discrete dose combinations.</div>

Journal of Probability and Statistics

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Table 3

Table 3: A Bayesian Adaptive Design in Cancer Phase I Trials Using Dose Combinations in the Presence of a Baseline Covariate 