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="tab4"><tr><td><table class="table"><colgroup><col style="width:5.15em"/><col style="width:4.11em"/><col style="width:2.98em"/><col style="width:4.56em"/><col style="width:4.56em"/><col style="width:4.56em"/><col style="width:2.96em"/></colgroup><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left">Covariate </td><td class="align_center">Design</td><td class="align_center">PS</td><td class="align_center"><span style="width: 42.8342ptpx;"><svg height="12.1489pt" id="M308" style="vertical-align:-3.3825pt" version="1.1" viewbox="-0.0498162 -8.7664 42.8342 12.1489" width="42.8342pt" 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="M46 650V622C120 617 128 613 128 525V125C128 42 120 34 40 28V0H311V28C221 34 212 39 212 124V281L286 262C297 261 316 261 331 263C429 275 526 338 526 468C526 533 501 579 462 609C422 638 364 650 293 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427 388 427C372 427 356 428 302 438C256 447 221 451 187 451C159 451 130 428 105 384C93 363 80 340 65 305L96 290C122 342 149 381 193 381C216 381 267 377 294 374S346 372 365 376L75 105C37 70 24 35 24 16C24 2 30 -5 35 -8C42 -8 46 -6 48 -2C58 14 75 35 90 41C102 46 116 46 147 32C200 8 267 -21 298 -21C347 -21 390 12 448 126L420 151C369 77 338 56 311 56C287 56 249 68 212 81C180 92 149 100 127 98C212 172 353 308 413 372L481 445Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.548,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.443,0)"><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></td><td class="align_center"><span style="width: 14.6979ptpx;"><svg height="14.1074pt" id="M311" style="vertical-align:-5.341pt" version="1.1" viewbox="-0.0498162 -8.7664 14.6979 14.1074" width="14.6979pt" 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="M409 504C401 567 396 607 392 642C354 654 312 665 266 665C137 665 60 583 60 487C60 374 161 325 225 290C300 250 355 215 355 141C355 68 311 21 235 21C131 21 86 122 71 183L41 176C48 128 61 42 68 21C78 16 93 8 118 0C142 -7 175 -15 216 -15C349 -15 438 69 438 174C438 287 344 333 265 374C186 414 138 449 138 522C138 576 172 631 249 631C336 631 363 562 380 499L409 504Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.162,3.132)"><path d="M493 498C488 549 483 613 482 650H43V617C122 611 130 603 130 521V129C130 47 122 39 42 33V0H319V33C226 39 217 47 217 129V580C217 609 221 611 250 611H324C386 611 407 605 422 585C438 567 447 539 458 494L493 498Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,10.093,5.233)"><path d="M507 520C499 588 433 708 316 708C242 708 176 657 176 599C176 563 197 520 251 455C218 440 186 424 152 401C84 355 25 277 25 179C25 72 94 -12 200 -12C256 -12 307 7 341 31C418 86 460 170 460 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class="align_center">56.4</td></tr><tr><td class="align_left" colspan="7"><hr/></td></tr><tr><td class="align_left" rowspan="3">Z = 1</td><td class="align_center">WC</td><td class="align_center">55.3</td><td class="align_center">25.7</td><td class="align_center">72.5</td><td class="align_center">85.5</td><td class="align_center">71.6</td></tr><tr><td class="align_center">IC</td><td class="align_center">47.6</td><td class="align_center">17.9</td><td class="align_center">59.5</td><td class="align_center">79.6</td><td class="align_center">62.7</td></tr><tr><td class="align_center">PT</td><td class="align_center">81.6</td><td class="align_center">16.2</td><td class="align_center">71.4</td><td class="align_center">88.0</td><td class="align_center">88.9</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Operating characteristics summarizing trial efficiency for <svg height="10.5386pt" id="M307" style="vertical-align:-1.57648pt" version="1.1" viewbox="-0.0498162 -8.96212 41.7337 10.5386" width="41.7337pt" 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="M669 636L663 650H260C230 650 221 652 208 675H186C177 621 162 548 144 481L173 479C195 534 211 560 226 578C248 604 266 615 373 615H544C460 511 114 112 23 16L31 0H561C577 34 611 135 622 170L594 182C566 125 544 88 515 65C481 38 416 35 319 35C249 35 197 37 152 41C270 184 542 501 669 636Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.628,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.891,0)"><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,-0.013,30.131,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.274,0)"><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> with designs using covariate (WC), ignoring covariate (IC), and parallel trials (PT) considering discrete dose combinations.</div>

Journal of Probability and Statistics

tab4

Table 4

Table 4: A Bayesian Adaptive Design in Cancer Phase I Trials Using Dose Combinations in the Presence of a Baseline Covariate 