Correlation Coefficients for a Study with Repeated Measures

<div>Average correlation and the MSE under the AR(1) correlation structure with a small variance <svg height="15.535pt" id="M114" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 35.3017 15.535" width="35.3017pt" 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="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.347,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.784)"><path d="M757 650H506L497 618C579 615 596 608 596 570S591 477 571 380L560 327C516 117 435 41 309 41C199 41 108 114 144 303L187 529C202 609 208 612 291 618L296 650H30L24 618C109 612 113 606 99 529L58 299C33 161 62 83 113 41C161 0 222 -17 283 -17C348 -17 417 3 470 48C546 111 584 203 603 311L615 380C631 474 647 531 658 567C667 599 672 616 750 618L757 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.622,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.885,0)"><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> (top) and a large variance <svg height="15.535pt" id="M115" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 41.565 15.535" width="41.565pt" 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="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.347,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.784)"><path d="M757 650H506L497 618C579 615 596 608 596 570S591 477 571 380L560 327C516 117 435 41 309 41C199 41 108 114 144 303L187 529C202 609 208 612 291 618L296 650H30L24 618C109 612 113 606 99 529L58 299C33 161 62 83 113 41C161 0 222 -17 283 -17C348 -17 417 3 470 48C546 111 584 203 603 311L615 380C631 474 647 531 658 567C667 599 672 616 750 618L757 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.622,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.885,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.125,0)"><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></svg> (bottom) when <i>ρ</i><sub><i>UW</i></sub> = 0.5 and <i>n</i> = 60 for a study with unequal numbers of visits (2, 3, or 4 visits).</div>

Computational and Mathematical Methods in Medicine

Correlation Coefficients for a Study with Repeated Measures

Figure 4