Richard J. Rossi - Applied Biostatistics for the Health Sciences

512 497

513 498

514 499

515 500

516 501

517 502

518 503

519 504

520 505

521 506

522 507

523 508

524 509

525 510

526 511

527 512

528 513

529 514

530 515

531 516

532 517

533 518

534 519

535 520

536 521

537 522

538 523

539 524

540 525

541 526

542 527

543 528

544 529

545 530

546 531

547 532

548 533

549 534

550 535

551 536

552 537

553 538

554 539

555 540

556 541

557 542

558 543

559 544

560 545

561 546

562 547

563 548

564 549

565 550

566 551

567 552

568 553

569 554

570 555

571 556

572 557

573 558

574 559

575 560

576 561

577 562

578 563

579 564

580 565

581 566

582 567

583 568

584 569

585 570

586 571

587 572

588 573

589 574

590 575

591 576

592 577

593 578

594 579

595 580

596 581

597 582

598 583

599 584

600 585

601 586

602 587

603 588

604 589

605 590

606 591

607 592

608 593

609 594

610 595

611 596

612 597

613 598

614 599

615 600

616 601

617 602

618 603

619 604

620 605

621 606

622 607

623 608

624 609

625 610

626 611

627 612

628 613

629 614

630 615

631 616

632 617

633 618

634 619

635 620

636 621

637 622

638 623

639 624

640 625

641 626

642 627

643 628

644 629

645 630

646 631

647 632

648 633

649 634

650 635

651 636

652 637

653 638

654 639

655 640

656 641

657 642

658 643

659 644

660 645

661 646

662 647

663 648

664 649

665 650

666 651

667 652

668 653

669 654

670 655

671 656

672 657

673 658

674 659

675 660

676 661

677 662

678 663

679 664

680 665

681 666

682 667

Applied Biostatistics for the Health Sciences is intended for use in an introductory biostatistics class for undergraduates in the health sciences including students studying premedicine, nursing, pharmacy, bioinformatics, healthcare informatics, biochemistry, and applied health sciences. This textbook is also appropriate for a first course in statistics for medical students or graduate students in public health. In fact, this book was written for introducing students to biostatistics as well as for preparing students for the material covered in upper division applied statistics courses. The only prerequisite for a course taught from this textbook is a typical course in high school algebra II or college algebra.

The topics chosen for this book were chosen for pedagogical reasons and have been tried, tested, and adjusted over the past 40 years of teaching introductory courses in statistics. Throughout Applied Biostatistics for the Health Sciences , the primary emphasis is placed on the correct usage, interpretation, and the conceptual ideas associated with each biostatistical method that is discussed.

The textbook is organized in two parts with Chapters 1– 7covering the basic inferential biostatistical methods used to describe sample data arising in a biomedical or health-related study. Chapters 8– 13cover several modeling approaches that are commonly used with biomedical and healthcare data. In particular, the following topics are presented in this textbook.

Chapter 1: Introduction to Biostatistics. Chapter 1provides an introduction to the ideas and basic terminology of biostatistics as well as the commonly used research protocols. Experiments are contrasted with observational studies and clinical trials are also discussed in Chapter 1. A description of the data sets used in several of the examples and exercises is given at the end of Chapter 1.

Chapter 2: Describing Populations. Chapter 2introduces variables, populations, population parameters, probability, and the binomial and normal probability models. Several biomedical parameters are introduced in Chapter 2including the prevalence of a disease, the specificity and sensitivity of a diagnostic test, and the relative risk associated with a disease and risk factor.

Chapter 3: Random Sampling. The basic ideas associated with random sampling are discussed in Chapter 3. In particular, the simple random sampling, stratified random sampling, random cluster sampling, and systematic random sampling plans are discussed including the determination of the appropriate sample size for estimating a mean or proportion with a prespecified bound on the error of estimation. The formulas for determining the overall sample size and its allocation for a stratified random sample may be considered as an optional topic and covered as time permits.

Chapter 4: Summarizing Random Samples. Several important graphical and numerical summary statistics for qualitative and quantitative variables are presented. In particular, along with the standard point estimators of the measures of location and dispersion, point estimators for estimating the prevalence of a disease, the sensitivity and specificity of a diagnostic test, the relative risk, and the coefficient of variation are presented in Chapter 4. The plug-in rule for estimating parameters is also included in this chapter.

Chapter 5: Measuring the Reliability of Statistics. The sampling distribution of an estimator is discussed in Chapter 5with emphasis on evaluating the reliability of a point estimator. The topics discussed in Chapter 5include properties of point estimators including the bias, standard error, bound on the error of estimation, and mean squared error associated with a point estimator. The Central Limit Theorem for the sample proportion and sample mean, the t distribution, and bootstrapping the sampling distribution of a point estimator are discussed in this chapter. The section on bootstrapping can be considered optional material to be covered if time permits.

Chapter 6: Confidence Intervals. Confidence intervals for a single proportion, a single mean, the difference of two proportions, the difference of two means, and the relative risk are presented in Chapter 6. Formulas for determining the sample size required for a prespecified margin of error are included for estimating a proportion, mean, and the difference between two proportions. Bootstrap confidence intervals are also discussed in this chapter and can be considered optional material.

Chapter 7: Testing Statistical Hypotheses. Chapter 7includes a general discussion of hypothesis testing and significance testing that is followed by the hypothesis tests for testing hypotheses about a single proportion, t tests for a single mean, paired t-tests, and the two-sample t-test. Formulas for determining the approximate sample size required for a test having a prespecified size and power are also presented for each testing procedure.

Chapter 8: Simple Linear Regression. Chapter 8is the first chapter in a series of chapters on modeling a response variable. The topics covered in Chapter 8include analyzing scatterplots, correlation, the simple linear regression model, fitting and assessing the fit of a simple linear regression model, and statistical inferences drawn from a fitted model.

Chapter 9: Multiple Regression. Chapter 9extends and broadens the methods discussed in Chapter 8to multiple regression models. The multiple regression topics that are discussed in Chapter 9include linear and nonlinear models, fitting and assessing the fit of a multiple regression model, drawing inferences from a fitted model, comparing nested regression models, dummy variable models, and variable selection procedures.