Biostatistics: A Methodology for the Health Sciences

888 Pages·2004·8.006 MB·English

by  Gerald van Belle, Patrick J. Heagerty, Lloyd D. Fisher, Thomas S. Lumley

Biostatistics
A Methodology for the Health Sciences
Second Edition
GERALD VAN BELLE
LLOYD D. FISHER
PATRICK J. HEAGERTY
THOMAS LUMLEY
Department of Biostatistics and
Department of Environmental and
Occupational Health Sciences
University of Washington
Seattle, Washington
A JOHN WILEY & SONS, INC., PUBLICATION
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LibraryofCongressCataloging-in-PublicationData:
Biostatistics:amethodologyforthehealthsciences/GeraldvanBelle... [etal.]–2nded.
p.cm.–(Wileyseriesinprobabilityandstatistics)
Firsted.publishedin1993,enteredunderFisher,Lloyd.
Includesbibliographicalreferencesandindex.
ISBN0-471-03185-2(cloth)
1.Biometry.I.VanBelle,Gerald.II.Fisher,Lloyd,1939–Biostatistics.III.Series.
QH323.5.B5622004
610′.1′5195–dc22
2004040491
PrintedintheUnitedStatesofAmerica.
10987654321
Ad majorem Dei gloriam
Contents
Preface to the First Edition ix
Preface to the Second Edition xi
1. Introduction to Biostatistics 1
2. Biostatistical Design of Medical Studies 10
3. Descriptive Statistics 25
4. Statistical Inference: Populations and Samples 61
5. One- and Two-Sample Inference 117
6. Counting Data 151
7. Categorical Data: Contingency Tables 208
8. Nonparametric, Distribution-Free, and Permutation Models:
Robust Procedures 253
9. Association and Prediction: Linear Models with One
Predictor Variable 291
10. Analysis of Variance 357
11. Association and Prediction: Multiple Regression Analysis
and Linear Models with Multiple Predictor Variables 428
12. Multiple Comparisons 520
13. Discrimination and Classification 550
14. Principal Component Analysis and Factor Analysis 584
vii
viii CONTENTS
15. Rates and Proportions 640
16. Analysis of the Time to an Event: Survival Analysis 661
17. Sample Sizes for Observational Studies 709
18. Longitudinal Data Analysis 728
19. Randomized Clinical Trials 766
20. Personal Postscript 787
Appendix 817
Author Index 841
Subject Index 851
Symbol Index 867
Preface to the First Edition
Thepurposeofthisbookisforreaderstolearnhowtoapplystatisticalmethodstothebiomedical
sciences.Thebookiswrittensothatthosewithnopriortraininginstatisticsandamathematical
knowledge through algebra can follow the text—although the more mathematical training one
has,theeasierthelearning.Thebookiswrittenforpeopleinawidevarietyofbiomedicalfields,
including (alphabetically) biologists, biostatisticians, dentists, epidemiologists, health services
researchers, health administrators, nurses, and physicians. The text appears to have a daunting
amountofmaterial.Indeed,thereisagreatdealofmaterial,butmoststudentswillnotcoverit
all.Also,over30%ofthetextisdevotedtonotes,problems,andreferences,sothatthereisnot
as much material as thereseems to beat first sight.In additionto not covering entirechapters,
thefollowingareoptionalmaterials:asterisks(∗)precedingasectionnumberorproblemdenote
moreadvancedmaterialthattheinstructormaywanttoskip;thenotesattheendofeachchapter
contain material for extending and enriching the primary material of the chapter, but this may
be skipped.
Althoughtheorderofauthorshipmayappearalphabetical,infactitisrandom(wetossedafair
cointodeterminethesequence)andthebookisanequalcollaborativeeffortoftheauthors.We
havemanypeopletothank.Ourfamilieshavebeenhelpfulandlong-sufferingduringthewriting
ofthebook:forLF,Ginny,Brad,andLaura;forGvB,Johanna,Loeske,WilliamJohn,Gerard,
Christine,Louis,andBudandStacy.Themanystudentswhoweretaughtwithvariousversions
of portions of this material were very helpful. We are also grateful to the many collaborating
investigators, who taught us much about science as well as the joys of collaborative research.
AmongthosedeservingthanksareforLF:EdAlderman,ChristerAllgulander,FredApplebaum,
Michele Battie, Tom Bigger, Stan Bigos, Jeff Borer, Martial Bourassa, Raleigh Bowden, Bob
Bruce,BernieChaitman,RegClift,RollieDickson,KrisDoney,EricFoster,BobFrye,Bernard
Gersh, Karl Hammermeister, Dave Holmes, Mel Judkins, George Kaiser, Ward Kennedy, Tom
Killip, Ray Lipicky, Paul Martin, George McDonald, Joel Meyers, Bill Myers, Michael Mock,
Gene Passamani, Don Peterson, Bill Rogers, Tom Ryan, Jean Sanders, Lester Sauvage, Rainer
Storb, Keith Sullivan, Bob Temple, Don Thomas, Don Weiner, Bob Witherspoon, and a large
numberofothers.ForGvB:RalphBradley,RichardCornell,PollyFeigl,PatFriel,AlHeyman,
Myles Hollander, Jim Hughes, Dave Kalman, Jane Koenig, Tom Koepsell, Bud Kukull, Eric
Larson, Will Longstreth,Dave Luthy, Lorene Nelson, Don Martin, Duane Meeter, Gil Omenn,
Don Peterson, Gordon Pledger, Richard Savage, Kirk Shy, Nancy Temkin, and many others.
In addition, GvB acknowledges the secretarial and moral support of Sue Goleeke. There were
manyexcellentandabletypistsovertheyears;specialthankstoMyrnaKramer,PatColey,and
JanAlcorn.WeowespecialthankstoAmyPlummerforsuperbworkintrackingdownauthors
andpublishersforpermissiontocitetheirwork.WethankRobertFisherforhelpwithnumerous
figures.Rob ChristdidanexcellentjobofusingLATEXforthefinalversionofthetext.Finally,
severalpeopleassistedwithrunningparticularexamplesandcreatingthetables;wethankBarry
Storer, Margie Jones, and Gary Schoch.
ix
x PREFACETOTHEFIRSTEDITION
Our initial contact with Wiley was the indefatigable Beatrice Shube. Her enthusiasm for
oureffort carried over toher successor,KateRoach. Theassociatemanaging editor,RoseAnn
Campise, was of great help during the final preparation of this manuscript.
With a work this size there are bound to be some errors, inaccuracies, and ambiguous
statements.Wewouldappreciatereceivingyourcomments.Wehavesetupaspecialelectronic-
mail account for your feedback:
http://www.biostat-text.info
Lloyd D. Fisher
Geraldvan Belle
Preface to the Second Edition
BiostatisticsdidnotspringfullyformedfromthebrowofR.A.Fisher,butevolvedovermany
years. This process is continuing,althoughit may not be obviousfrom the outside.It has been
ten years since the first edition of this book appeared (and rather longer since it was begun).
Overthistime,newareasofbiostatisticshavebeendevelopedandemphasesandinterpretations
have changed.
The original authors, faced with the daunting task of updating a 1000-page text, decided
to invite two colleagues to take the lead in this task. These colleagues, experts in longitudinal
data analysis, survival analysis, computing, and all things modern and statistical, have given a
twenty-first-century thrust to the book.
Theauthorsequenceforthefirsteditionwasdeterminedbythetossofacoin(seethePreface
to the First Edition). For the second edition it was decided to switch the sequence of the first
two authors and add the new authors in alphabetical sequence.
This second edition adds a chapter on randomized trials and another on longitudinal data
analysis. Substantial changes have been made in discussing robust statistics, model building,
survival analysis, and discrimination. Notes have been added, throughout, and many graphs
redrawn. We have tried to eliminate errata found in the first edition, and while more have
undoubtedly been added, we hope there has been a net improvement. When you find mistakes
we would appreciate hearing about them at http://www.vanbelle.org/biostatistics/.
Anothermajorchangeoverthepastdecadeorsohasbeentechnological.Statisticalsoftware
and the computers to run it have become much more widely available—many of the graphs
andnewanalysesinthisbookwereproducedonalaptopthatweighsonlyslightlymorethana
copy of the first edition—and the Internet provides ready access to information that used to be
availableonly in universitylibraries.In order to accommodate thenew sectionsand to attempt
tokeepupwithfuturechanges,wehaveshiftedsomematerialtoasetofWebappendices.These
may be found at http://www.biostat-text.info. The Web appendices include notes, data sets and
sampleanalyses,linkstootheronlineresources,allbutabareminimumofthestatisticaltables
from the first edition,and other material for which ink on paper is a less suitablemedium.
These advances in technology have not solved the problem of deadlines, and we would
particularly like to thank Steve Quigley at Wiley for his equanimity in the face of schedule
slippage.
Geraldvan Belle
Lloyd Fisher
Patrick Heagerty
Thomas Lumley
Seattle,June15,2003
xi
C H A P T E R 1
Introduction to Biostatistics
1.1 INTRODUCTION
We welcome the reader who wishes to learn biostatistics. In this chapter we introduce you to
the subject. We define statistics and biostatistics. Then examples are given where biostatistical
techniques are useful.Theseexamples show that biostatisticsis an important toolin advancing
our biologicalknowledge; biostatisticshelps evaluate many life-and-death issues in medicine.
We urge you to read the examples carefully. Ask yourself, “what can be inferred from the
informationpresented?”Howwouldyoudesignastudyorexperimenttoinvestigatetheproblem
athand?Whatwouldyoudowiththedataaftertheyarecollected?Wewantyoutorealizethat
biostatisticsis a tool that can be used to benefit you and society.
Thechaptercloseswithadescriptionofwhatyoumayaccomplishthroughuseofthisbook.
To paraphrase Pythagoras, there is no royal road to biostatistics.You need to be involved.You
need to work hard. You need to think. You need to analyze actual data. The end result will be
a tool that has immediate practical uses. As you thoughtfully consider the material presented
here, you will develop thought patterns that are useful in evaluating information in all areas of
your life.
1.2 WHAT IS THE FIELD OF STATISTICS?
Muchofthejoyandgriefinlifearisesinsituationsthatinvolveconsiderableuncertainty.Here
are a few such situations:
1. Parentsofachildwithageneticdefectconsiderwhetherornottheyshouldhaveanother
child. They will base their decision on the chance that the next child will have the same
defect.
2. Tochoosethebesttherapy,aphysicianmustcomparetheprognosis,orfuturecourse,of
a patient under several therapies. A therapy may be a success, a failure, or somewhere
in between; the evaluation of the chance of each occurrence necessarily enters into the
decision.
3. Inanexperimenttoinvestigatewhetherafoodadditiveiscarcinogenic (i.e.,causesorat
least enhances the possibility of having cancer), the U.S. Food and Drug Administration
hasanimals treated withand withouttheadditive.Often,cancerwilldevelopin boththe
treated and untreated groups of animals. In both groups there will be animals that do
Biostatistics:AMethodologyfortheHealthSciences,SecondEdition,byGeraldvanBelle,LloydD.Fisher,
PatrickJ.Heagerty,andThomasS.Lumley
ISBN0-471-03185-2 Copyright2004JohnWiley&Sons,Inc.
1
2 INTRODUCTIONTOBIOSTATISTICS
not develop cancer. There is a need for some method of determining whether the group
treated with the additivehas “too much” cancer.
4. Itiswellknownthat“smokingcausescancer.”Smokingdoesnotcausecancerinthesame
manner that striking a billiard ball with another causes the second billiard ball to move.
Many people smoke heavily for long periods of time and do not develop cancer. The
formation of cancer subsequent to smoking is not an invariable consequence but occurs
only a fraction of the time. Data collected to examine the association between smoking
and cancer must be analyzed with recognition of an uncertain and variable outcome.
5. In designing and planning medical care facilities, planners take into account differing
needs for medical care. Needs change because there are new modes of therapy, as well
as demographic shifts, that may increase or decrease the need for facilities. All of the
uncertaintyassociatedwiththefuturehealthofapopulationanditsfuturegeographicand
demographic patterns should be taken into account.
Inherent inall oftheseexamples is theideaofuncertainty.Similar situationsdo notalways
resultinthesameoutcome.Statisticsdealswiththisvariability.Thissomewhatvagueformula-
tion will become clearer in this book. Many definitions of statistics explicitly bring in the idea
of variability.Some definitions of statisticsare given in the Notes at the end of the chapter.
1.3 WHY BIOSTATISTICS?
Biostatistics isthestudyofstatisticsasappliedtobiologicalareas.Biologicallaboratoryexper-
iments, medical research (including clinical research), and health services research all use
statisticalmethods. Many other biologicaldisciplines rely on statisticalmethodology.
Whyshouldonestudybiostatisticsratherthanstatistics,sincethemethodshavewideappli-
cability?There are three reasons for focusing on biostatistics:
1. Some statistical methods are used more heavily in biostatistics than in other fields. For
example,ageneralstatisticaltextbookwouldnotdiscussthelife-tablemethodofanalyzing
survival data—of importance in many biostatistical applications. The topics in this book
are tailored to the applications in mind.
2. Examples are drawn from the biological, medical, and health care areas; this helps you
maintain motivation. It also helps you understand how to apply statistical methods.
3. Athirdreasonforabiostatisticaltextistoteachthematerialtoanaudienceofhealthpro-
fessionals.Inthiscase,theinteractionbetweenstudentsandteacher,butespeciallyamong
thestudents themselves, is of great value in learning and applying the subject matter.
1.4 GOALS OF THIS BOOK
Suppose that we wanted to learn something about drugs; we can think of four different levels
of knowledge. At the first level, a person may merely know that drugs act chemically when
introducedintothebodyandproducemanydifferenteffects.Asecond,higherlevelofknowledge
is to know that a specific drug is given in certain situations, but we have no idea why the
particular drug works. We do not know whether a drug might be useful in a situation that we
have not yet seen. At the next, third level, we have a good idea why things work and also
know how to administer drugs. At this level we do not have complete knowledge of all the
biochemicalprinciplesinvolved,butwedohaveconsiderableknowledgeabouttheactivityand
workings of the drug.
Finally,atthefourthandhighestlevel,wehavedetailedknowledgeofalloftheinteractions
ofthedrug;weknowthecurrentresearch.Thislevelisappropriateforresearchers:thoseseeking