BMTRY 701 Biostatistical Methods IIBiostatistical Methods IISlide 3Slide 4Expectations (from R. Carter)Other ExpectationsAbout the instructorComputingRegressionSome motivating examplesSlide 11Slide 12More motivating examplesSlide 14Brief OutlineLinear RegressionGraphical DisplaysLinear regression examplePurposes of RegressionBoxplotSlide 21HistogramSlide 23Slide 24Density PlotSlide 26Dot plotAnd…the scatterplotMeasuring the association between X and YSimple vs. Multiple linear regresssionAssociation versus CausationBasic Regression ModelSlide 33Model FeaturesProbability Distribution of YParametersSlide 37SENIC DataSlide 39SENIC Simple Linear Regression ExampleStata Regression ResultsAnother Example: Famous dataScatterplot of 200 records of father son dataRegression ResultsThis is where the term “regression” came fromAside: Design of StudiesEstimation of the ModelLeast SquaresSlide 49Slide 50Slide 51BMTRY 701Biostatistical Methods IIElizabeth Garrett-Mayer, PhDAssociate ProfessorDirector of Biostatistics, Hollings Cancer [email protected] Methods IIDescription: This is a one-semester course intended for graduate students pursuing degrees in biostatistics and related fields such as epidemiology and bioinformatics. Topics covered will include linear, logistic, poisson, and Cox regression. Advanced topics will be included, such as ridge regression or hierarchical linear regression if time permits. Estimation, interpretation, and diagnostic approaches will be discussed. Software instruction will be provided in class in R and Stata. Students will be evaluated via homeworks (55%), two in-class exams (35%) and class participation (10%). This is a four credit course.Textbook: Applied Linear Statistical Models. Kutner, Nachtsheim, Neter and Li. McGraw-Hill, Fifth EditionPrerequisites: Biometry 700Course Objectives: Upon successful completion of the course, the student will be able to•Apply, interpret and diagnose linear regression models•Apply, interpret and diagnose logistic, poisson and Cox regresssion modelsBiostatistical Methods IIInstructor: Elizabeth Garrett-MayerWebsite:http://people.musc.edu/~elg26/teaching/methods2.2009/methods2.2009.htmContact Info: Hollings Cancer Center, Rm 118G [email protected] (preferred mode of contact is email) 792-7764Time: Mondays and Wednesdays, 1:30-3:30Location: Cannon Place, Room 305VBiostatistical Methods IILecture schedule is on the websiteFirst time teaching this class•syllabus is a ‘work in progress’•timing of topics subject to change•lectures may appear on website last-minuteComputing•R•Stata•integrated into lecture timeHomeworks, articles, datasets will also be posted to website•some/most problems will be from textbook•some datasets will be from textbook CDIf you want printed versions of lectures:•download and print prior to lecture; OR•work interactively on your laptop during classWe will take a break about halfway through each lectureExpectations (from R. Carter)Academic•Participate in class discussions•Invest resources in YOUR education•Complete homework assignments on time•The results of the homework should be communicated so that a person knowledgable in the methodology could reproduce your results.•Create your own study groupsChallenge one anothereveryone needs to contributeyou may do homeworks together, but everyone must turn in his/her own homework. written sections of homework should be ‘independently’ developedGeneral•Be on time to class•Be discrete with interruptions (pages, phones, etc.)•Do NOT turn in raw computer outputOther ExpectationsMethods I!You should be very familiar with•confidence intervals•hypothesis testingt-testsZ-tests•graphical displays of data•exploratory data analysisestimating means, medians, quantiles of dataestimating variances, standard deviationsAbout the instructorB.A. from Bowdoin College, 1994•Double Major in Mathematics and Economics •Minor in ClassicsPh.D. in Biostatistics from Johns Hopkins, 2000•Dissertation research in latent class models, Adviser Scott ZegerAssistant Professor in Oncology and Biostatistics at JHU, 2000-2007Taught course in Statistics for Psychosocial Research for 8 yearsApplied Research Areas:•oncologyBiostats Research Areas: •latent variable modeling•class discovery in microarray data•methodology for early phase oncology clinical trialsCame to MUSC in Feb 2007ComputingWho knows what?Who WANTS to know what?Who will bring a laptop to class?What software do you have and/or prefer?Should we get a lab classroom?RegressionPurposes of Regresssion1. Describe association between Y and X’s2. Make predictions:Interpolation: making prediction within a range of X’sExtrapolation: making prediction outside a range of X’s3. To “adjust” or “control for” confounding variablesWhat is “Y”?•an outcome variable•‘dependent’ variable•‘response’Type of regression depends on type of Y•continuous (linear regression)•binary (logistic regression)•time-to-event (Cox regression)•rare event or rate (poisson regression)Some motivating examplesExample 1: Suppose we are interested in studying the relationship between fasting blood glucose (FBG) levels and the number hours per day of aerobic exercise. Let Y denote the fasting blood glucose level•Let X denote the number of hours of exercise•One may be interested in studying the relationship of Y and XSimple linear regression can be used to quantify this relationshipSome motivating examplesExample 2: Consider expanding example 1 to include other factors that could be related FBG.Let X1 denote hours of exerciseLet X2 denote BMILet X3 indicate if the person has diabetes. . . (other covariates possible)One may be interested in studying the relationship of all X′s on Y and identifying the “best” combination of factorsNote: Some of the X′s may correlated (e.g., exercise and bmi)Multiple (or multivariable, not multivariate) linear regression can be used to quantify this relationshipSome motivating examplesExample 3: Myocardial infarction (MI, heart attack) is often a life-altering eventLet Y denote the occurrence (Y = 1) of an MI after treatment, let Y = 0 denote no MILet X1 denote the dosage of aspirin takenLet X2 denote the age of the person. . .