Biostatistics: A Computing Approach A Computing Approach

Focusing on visualization and computational approaches with an emphasis on the importance of simulation, Biostatistics introduces modern and classical biostatistical methods and compares their respective usefulness. The book covers essential topics in biostatistical science, including simple linear regression, multivariate regression, repeated measure, nonparametric analysis, survival analysis, sample size, and power calculations. Assuming only basic knowledge of probability and statistics, the text offers numerous practical applications and detailed worked examples taken from the medical area, all computed using R and SAS, as well as exercises with solutions.

The emergence of high-speed computing has facilitated the development of many exciting statistical and mathematical methods in the last 25 years, broadening the landscape of available tools in statistical investigations of complex data. Biostatistics: A Computing Approach focuses on visualization and computational approaches associated with both modern and classical techniques. Furthermore, it promotes computing as a tool for performing both analyses and simulations that can facilitate such understanding. As a practical matter, programs in R and SAS are presented throughout the text. In addition to these programs, appendices describing the basic use of SAS and R are provided. Teaching by example, this book emphasizes the importance of simulation and numerical exploration in a modern-day statistical investigation. A few statistical methods that can be implemented with simple calculations are also worked into the text to build insight about how the methods really work. Suitable for students who have an interest in the application of statistical methods but do not necessarily intend to become statisticians, this book has been developed from Introduction to Biostatistics II, which the author taught for more than a decade at the University of Pittsburgh.

PrefaceReview of Topics in Probability and StatisticsIntroduction to ProbabilityConditional ProbabilityRandom VariablesThe Uniform distributionThe Normal distributionThe Binomial DistributionThe Poisson DistributionThe Chi–Squared DistributionStudent’s t–distributionThe F-distributionThe Hypergeometric DistributionThe Exponential DistributionExercisesUse of Simulation TechniquesIntroductionWhat can we accomplish with simulations?How to employ a simple simulation strategyGeneration of Pseudorandom NumbersGenerating Discrete and Continuous random variablesTesting Random Number GeneratorsA Brief Note on the Efficiency of Simulation AlgorithmsExercisesThe Central Limit TheoremIntroductionThe Strong Law of Large NumbersThe Central Limit TheoremSummary of the Inferential Properties of the Sample MeanAppendix: Program ListingsExercisesCorrelation and RegressionIntroductionPearson’s Correlation CoefficientSimple Linear RegressionMultiple RegressionVisualization of DataModel Assessment and Related TopicsPolynomial RegressionSmoothing TechniquesAppendix: A Short Tutorial in Matrix AlgebraExercisesAnalysis of VarianceIntroductionOne–Way Analysis of VarianceGeneral ContrastMultiple Comparisons ProceduresGabriel’s methodDunnett’s ProcedureTwo-Way Analysis of Variance: Factorial DesignTwo-Way Analysis of Variance: Randomized Complete BlocksAnalysis of CovarianceExercisesDiscreteMeasures of RiskIntroductionOdds Ratio (OR) and Relative Risk (RR)Calculating risk in the presence of confoundingLogistic RegressionUsing SAS and R for Logistic RegressionComparison of Proportions for Paired DataExercisesMultivariate AnalysisThe Multivariate Normal DistributionOne and Two Sample Multivariate InferenceMultivariate Analysis of VarianceMultivariate Regression AnalysisClassification MethodsExercisesAnalysis of Repeated Measures DataIntroductionPlotting Repeated Measures DataUnivariate Approaches for the Analysis of Repeated Measures DataCovariance Pattern ModelsMultivariate ApproachesModern Approaches for the Analysis of Repeated Measures DataAnalysis of Incomplete Repeated Measures DataExercisesNonparametricMethodsIntroductionComparing Paired DistributionsComparing Two Independent DistributionsKruskal–Wallis TestSpearman’s rhoThe BootstrapExercisesAnalysis of Time to Event DataIncidence Density (ID)Introduction to Survival AnalysisEstimation of the Survival CurveEstimating the Hazard FunctionComparing Survival in Two GroupsCox Proportional Hazards ModelCumulative IncidenceExercisesSample size and power calculationsSample sizes and power for tests of normally distributed dataSample size and power for Repeated Measures DataSample size and power for survival analysisConstructing Power CurvesExercisesAppendix A: Using SASIntroductionData input in SASSome Graphical Procdures: PROC PLOT and PROC CHARTSome Simple Data Analysis ProceduresDiagnosing errors in SAS programsExercisesAppendix B: Using RIntroductionGetting startedInput/OutputSome Simple Data Analysis ProceduresUsing R for plotsComparing an R–session to a SAS sessionDiagnosing problems in R programsExercisesReferencesIndex