Читать книгу Applied Biostatistics for the Health Sciences - Richard J. Rossi - Страница 10

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 1–7 covering the basic inferential biostatistical methods used to describe sample data arising in a biomedical or health-related study. Chapters 8–13 cover 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 1 provides 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 2 introduces variables, populations, population parameters, probability, and the binomial and normal probability models. Several biomedical parameters are introduced in Chapter 2 including 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 5 with emphasis on evaluating the reliability of a point estimator. The topics discussed in Chapter 5 include 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 7 includes 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 8 is the first chapter in a series of chapters on modeling a response variable. The topics covered in Chapter 8 include 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 9 extends and broadens the methods discussed in Chapter 8 to multiple regression models. The multiple regression topics that are discussed in Chapter 9 include 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.

 Chapter 10: Logistic Regression. Because building a logistic regression model is similar to building a linear regression model, the discussion of logistic regression follows immediately after the two chapters on linear regression. Topics discussed in Chapter 10 include the odds of an event, the odds ratio, logistic regression models, fitting and assessing the fit of a logistic regression model, drawing inferences from a logistic regression model, and variable selection.

 Chapter 11: Design of Experiments. Chapter 11 provides an introduction to designing an experiment and precedes the typical chapter on analysis of variance. Topics covered in Chapter 11 include a discussion of experiments and observational studies, the completely randomized and randomized block designs, factorial experiments, and linear models for designed experiments.

 Chapter 12: Analysis of Variance. Chapter 12 is the traditional chapter on analysis of variance. In Chapter 12, analysis of variance is discussed for single factor, randomized block, and factorial studies including discussions of the F-tests, the Bonferroni method of separating means, and methods for determining the number of replications needed for a study.

 Chapter 13: Survival Analysis. Chapter 13 introduces methods for analyzing survival data. In particular, survival data, survivor functions, censoring, the Kaplan–Meier nonparametric estimator, the log-rank test, Cox’s proportional hazards semiparametric estimator, and logistic regression for survival data are discussed.

This book was intended neither to cover all of the methods used in the statistical analysis of biomedical and healthcare data nor to be used as cookbook with recipes for several different statistical analyses. The primary emphasis of this book is to introduce students to the basic ideas of biostatistics and modeling approaches used in biostatistics.

It is also my experience that the order of presentation is appropriate for the nurture and development of the student’s confidence and statistical maturity. I also believe that the statistical methods and ideas presented in Applied Biostatistics for the Health Sciences will provide a student with the necessary statistical tools required to succeed in advanced statistics courses such as linear or logistic regression, design and analysis of experimental data, multivariate statistics, analysis of microarray data, and survival analysis.