Regression Methods for Medical Research

Bee Choo Tai, David Machin

• Publisher: Wiley-Blackwell
• Year: 2013
• Print ISBN: 9781444331448
• eBook ISBN: 9781118721988
• Edition: 1
• Topic: Medicine
• Subtopic: Public Health, Administration & Care

Regression Methods for Medical Research provides medical researchers with the skills they need to critically read and interpret research using more advanced statistical methods. The statistical requirements of interpreting and publishing in medical journals, together with rapid changes in science and technology, increasingly demands an understanding of more complex and sophisticated analytic procedures.

The text explains the application of statistical models to a wide variety of practical medical investigative studies and clinical trials. Regression methods are used to appropriately answer the key design questions posed and in so doing take due account of any effects of potentially influencing co-variables. It begins with a revision of basic statistical concepts, followed by a gentle introduction to the principles of statistical modelling. The various methods of modelling are covered in a non-technical manner so that the principles can be more easily applied in everyday practice. A chapter contrasting regression modelling with a regression tree approach is included. The emphasis is on the understanding and the application of concepts and methods. Data drawn from published studies are used to exemplify statistical concepts throughout.

Regression Methods for Medical Research is especially designed for clinicians, public health and environmental health professionals, para-medical research professionals, scientists, laboratory-based researchers and students.

1 Introduction

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SUMMARY

A very large number of clinical studies with human subjects have and are being ­conducted in a wide range of settings. The design and analysis of such studies demands the use of statistical models in this process. To describe such situations involves specifying the model, including defining population regression coefficients (the parameters), and then stipulating the way these are to be estimated from the data arising from the subjects (the sample) who have been recruited to the study. This chapter introduces the simple linear regression model to describe studies in which the measure made on the subjects can be assumed to be a continuous variable, the value of which is thought to depend either on a single binary or a continuous covariate measure.

Associated statistical methods are also described defining the null hypothesis, estimating means and standard deviations, comparing groups by use of a z- or t-test, confidence intervals and p-values. We give examples of how a statistical computer package facilitates the relevant analyses and also provides support for suitable graphical display.

Finally, examples from the medical and associated literature are used to illustrate the wide range of application of regression techniques: further details of some of these examples are included in later chapters.

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INTRODUCTION

The aim of this book is to introduce those who are involved with medical studies whether laboratory, clinic, or population based, to the wide range of regression techniques which are pertinent to the design, analysis, and reporting of the studies concerned. Thus our intended readership is expected to range from health care professionals of all disciplines who are concerned with patient care, to those more involved with the non-clinical aspects such as medical support and research in the laboratory and beyond.

Even in the simplest of medical studies in which, for example, recording of a single ­feature from a series of samples taken from individual patients is made, one may ask questions as to why the resulting values differ from each other. It may be that they differ between the genders and/or between the different ages of the patients concerned, or because of the severity of their illnesses. In more formal terms we examine whether or not the value of the observed variable, y, depends on one or more of the (covariate) variables, often termed the x’s. Although the term covariate is used here in a generic sense, we will emphasize that individually they may play different roles in the design and hence analysis of the study of which they are a part. If one or more covariates does influence the outcome, then we are essentially claiming that part of the variation in y is a result of individual patients having different values of the x’s concerned. In which case, any variation remaining after taking into consideration these covariates is termed the residual or random variation. If the covariates do not have influence, then we have not explained (strictly not explained an important part of) the variation in y by the x’s. Nevertheless, there may be other covariates of which we are not aware that would.

Measurements made on human subjects rarely give exactly the same results from one occasion to the next. Even in adults, height varies a little during the course of the day. If one measures the cholesterol levels of an individual on one particular day and then again the following day, under exactly the same conditions, greater variation in this than that of height would be expected. Any variation that we cannot ascribe to one or more covariates is usually termed random variation, although, as we have indicated, it may be that an unknown covariate may account for some of this. The levels of inherent variability may be very high so that, perhaps in the circumstances where a subject has an illness, the oscillations in these measurements may disguise, at least in the early stages of treatment, the beneficial effect of treatment given to improve the condition.

STATISTICAL MODELS

Whatever the type of study, it is usually convenient to think of the underlying structure of the design in terms of a statistical model. This model encapsulates the research question we intend to formulate and ultimately answer. Once the model is specified, the object of the corresponding study (and hence the eventual analysis) is to estimate the parameters of this model as precisely as is reasonable.

Comparing two means

Suppose a study is designed to investigate the relationship between high density lipoprotein (HDL) cholesterol levels and gender. Once the study has been conducted, the observed data for each gender may be plotted in a histogram format as in Figure 1.1.

These figures illustrate a typical situation in that there is considerable variation in the value of the continuous variable HDL ranging from approximately 0.4 to 2.0 mmol/L. Further, both distributions tend to peak towards the centre of their ranges and there is a suggestion of a difference between males and females. In fact the mean value is higher at

= 1.2135 for the females compared with

= 1.0085 mmol/L for the males.

Formal comparisons between these two groups can be made using a statistical significance test. Thus, we can regard

and

as estimates of the true or population mean values μ_F and μ_M. The corresponding standard deviations are given by s_F = 0.3425 and s_M = 0.2881 mmol/L, and these estimate the respective population values σ_F and σ_M. To test the null hypothesis of no difference in HDL levels between males and females, the usual procedure is to assume HDL within each group has an app...

Table of contents

• Cover
• Title page
• Copyright page
• Dedication
• Preface
• 1 Introduction
• 2 Linear Regression: Practical Issues
• 3 Multiple Linear Regression
• 4 Logistic Regression
• 5 Poisson Regression
• 6 Time-to-Event Regression
• 7 Model Building
• 8 Repeated Measures
• 9 Regression Trees
• 10 Further Time-to-Event Models
• 11 Further Topics
• Statistical Tables
• References
• Index