> help.start() > help.start() > exp(-5) > exp(-5) [1] 0.006738 [1] 0.006738 9 9 > log(3.8 > log(3.8 + ) + ) 50 [1] 1.335001 [1] 1.335001 40 30 Virasakdi Chongsuvivatwong 20 10 Analysis of epidemiological0 data using R and Epicalc Epidemiology Unit Prince of Songkla University THAILAND EPICALC–OK.indd 1 20.2.2008 15:24:54 Analysis of Epidemiological Data Using R and Epicalc Author: Virasakdi Chongsuvivatwong [email protected] Epidemiology Unit Prince of Songkla University THAILAND Preface Data analysis is very important in epidemiological research. The capacity of computing facilities has been steadily increasing, moving state of the art epidemiological studies along the same direction of computer advancement. Currently, there are many commercial statistical software packages widely used by epidemiologists around the world. For developed countries, the cost of software is not a major problem. For developing countries however, the real cost is often too high. Several researchers in developing countries thus eventually rely on a pirated copy of the software. Freely available software packages are limited in number and readiness of use. EpiInfo, for example, is free and useful for data entry and simple data analysis. Advanced data analysts however find it too limited in many aspects. For example, it is not suitable for data manipulation for longitudinal studies. Its regression analysis facilities cannot cope with repeated measures and multi-level modelling. The graphing facilities are also limited. A relatively new and freely available software called R is promising. Supported by leading statistical experts worldwide, it has almost everything that an epidemiological data analyst needs. However, it is difficult to learn and to use compared with similar statistical packages for epidemiological data analysis such as Stata. The purpose of this book is therefore to bridge this gap by making R easy to learn for researchers from developing countries and also to promote its use. My experience in epidemiological studies spans over twenty years with a special fondness of teaching data analysis. Inspired by the spirit of the open-source software philosophy, I have spent a tremendous effort exploring the potential and use of R. For four years, I have been developing an add-on package for R that allows new researchers to use the software with enjoyment. More than twenty chapters of lecture notes and exercises have been prepared with datasets ready for self-study. Supported by WHO, TDR and the Thailand Research Fund, I have also run a number of workshops for this software in developing countries including Thailand, Myanmar, North Korea, Maldives and Bhutan, where R and Epicalc was very much welcomed. With this experience, I hereby propose that the use of this software should be encouraged among epidemiological researchers, especially for those who cannot afford to buy expensive commercial software packages. i R is an environment that can handle several datasets simultaneously. Users get access to variables within each dataset either by copying it to the search path or by including the dataset name as a prefix. The power of R in this aspect is a drawback in data manipulation. When creating a variable or modifying an existing one, without prefixing the dataset name, the new variable is isolated from its parental dataset. If prefixing is the choice, the original data is changed but not the copy in the search path. Careful users need to remove the copy in the search path and recopy the new dataset into it. The procedure in this aspect is clumsy. Not being tidy will eventually end up with too many copies in the search path overloading the system or confusing the analyst on where the variable is actually located. Epicalc presents a concept solution for common types of work where the data analyst works on one dataset at a time using only a few commands. In Epicalc the user can virtually eliminate the necessity of specifying the dataset and can avoid overloading of the search path very effectively and efficiently. In addition to make tidying of memory easy to accomplished, Epicalc makes it easy to recognize the variables by adopting variable labels or descriptions which have been prepared from other software such as SPSS or Stata or locally prepared by Epicalc itself. R has very powerful graphing functions that the user has to spend time learning. Epicalc exploits this power by producing a nice plot of the distribution automatically whenever a single variable is summarised. A breakdown of the first variable by a second categorical variable is also simple and graphical results are automatically displayed. This automatic graphing strategy is also applied to one- way tabulation and two-way tabulation. Description of the variables and the value or category labels are fully exploited with these descriptive graphs. Additional epidemiological functions added in by Epicalc include calculation of sample size, matched 1:n (n can vary) tabulation, kappa statistics, drawing of ROC curve from a table or from a logistic regression results, population pyramid plots from age and sex and follow-up plots. R has several advanced regression modelling functions such as multinomial logistic regression, ordinal logistic regression, survival analysis and multi-level modelling. By using Epicalc nice tables of odds ratios and 95% CI are produced, ready for simple transferal into a manuscript document with minimal further modification required. Although use of Epicalc implies a different way of working with R from conventional use, installation of Epicalc has no effect on any existing or new functions of R. Epicalc functions only increase efficiency of data analysis and makes R easier to use. ii This book is essentially about learning R with an emphasis on Epicalc. Readers should have some background in basic computer usage. With R, Epicalc and the supplied datasets, the users should be able to go through each lesson learning the concepts of data management, related statistical theories and the practice of data analysis and powerful graphing. The first four chapters introduce R concepts and simple handling of important basic elements such as scalars, vectors, matrices, arrays and data frames. Chapter 5 deals with simple data exploration. Date and time variables are defined and dealt with in Chapter 6 and fully exploited in a real dataset in Chapter 7. Descriptive statistics and one-way tabulations are automatically accompanied by corresponding graphs making it rather unlikely that important information is overlooked. Finally, time plots of exposure and disease onsets are plotted with a series of demonstrating commands. Chapter 8 continues to investigate the outbreak by two-way tabulation. Various kinds of risk assessment, such as the risk ratio and protective efficacy, are analysed with numeric and graphic results. Chapter 9 extends the analysis of the dataset to deal with levels of association or odds ratios. Stratified tabulation, the Mantel-Haenzsel odds ratio, and test of homogeneity of odds ratios are explained in detail. All results are complemented by simultaneous plots. With these graphs, the concept of confounding is made more understandable. Before proceeding further, the reader has a thorough exercise of data cleaning and standard data manipulation in Chapter 10. Simple looping commands are introduced to increase the efficiency of data management. Subsequently, and from time to time in the book, readers will learn how to develop these loops to create powerful graphs. Scatter plots, simple linear regression and analysis of variance are presented in Chapter 11. Stratified scatter plots to enhance the concept of confounding and interaction for continuous outcome variables are given in Chapter 12. Curvilinear models are discussed in Chapter 13. Linear modelling is extended to generalized linear modelling in Chapter 14. For binary outcome variables, Chapter 15 introduces logistic regression with additional comparison with stratified cross-tabulation learned in Chapter 9. The concept of a matched case control study is discussed in Chapter 16 with matched tabulation for 1:1 and 1:n matching. Finally, conditional logistic regression is applied. Chapter 17 introduces polytomous logistic regression using a case-control study in which one type of case series is compared with two types of control groups. Ordinal logistic regression is applied for ordered outcomes in Chapter 18. iii For a cohort study, with grouped exposure datasets, Poisson regression is used in Chapter 19. Extra-Poisson regression for overdispersion is also discussed. This includes modeling the outcome using the negative binomial error distribution. Multi-level modelling and longitudinal data analysis are discussed in Chapter 20. For cohort studies with individual follow-up times, survival analysis is discussed in Chapter 21 and the Cox proportional hazard model is introduced in Chapter 22. In chapter 23 the focus is on analyzing datasets involving attitudes, such as those encountered in the social sciences. Chapter 24 deals with day-to-day work in calculation of sample sizes and the technique of documentation that all professional data analysts must master is explained in Chapter 25. Some suggested strategies for handling large datasets are given in chapter 26. The book ends with a demonstration of the tableStack command, which dramatically shortens the preparation of a tidy stack of tables with a special technique of copy and paste into a manuscript. At the end of each chapter some references are given for further reading. Most chapters also end with some exercises to practice on. Solutions to these are given at the end of the book. Colour It is assumed that the readers of this book will simultaneously practice the commands and see the results on the screen. The explanations in the text sometimes describe the colour of graphs that appear in black and white in this book (the reason for this is purely for reducing the printing costs). The electronic copy of the book, however, does include colour.