Quantitative Methods for Health Research

Nigel Bruce, PhD is Emeritus Professor of Public Health at the Department of Public Health and Policy, University of Liverpool, UK. Daniel Pope, PhD is Senior Lecturer in Epidemiology and Public Health at the Department of Public Health and Policy, University of Liverpool, UK. Debbi Stanistreet, PhD is Senior Lecturer and Faculty Director of Widening Participation at the Department of Public Health and Policy, University of Liverpool, UK.

• Preface xvAbout the Companion Website xxi1 Philosophy of Science and Introduction to Epidemiology 1Introduction and Learning Objectives 11.1 Approaches to Scientific Research 21.1.1 History and Nature of Scientific Research 21.1.2 What is Epidemiology? 61.1.3 What are Statistics? 71.1.4 Approach to Learning 81.2 Formulating a Research Question 81.2.1 Importance of a Well-Defined Research Question 81.2.2 Development of Research Ideas 101.3 Rates: Incidence and Prevalence 111.3.1 Why Do We Need Rates? 111.3.2 Measures of Disease Frequency 121.3.3 Prevalence Rate 121.3.4 Incidence Rate 121.3.5 Relationship Between Incidence, Duration, and Prevalence 151.4 Concepts of Prevention 161.4.1 Introduction 161.4.2 Primary, Secondary, and Tertiary Prevention 171.5 Answers to Self-Assessment Exercises 182 Routine Data Sources and Descriptive Epidemiology 25Introduction and Learning Objectives 252.1 Routine Collection of Health Information 262.1.1 Deaths (Mortality) 262.1.2 Compiling Mortality Statistics: The Example of England and Wales 282.1.3 Suicide Among Men 292.1.4 Suicide Among Young Women 312.1.5 Variations in Deaths of Very Young Children 312.2 Descriptive Epidemiology 332.2.1 What is Descriptive Epidemiology? 332.2.2 International Variations in Rates of Lung Cancer 332.2.3 Illness (Morbidity) 342.2.4 Sources of Information on Morbidity 352.2.5 Notification of Infectious Disease 352.2.6 Illness Seen in General Practice 382.3 Information on the Environment 392.3.1 Air Pollution and Health 392.3.2 Routinely Available Data on Air Pollution 392.4 Displaying, Describing, and Presenting Data 412.4.1 Displaying the Data 412.4.2 Calculating the Frequency Distribution 422.4.3 Describing the Frequency Distribution 442.4.4 The Relative Frequency Distribution 572.4.5 Scatterplots, Linear Relationships and Correlation 602.5 Routinely Available Health Data 692.5.1 Introduction 692.5.2 Classification of Routine Health Information Sources 692.5.3 Demographic Data 712.5.4 Health Event Data 732.5.5 Population-Based Health Information 782.5.6 Deprivation Indices 792.5.7 Routine Data Sources for Countries Other Than the UK 802.6 Descriptive Epidemiology in Action 802.6.1 The London Smogs of the 1950s 802.6.2 Ecological Studies 822.7 Overview of Epidemiological Study Designs 842.8 Answers to Self-Assessment Exercises 863 Standardisation 101Introduction and Learning Objectives 1013.1 Health Inequalities in Merseyside 1013.1.1 Socio-Economic Conditions and Health 1013.1.2 Comparison of Crude Death Rates 1023.1.3 Usefulness of a Summary Measure 1043.2 Indirect Standardisation: Calculation of the Standardised Mortality Ratio (SMR) 1053.2.1 Mortality in Liverpool 1053.2.2 Interpretation of the SMR 1073.2.3 Dealing With Random Variation: The 95 per cent Confidence Interval 1073.2.4 Increasing Precision of the SMR Estimate 1083.2.5 Mortality in Sefton 1083.2.6 Comparison of SMRs 1103.2.7 Indirectly Standardised Mortality Rates 1103.3 Direct Standardisation 1103.3.1 Introduction 1103.3.2 An Example: Changes in Deaths From Stroke Over Time 1113.3.3 Using the European Standard Population 1123.3.4 Direct or Indirect: Which Method is Best? 1133.4 Standardisation for Factors Other Than Age 1143.5 Answers to Self-Assessment Exercises 1154 Surveys 123Introduction and Learning Objectives 123Resource Papers 1244.1 Purpose and Context 1244.1.1 Defining the Research Question 1244.1.2 Political Context of Research 1264.2 Sampling Methods 1274.2.1 Introduction 1274.2.2 Sampling 1274.2.3 Probability 1294.2.4 Simple Random Sampling 1304.2.5 Stratified Sampling 1314.2.6 Cluster Random Sampling 1324.2.7 Multistage Random Sampling 1334.2.8 Systematic Sampling 1334.2.9 Convenience Sampling 1334.2.10 Sampling People Who are Difficult to Contact 1334.2.11 Quota Sampling 1344.2.12 Sampling in Natsal- 3 1354.3 The Sampling Frame 1374.3.1 Why Do We Need a Sampling Frame? 1374.3.2 Losses in Sampling 1374.4 Sampling Error, Confidence Intervals, and Sample Size 1394.4.1 Sampling Distributions and the Standard Error 1394.4.2 The Standard Error 1404.4.3 Key Properties of the Normal Distribution 1454.4.4 Confidence Interval (CI) for the Sample Mean 1464.4.5 Estimating Sample Size 1494.4.6 Sample Size for Estimating a Population Mean 1494.4.7 StandardErrorand95percentCIforaPopulationProportion 1504.4.8 Sample Size to Estimate a Population Proportion 1514.5 Response 1534.5.1 Determining the Response Rate 1534.5.2 Assessing Whether the Sample is Representative 1544.5.3 Maximising the Response Rate 1544.6 Measurement 1574.6.1 Introduction: The Importance of Good Measurement 1574.6.2 Interview or Self-Completed Questionnaire? 1574.6.3 Principles of Good Questionnaire Design 1584.6.4 Development of a Questionnaire 1614.6.5 Checking How Well the Interviews and Questionnaires Have Worked 1614.6.6 Assessing Measurement Quality 1654.6.7 Overview of Sources of Error 1694.7 Data Types and Presentation 1714.7.1 Introduction 1714.7.2 Types of Data 1724.7.3 Displaying and Summarising the Data 1734.8 Answers to Self-Assessment Exercises 1765 Cohort Studies 185Introduction and Learning Objectives 185Resource Papers 1865.1 Why Do a Cohort Study? 1865.1.1 Objectives of the Study 1865.1.2 Study Structure 1885.2 Obtaining the Sample 1885.2.1 Introduction 1885.2.2 Sample Size 1905.3 Measurement 1905.3.1 Importance of Good Measurement 1905.3.2 Identifying and Avoiding Measurement Error 1905.3.3 The Measurement of Blood Pressure 1915.3.4 Case Definition 1925.4 Follow-Up 1935.4.1 Nature of the Task 1935.4.2 Deaths (Mortality) 1935.4.3 Non-Fatal Cases (Morbidity) 1945.4.4 Challenges Faced with Follow-Up of a Cohort in a Different Setting 1945.4.5 Assessment of Changes During Follow-Up Period 1965.5 Basic Presentation and Analysis of Results 1985.5.1 Initial Presentation of Findings 1985.5.2 Relative Risk 1995.5.3 Hypothesis Test for Categorical Data: The Chi-Squared Test 2015.5.4 Hypothesis Tests for Continuous Data: The z-Test and the t-Test 2095.6 How Large Should a Cohort Study Be? 2145.6.1 Perils of Inadequate Sample Size 2145.6.2 Sample Size for a Cohort Study 2155.6.3 Example of Output from Sample Size Calculation 2165.7 Assessing Whether an Association is Causal 2185.7.1 The Hill Viewpoints 2185.7.2 Confounding: What Is It and How Can It Be Addressed? 2205.7.3 Does Smoking Cause Heart Disease? 2225.7.4 Confounding in the Physical Activity and Cancer Study 2225.7.5 Methods for Dealing with Confounding 2245.8 Simple Linear Regression 2245.8.1 Approaches to Describing Associations 2245.8.2 Finding the Best Fit for a Straight Line 2265.8.3 Interpreting the Regression Line 2275.8.4 Using the Regression Line 2285.8.5 Hypothesis Test of the Association Between the Explanatory and Outcome Variables 2285.8.6 How Good is the Regression Model? 2295.8.7 Interpreting SPSS Output for Simple Linear Regression Analysis 2315.8.8 First Table: Variables Entered/Removed 2325.9 Introduction to Multiple Linear Regression 2355.9.1 Principles of Multiple Regression 2355.9.2 Using Multivariable Linear Regression to Study Independent Associations 2355.9.3 Investigation of the Effect of Work Stress on Bodyweight 2355.9.4 Multiple Regression in the Cancer Study 2395.9.5 Overview of Regression Methods for Different Types of Outcome 2405.10 Answers to Self-Assessment Exercises 2426 Case–Control Studies 251Introduction and Learning Objectives 251Resource Papers 2526.1 Why do a Case–Control Study? 2536.1.1 Study Objectives 2536.1.2 Study Structure 2546.1.3 Approach to Analysis 2556.1.4 Retrospective Data Collection 2576.1.5 Applications of the Case–Control Design 2586.2 Key Elements of Study Design 2596.2.1 Selecting the Cases 2596.2.2 The Controls 2606.2.3 Exposure Assessment 2626.2.4 Bias in Exposure Assessment 2636.3 Basic Unmatched and Matched Analysis 2656.3.1 The Odds Ratio (OR) 2656.3.2 Calculation of the OR–Simple Matched Analysis 2696.3.3 Hypothesis Tests for Case–Control Studies 2716.4 Sample Size for a Case–Control Study 2736.4.1 Introduction 2736.4.2 What Information is Required? 2736.4.3 An Example of Sample Size Calculation Using OpenEpi 2746.5 Confounding and Logistic Regression 2766.5.1 Introduction 2766.5.2 Stratification 2776.5.3 Logistic Regression 2786.5.4 Example: Multivariable Logistic Regression 2816.5.5 Matched Studies – Conditional Logistic Regression 2876.5.6 Interpretation of Adjusted Results from the New Zealand Study 2876.6 Answers to Self-Assessment Exercises 2897 Intervention Studies 297Introduction and Learning Objectives 297Typology of Intervention Study Designs Described in This Chapter 297Terminology 298Resource Papers 2997.1 Why Do an Intervention Study? 2997.1.1 Study Objectives 2997.1.2 Structure of a Randomised, Controlled Intervention Study 3007.2 Key Elements of Intervention Study Design 3037.2.1 Defining Who Should be Included and Excluded 3037.2.2 Intervention and Control 3047.2.3 Randomisation 3067.2.4 Outcome Assessment 3077.2.5 Blinding 3087.2.6 Ethical Issues for Intervention Studies 3087.3 The Analysis of Intervention Studies 3097.3.1 Review of Variables at Baseline 3107.3.2 Loss to Follow-Up 3117.3.3 Compliance with the Treatment Allocation 3117.3.4 Analysis by Intention-to-Treat 3127.3.5 Analysis per Protocol 3137.3.6 What is the Effect of the Intervention? 3137.3.7 Drawing Conclusions 3157.3.8 Adjustment for Variables Known to Influence the Outcome 3157.3.9 Paired Comparisons 3157.3.10 The Crossover Trial 3177.4 Testing More-Complex Interventions 3187.4.1 Introduction 3187.4.2 Randomised Trial of Individuals for a Complex Intervention 3197.4.3 Factorial Design 3227.4.4 Analysis and Interpretation 3237.4.5 Departure from the Ideal Blinded RCT Design 3277.4.6 The Cluster Randomised Trial 3287.4.7 The Community (Cluster) Randomised Trial 3307.4.8 Non-Randomised Intervention Designs 3327.4.9 The Natural Experiment 3337.5 Analysis of Intervention Studies Using a Cluster Design 3347.5.1 Why Does the Use of Clusters Make a Difference? 3347.5.2 Summarising Clustering Effects: The Intra-Class Correlation Coefficient 3347.5.3 Multi-Level Modelling 3357.5.4 Analysis of the Cluster RCT of Physical Activity 3357.6 How Big Should the Intervention Study Be? 3377.6.1 Introduction 3377.6.2 Sample Size for a Trial with Categorical Data Outcomes 3377.6.3 One-Sided and Two-Sided Tests 3397.6.4 Sample Size for a Trial with Continuous Data Outcomes 3397.6.5 Sample Size for an Intervention Study Using Cluster Design 3407.6.6 Estimation of Sample Size is not a Precise Science 3417.7 Intervention Study Registration, Management, and Reporting 3417.7.1 Introduction 3417.7.2 Registration 3427.7.3 Trial Management 3427.7.4 Reporting Standards (CONSORT) 3437.8 Answers to Self-Assessment Exercises 3448 Life Tables, Survival Analysis, and Cox Regression 355Introduction and Learning Objectives 355Resource Papers 3568.1 Survival Analysis 3568.1.1 Introduction 3568.1.2 Why Do We Need Survival Analysis? 3568.1.3 Censoring 3578.1.4 Kaplan–Meier Survival Curves 3598.1.5 Kaplan–Meier Survival Curves 3618.1.6 The Log-Rank Test 3628.1.7 Interpretation of the Kaplan–Meier Survival Curve 3658.2 Cox Regression 3718.2.1 Introduction 3718.2.2 The Hazard Function 3718.2.3 Assumption of Proportional Hazards 3728.2.4 The Cox Regression Model 3728.2.5 Checking the Assumption of Proportional Hazards 3728.2.6 Interpreting the Cox Regression Model 3738.2.7 Prediction 3748.2.8 Application of Cox Regression 3758.3 Current Life Tables 3778.3.1 Introduction 3778.3.2 Current Life Tables and Life Expectancy at Birth 3778.3.3 Life Expectancy at Other Ages 3798.3.4 Healthy or Disability-Free Life Expectancy 3798.3.5 Abridged Life Tables 3808.3.6 Summary 3818.4 Answers to Self-Assessment Exercises 3819 Systematic Reviews and Meta-Analysis 385Introduction and Learning Objectives 385Increasing Power by Combining Studies 386Resource Papers 3879.1 The Why and How of Systematic Reviews 3879.1.1 Why is it Important that Reviews be Systematic? 3879.1.2 Method of Systematic Review – Overview and Developing a Protocol 3889.1.3 Deciding on the Research Question and Objectives for the Review 3899.1.4 Defining Criteria for Inclusion and Exclusion of Studies 3909.1.5 Identifying Relevant Studies 3919.1.6 Assessment of Methodological Quality 3969.1.7 Extracting Data 3999.1.8 Describing the Results 3999.2 The Methodology of Meta-Analysis 4029.2.1 Method of Meta-Analysis – Overview 4029.2.2 Assessment of Publication Bias – the Funnel Plot 4039.2.3 Heterogeneity 4059.2.4 Calculating the Pooled Estimate 4079.2.5 Presentation of Results: Forest Plot 4089.2.6 Sensitivity Analysis 4099.2.7 Statistical Software for the Conduct of Meta-Analysis 4109.2.8 Another Example of the Value of Meta-Analysis – Identifying a Dangerous Treatment 4119.3 Systematic Reviews and Meta-Analyses of Observational Studies 4149.3.1 Introduction 4149.3.2 Why Conduct a Systematic Review of Observational Studies? 4149.3.3 Approach to Meta-Analysis of Observational Studies 4159.3.4 Method of Systematic Review of Observational Studies 4169.3.5 Method of Meta-Analysis of Observational Studies 4169.4 Reporting and Publishing Systematic Reviews and Meta-Analyses 4189.5 The Cochrane Collaboration 4199.5.1 Introduction 4199.5.2 Cochrane Collaboration Logo 4229.5.3 Collaborative Review Groups 4229.5.4 Cochrane Library 4229.6 Answers to Self-Assessment Exercises 42310 Prevention Strategies and Evaluation of Screening 429Introduction and Learning Objectives 429Resource Papers 43010.1 Concepts of Risk 43010.1.1 Relative and Attributable Risk 43010.1.2 Calculation of AR 43110.1.3 Attributable Fraction (AF) for a Dichotomous Exposure 43210.1.4 Attributable Fraction for Continuous and Multiple Category Exposures 43410.1.5 Years of Life Lost (YLL) and Years Lived with Disability (YLD) 43410.1.6 Disability-Adjusted Life Years (DALYs) 43610.1.7 Burden Attributable to Specific Risk Factors 43810.2 Strategies of Prevention 44010.2.1 The Distribution of Risk in Populations 44010.2.2 High-Risk and Population Approaches to Prevention 44310.2.3 Safety and the Population Strategy 44610.2.4 The High-Risk and Population Strategies Revisited 44710.2.5 Implications of Genomic Research for Disease Prevention 44810.3 Evaluation of Screening Programmes 45010.3.1 Purpose of Screening 45110.3.2 Criteria for Programme Evaluation 45110.3.3 Assessing Validity of a Screening Test 45210.3.4 Methodological Issues in Studies of Screening Programme Effectiveness 46010.3.5 Are the Wilson–Jungner Criteria Relevant Today? 46110.4 Cohort and Period Effects 46310.4.1 Analysis of Change in Risk Over Time 46310.4.2 Example: Suicide Trends in UK Men and Women 46410.5 Answers to Self-Assessment Exercises 46811 Probability Distributions, Hypothesis Testing, and Bayesian Methods 477Introduction and Learning Objectives 477Resource Papers 47811.1 Probability Distributions 47811.1.1 Probability – A Brief Review 47811.1.2 Introduction to Probability Distributions 47911.1.3 Types of Probability Distribution 48111.1.4 Probability Distributions: Implications for Statistical Methods 48711.2 Data That Do Not Fit a Probability Distribution 48811.2.1 Robustness of an Hypothesis Test 48811.2.2 Transforming the Data 48811.2.3 Principles of Non-Parametric Hypothesis Testing 49211.3 Hypothesis Testing: Summary of Common Parametric and Non-Parametric Methods 49311.3.1 Introduction 49311.3.2 Review of Hypothesis Tests 49411.3.3 Fundamentals of Hypothesis Testing 49411.3.4 Summary: Stages of Hypothesis Testing 49511.3.5 Comparing Two Independent Groups 49611.3.6 Comparing Two Paired (or Matched) Groups 50011.3.7 Testing for Association Between Two Groups 50611.3.8 Comparing More Than Two Groups 50811.3.9 Association Between Categorical Variables 51311.4 Choosing an Appropriate Hypothesis Test 51711.4.1 Introduction 51711.4.2 Using a Guide Table for Selecting a Hypothesis Test 51711.4.3 The Problem of Multiple Significance Testing 52011.5 Bayesian Methods 52011.5.1 Introduction: A Different Approach to Inference 52011.5.2 Bayes’ Theorem and Formula 52111.5.3 Application and Relevance 52211.6 Answers to Self-Assessment Exercises 525Bibliography 529Index 533