Analysis of Incidence Rates

 
 
Routledge Cavendish (Verlag)
  • erschienen am 16. April 2019
  • |
  • 492 Seiten
 
E-Book | PDF mit Adobe DRM | Systemvoraussetzungen
978-0-429-62120-8 (ISBN)
 
Incidence rates are counts divided by person-time; mortality rates are a well-known example. Analysis of Incidence Rates offers a detailed discussion of the practical aspects of analyzing incidence rates. Important pitfalls and areas of controversy are discussed. The text is aimed at graduate students, researchers, and analysts in the disciplines of epidemiology, biostatistics, social sciences, economics, and psychology. Features: Compares and contrasts incidence rates with risks, odds, and hazards. Shows stratified methods, including standardization, inverse-variance weighting, and Mantel-Haenszel methods Describes Poisson regression methods for adjusted rate ratios and rate differences. Examines linear regression for rate differences with an emphasis on common problems. Gives methods for correcting confidence intervals. Illustrates problems related to collapsibility. Explores extensions of count models for rates, including negative binomial regression, methods for clustered data, and the analysis of longitudinal data. Also, reviews controversies and limitations. Presents matched cohort methods in detail. Gives marginal methods for converting adjusted rate ratios to rate differences, and vice versa. Demonstrates instrumental variable methods. Compares Poisson regression with the Cox proportional hazards model. Also, introduces Royston-Parmar models. All data and analyses are in online Stata files which readers can download. Peter Cummings is Professor Emeritus, Department of Epidemiology, School of Public Health, University of Washington, Seattle WA. His research was primarily in the field of injuries. He used matched cohort methods to estimate how the use of seat belts and presence of airbags were related to death in a traffic crash. He is author or co-author of over 100 peer-reviewed articles.
  • Englisch
  • Milton
  • |
  • Großbritannien
Taylor & Francis Ltd
  • Für höhere Schule und Studium
63 schwarz-weiße Abbildungen, 77 schwarz-weiße Tabellen
978-0-429-62120-8 (9780429621208)
weitere Ausgaben werden ermittelt

Peter Cummings is Professor Emeritus, Department of Epidemiology, School of Public Health, University of Washington, Seattle WA. His research was primarily in the field of injuries. He used matched cohort methods to estimate how the use of seat belts and presence of airbags were related to death in a traffic crash. He is author or co-author of over 100 peer-reviewed articles.

  • Cover
  • Half Title
  • Series Page
  • Title Page
  • Copyright Page
  • Table of Contents
  • Preface
  • Author
  • 1. Do Storks Bring Babies?
  • 1.1 Karl Pearson and Spurious Correlation
  • 1.2 Jerzy Neyman, Storks, and Babies
  • 1.3 Is Poisson Regression the Solution to the Stork Problem?
  • 1.4 Further Reading
  • 2. Risks and Rates
  • 2.1 What Is a Rate?
  • 2.2 Closed and Open Populations
  • 2.3 Measures of Time
  • 2.4 Numerators for Rates: Counts
  • 2.5 Numerators that May Be Mistaken for Counts
  • 2.6 Prevalence Proportions
  • 2.7 Denominators for Rates: Count Denominators for Incidence Proportions (Risks)
  • 2.8 Denominators for Rates: Person-Time for Incidence Rates
  • 2.9 Rate Numerators and Denominators for Recurrent Events
  • 2.10 Rate Denominators Other than Person-Time
  • 2.11 Different Incidence Rates Tell Different Stories
  • 2.12 Potential Advantages of Incidence Rates Compared With Incidence Proportions (Risks)
  • 2.13 Potential Advantages of Incidence Proportions (Risks) Compared with Incidence Rates
  • 2.14 Limitations of Risks and Rates
  • 2.15 Radioactive Decay: An Example of Exponential Decline
  • 2.16 The Relevance of Exponential Decay to Human Populations
  • 2.17 Relationships Between Rates, Risks, and Hazards
  • 2.18 Further Reading
  • 3. Rate Ratios and Differences
  • 3.1 Estimated Associations and Causal Effects
  • 3.2 Sources of Bias in Estimates of Causal Effect
  • 3.3 Estimation versus Prediction
  • 3.4 Ratios and Differences for Risks and Rates
  • 3.5 Relationships between Measures of Association in a Closed Population
  • 3.6 The Hypothetical TEXCO Study
  • 3.7 Breaking the Rules: Army Data for Companies A and B
  • 3.8 Relationships between Odds Ratios, Risk Ratios, and Rate Ratios in Case-Control Studies
  • 3.9 Symmetry of Measures of Association
  • 3.10 Convergence Problems for Estimating Associations
  • 3.11 Some History Regarding the Choice between Ratios and Differences
  • 3.12 Other Influences on the Choice between Use of Ratios or Differences
  • 3.13 The Data May Sometimes Be Used to Choose between a Ratio or a Difference
  • 4. The Poisson Distribution
  • 4.1 Alpha Particle Radiation
  • 4.2 The Poisson Distribution
  • 4.3 Prussian Soldiers Kicked to Death by Horses
  • 4.4 Variances, Standard Deviations, and Standard Errors for Counts and Rates
  • 4.5 An Example: Mortality from Alzheimer's Disease
  • 4.6 Large Sample P-values for Counts, Rates, and Their Differences using the Wald Statistic
  • 4.7 Comparisons of Rates as Differences versus Ratios
  • 4.8 Large Sample P-values for Counts, Rates, and Their Differences using the Score Statistic
  • 4.9 Large Sample Confidence Intervals for Counts, Rates, and Their Differences
  • 4.10 Large Sample P-values for Counts, Rates, and Their Ratios
  • 4.11 Large Sample Confidence Intervals for Ratios of Counts and Rates
  • 4.12 A Constant Rate Based on More Person-Time Is More Precise
  • 4.13 Exact Methods
  • 4.14 What Is a Poisson Process?
  • 4.15 Simulated Examples
  • 4.16 What If the Data Are Not from a Poisson Process? Part 1, Overdispersion
  • 4.17 What If the Data Are Not from a Poisson Process? Part 2, Underdispersion
  • 4.18 Must Anything Be Rare?
  • 4.19 Bicyclist Deaths in 2010 and 2011
  • 5. Criticism of Incidence Rates
  • 5.1 Florence Nightingale, William Farr, and Hospital Mortality Rates. Debate in 1864
  • 5.2 Florence Nightingale, William Farr, and Hospital Mortality Rates. Debate in 1996-1997
  • 5.3 Criticism of Rates in the British Medical Journal in 1995
  • 5.4 Criticism of Incidence Rates in 2009
  • 6. Stratified Analysis: Standardized Rates
  • 6.1 Why Standardize?
  • 6.2 External Weights from a Standard Population: Direct Standardization
  • 6.3 Comparing Directly Standardized Rates
  • 6.4 Choice of the Standard Influences the Comparison of Standardized Rates
  • 6.5 Standardized Comparisons versus Adjusted Comparisons from Variance-Minimizing Methods
  • 6.6 Stratified Analyses
  • 6.7 Variations on Directly Standardized Rates
  • 6.8 Internal Weights from a Population: Indirect Standardization
  • 6.9 The Standardized Mortality Ratio (SMR)
  • 6.10 Advantages of SMRs Compared with SRRs (Ratios of Directly Standardized Rates)
  • 6.11 Disadvantages of SMRs Compared with SRRs (Ratios of Directly Standardized Rates)
  • 6.12 The Terminology of Direct and Indirect Standardization
  • 6.13 P-values for Directly Standardized Rates
  • 6.14 Confidence Intervals for Directly Standardized Rates
  • 6.15 P-values and CIs for SRRs (Ratios of Directly Standardized Rates)
  • 6.16 Large Sample P-values and CIs for SMRs
  • 6.17 Small Sample P-values and CIs for SMRs
  • 6.18 Standardized Rates Should Not Be used as Regression Outcomes
  • 6.19 Standardization Is Not Always the Best Choice
  • 7. Stratified Analysis: Inverse-Variance and Mantel-Haenszel Methods
  • 7.1 Inverse-variance Methods
  • 7.2 Inverse-Variance Analysis of Rate Ratios
  • 7.3 Inverse-Variance Analysis of Rate Differences
  • 7.4 Choosing between Rate Ratios and Differences
  • 7.5 Mantel-Haenszel Methods
  • 7.6 Mantel-Haenszel Analysis of Rate Ratios
  • 7.7 Mantel-Haenszel Analysis of Rate Differences
  • 7.8 P-values for Stratified Rate Ratios or Differences
  • 7.9 Analysis of Sparse Data
  • 7.10 Maximum-Likelihood Stratified Methods
  • 7.11 Stratified Methods versus Regression
  • 8. Collapsibility and Confounding
  • 8.1 What Is Collapsibility?
  • 8.2 The British X-Trial: Introducing Variation in Risk
  • 8.3 Rate Ratios and Differences Are Noncollapsible because Exposure Influences Person-Time
  • 8.4 Which Estimate of the Rate Ratio Should We Prefer?
  • 8.5 Behavior of Risk Ratios and Differences
  • 8.6 Hazard Ratios and Odds Ratios
  • 8.7 Comparing Risks with Other Outcome Measures
  • 8.8 The Italian X-Trial: 3-Levels of Risk under No Exposure
  • 8.9 The American X-Cohort Study: 3-Levels of Risk in a Cohort Study
  • 8.10 The Swedish X-Cohort Study: A Collapsible Risk Ratio in Confounded Data
  • 8.11 A Summary of Findings
  • 8.12 A Different View of Collapsibility
  • 8.13 Practical Implications: Avoid Common Outcomes
  • 8.14 Practical Implications: Use Risks or Survival Functions
  • 8.15 Practical Implications: Case-Control Studies
  • 8.16 Practical Implications: Uniform Risk
  • 8.17 Practical Implications: Use All Events
  • 9. Poisson Regression for Rate Ratios
  • 9.1 The Poisson Regression Model for Rate Ratios
  • 9.2 A Short Comparison with Ordinary Linear Regression
  • 9.3 A Poisson Model without Variables
  • 9.4 A Poisson Regression Model with One Explanatory Variable
  • 9.5 The Iteration Log
  • 9.6 The Header Information above the Table of Estimates
  • 9.7 Using a Generalized Linear Model to Estimate Rate Ratios
  • 9.8 A Regression Example: Studying Rates over Time
  • 9.9 An Alternative Parameterization for Poisson Models: A Regression Trick
  • 9.10 Further Comments about Person-Time
  • 9.11 A Short Summary
  • 10. Poisson Regression for Rate Differences
  • 10.1 A Regression Model for Rate Differences
  • 10.2 Florida and Alaska Cancer Mortality: Regression Models that Fail
  • 10.3 Florida and Alaska Cancer Mortality: Regression Models that Succeed
  • 10.4 A Generalized Linear Model with a Power Link
  • 10.5 A Caution
  • 11. Linear Regression
  • 11.1 Limitations of Ordinary Least Squares Linear Regression
  • 11.2 Florida and Alaska Cancer Mortality Rates
  • 11.3 Weighted Least Squares Linear Regression
  • 11.4 Importance Weights for Weighted Least Squares Linear Regression
  • 11.5 Comparison of Poisson, Weighted Least Squares, and Ordinary Least Squares Regression
  • 11.6 Exposure to aCarcinogen: Ordinary Linear Regression Ignores the Precision of Each Rate
  • 11.7 Differences in Homicide Rates: Simple Averages versus Population-Weighted Averages
  • 11.8 The Place of Ordinary Least Squares Linear Regression for the Analysis of Incidence Rates
  • 11.9 Variance Weighted Least Squares Regression
  • 11.10 Cautions regarding Inverse-Variance Weights
  • 11.11 Why Use Variance Weighted Least Squares?
  • 11.12 A Short Comparison of Weighted Poisson Regression, Variance Weighted Least Squares, and Weighted Linear Regression
  • 11.13 Problems When Age-Standardized Rates are Used as Outcomes
  • 11.14 Ratios and Spurious Correlation
  • 11.15 Linear Regression with ln (Rate) as the Outcome
  • 11.16 Predicting Negative Rates
  • 11.17 Summary
  • 12. Model Fit
  • 12.1 Tabular and Graphic Displays
  • 12.2 Goodness of Fit Tests: Deviance and Pearson Statistics
  • 12.3 A Conditional Moment Chi-Squared Test of Fit
  • 12.4 Limitations of Goodness-of-Fit Statistics
  • 12.5 Measures of Dispersion
  • 12.6 Robust Variance Estimator as a Test of Fit
  • 12.7 Comparing Models using the Deviance
  • 12.8 Comparing Models using Akaike and Bayesian Information Criterion
  • 12.9 Example 1: Using Stata's Generalized Linear Model Command to Decide between a Rate Ratio or a Rate Difference Model for the Randomized Controlled Trial of Exercise and Falls
  • 12.10 Example 2: A Rate Ratio or a Rate Difference Model for Hypothetical Data Regarding the Association between Fall Rates and Age
  • 12.11 A Test of the Model Link
  • 12.12 Residuals, Influence Analysis, and Other Measures
  • 12.13 Adding Model Terms to Improve Fit
  • 12.14 A Caution
  • 12.15 Further Reading
  • 13. Adjusting Standard Errors and Confidence Intervals
  • 13.1 Estimating the Variance without Regression
  • 13.2 Poisson Regression
  • 13.3 Rescaling the Variance using the Pearson Dispersion Statistic
  • 13.4 Robust Variance
  • 13.5 Generalized Estimating Equations
  • 13.6 Using the Robust Variance to Study Length of Hospital Stay
  • 13.7 Computer Intensive Methods
  • 13.8 The Bootstrap Idea
  • 13.9 The Bootstrap Normal Method
  • 13.10 The Bootstrap Percentile Method
  • 13.11 The Bootstrap Bias-Corrected Percentile Method
  • 13.12 The Bootstrap Bias-Corrected and Accelerated Method
  • 13.13 The Bootstrap-T Method
  • 13.14 Which Bootstrap CI Is Best?
  • 13.15 Permutation and Randomization
  • 13.16 Randomization to Nearly Equal Groups
  • 13.17 Better Randomization Using the Randomized Block Design of the Original Study
  • 13.18 A Summary
  • 14. Storks and Babies, Revisited
  • 14.1 Neyman's Approach to His Data
  • 14.2 Using Methods for Incidence Rates
  • 14.3 A Model That uses the Stork/Women Ratio
  • 15. Flexible Treatment of Continuous Variables
  • 15.1 The Problem
  • 15.2 Quadratic Splines
  • 15.3 Fractional Polynomials
  • 15.4 Flexible Adjustment for Time
  • 15.5 Which Method Is Best?
  • 16. Variation in Size of an Association
  • 16.1 An Example: Shoes and Falls
  • 16.2 Problem 1: Using Subgroup P-values for Interpretation
  • 16.3 Problem 2: Failure to Include Main Effect Terms When Interaction Terms Are Used
  • 16.4 Problem 3: Incorrectly Concluding that There Is No Variation in Association
  • 16.5 Problem 4: Interaction May Be Present on a Ratio Scale but Not on a Difference Scale, and Vice Versa
  • 16.6 Problem 5: Failure to Report All Subgroup Estimates in an Evenhanded Manner
  • 17. Negative Binomial Regression
  • 17.1 Negative Binomial Regression Is a Random Effects or Mixed Model
  • 17.2 An Example: Accidents among Workers in a Munitions Factory
  • 17.3 Introducing Equal Person-Time in the Homicide Data
  • 17.4 Letting Person-Time Vary in the Homicide Data
  • 17.5 Estimating a Rate Ratio for the Homicide Data
  • 17.6 Another Example using Hypothetical Data for Five Regions
  • 17.7 Unobserved Heterogeneity
  • 17.8 Observing Heterogeneity in the Shoe Data
  • 17.9 Underdispersion
  • 17.10 A Rate Difference Negative Binomial Regression Model
  • 17.11 Conclusion
  • 18. Clustered Data
  • 18.1 Data from 24 Fictitious Nursing Homes
  • 18.2 Results from 10,000 Data Simulations for the Nursing Homes
  • 18.3 A Single Random Set of Data for the Nursing Homes
  • 18.4 Variance Adjustment Methods
  • 18.5 Generalized Estimating Equations (GEE)
  • 18.6 Mixed Model Methods
  • 18.7 What Do Mixed Models Estimate?
  • 18.8 Mixed Model Estimates for the Nursing Home Intervention
  • 18.9 Simulation Results for Some Mixed Models
  • 18.10 Mixed Models Weight Observations Differently than Poisson Regression
  • 18.11 Which Should We Prefer for Clustered Data, Variance-Adjusted or Mixed Models?
  • 18.12 Additional Model Commands for Clustered Data
  • 18.13 Further Reading
  • 19. Longitudinal Data
  • 19.1 Just Use Rates
  • 19.2 Using Rates to Evaluate Governmental Policies
  • 19.3 Study Designs for Governmental Policies
  • 19.4 A Fictitious Water Treatment and U.S. Mortality 1999-2013
  • 19.5 Poisson Regression
  • 19.6 Population-Averaged Estimates (GEE)
  • 19.7 Conditional Poisson Regression, a Fixed-Effects Approach
  • 19.8 Negative Binomial Regression
  • 19.9 Which Method Is Best?
  • 19.10 Water Treatment in Only 10 States
  • 19.11 Conditional Poisson Regression for the 10-State Water-Treatment Data
  • 19.12 A Published Study
  • 20. Matched Data
  • 20.1 Matching in Case-Control Studies
  • 20.2 Matching in Randomized Controlled Trials
  • 20.3 Matching in Cohort Studies
  • 20.4 Matching to Control Confounding in Some Randomized Trials and Cohort Studies
  • 20.5 A Benefit of Matching
  • Only Matched Sets with at Least One Outcome Are Needed
  • 20.6 Studies Designs that Match a Person to Themselves
  • 20.7 A Matched Analysis Can Account for Matching Ratios that Are Not Constant
  • 20.8 Choosing between Risks and Rates for the Crash Data in Tables 20.1 and 20.2
  • 20.9 Stratified Methods for Estimating Risk Ratios for Matched Data
  • 20.10 Odds Ratios, Risk Ratios, Cell A, and Matched Data
  • 20.11 Regression Analysis of Matched Data for the Odds Ratio
  • 20.12 Regression Analysis of Matched Data for the Risk Ratio
  • 20.13 Matched Analysis of Rates with One Outcome Event
  • 20.14 Matched Analysis of Rates for Recurrent Events
  • 20.15 The Randomized Trial of Exercise and Falls
  • Additional Analyses
  • 20.16 Final Words
  • 21. Marginal Methods
  • 21.1 What Are Margins?
  • 21.2 Converting Logistic Regression Results into Risk Ratios or Risk Differences: Marginal Standardization
  • 21.3 Estimating a Rate Difference from a Rate Ratio Model
  • 21.4 Death by Age and Sex: A Short Example
  • 21.5 Skunk Bite Data: A Long Example
  • 21.6 Obtaining the Rate Difference: Crude Rates
  • 21.7 Using the Robust Variance
  • 21.8 Adjusting for Age
  • 21.9 Full Adjustment for Age and Sex
  • 21.10 Marginal Commands for Interactions
  • 21.11 Marginal Methods for a Continuous Variable
  • 21.12 Using a Rate Difference Model to Estimate a Rate Ratio: Use the ln Scale
  • 22. Bayesian Methods
  • 22.1 Cancer Mortality Rate in Alaska
  • 22.2 The Rate Ratio for Falling in a Trial of Exercise
  • 23. Exact Poisson Regression
  • 23.1 A Simple Example
  • 23.2 A Perfectly Predicted Outcome
  • 23.3 Memory Problems
  • 23.4 A Caveat
  • 24. Instrumental Variables
  • 24.1 The Problem: What Does a Randomized Controlled Trial Estimate?
  • 24.2 Analysis by Treatment Received May Yield Biased Estimates of Treatment Effect
  • 24.3 Using an Instrumental Variable
  • 24.4 Two-Stage Linear Regression for Instrumental Variables
  • 24.5 Generalized Method of Moments
  • 24.6 Generalized Method of Moments for Rates
  • 24.7 What Does an Instrumental Variable Analysis Estimate?
  • 24.8 There Is No Free Lunch
  • 24.9 Final Comments
  • 25. Hazards
  • 25.1 Data for a Hypothetical Treatment with Exponential Survival Times
  • 25.2 Poisson Regression and Exponential Proportional Hazards Regression
  • 25.3 Poisson and Cox Proportional Hazards Regression
  • 25.4 Hypothetical Data for a Rate that Changes over Time
  • 25.5 A Piecewise Poisson Model
  • 25.6 A More Flexible Poisson Model: Quadratic Splines
  • 25.7 Another Flexible Poisson Model: Restricted Cubic Splines
  • 25.8 Flexibility with Fractional Polynomials
  • 25.9 When Should a Poisson Model Be Used? Randomized Trial of a Terrible Treatment
  • 25.10 A Real Randomized Trial, the PLCO Screening Trial
  • 25.11 What If Events Are Common?
  • 25.12 Cox Model or a Flexible Parametric Model?
  • 25.13 Collapsibility and Survival Functions
  • 25.14 Relaxing the Assumption of Proportional Hazards in the Cox Model
  • 25.15 Relaxing the Assumption of Proportional Hazards for the Poisson Model
  • 25.16 Relaxing Proportional Hazards for the Royston-Parmar Model
  • 25.17 The Life Expectancy Difference or Ratio
  • 25.18 Recurrent or Multiple Events
  • 25.19 A Short Summary
  • Bibliography
  • Index

Dateiformat: PDF
Kopierschutz: Adobe-DRM (Digital Rights Management)

Systemvoraussetzungen:

Computer (Windows; MacOS X; Linux): Installieren Sie bereits vor dem Download die kostenlose Software Adobe Digital Editions (siehe E-Book Hilfe).

Tablet/Smartphone (Android; iOS): Installieren Sie bereits vor dem Download die kostenlose App Adobe Digital Editions (siehe E-Book Hilfe).

E-Book-Reader: Bookeen, Kobo, Pocketbook, Sony, Tolino u.v.a.m. (nicht Kindle)

Das Dateiformat PDF zeigt auf jeder Hardware eine Buchseite stets identisch an. Daher ist eine PDF auch für ein komplexes Layout geeignet, wie es bei Lehr- und Fachbüchern verwendet wird (Bilder, Tabellen, Spalten, Fußnoten). Bei kleinen Displays von E-Readern oder Smartphones sind PDF leider eher nervig, weil zu viel Scrollen notwendig ist. Mit Adobe-DRM wird hier ein "harter" Kopierschutz verwendet. Wenn die notwendigen Voraussetzungen nicht vorliegen, können Sie das E-Book leider nicht öffnen. Daher müssen Sie bereits vor dem Download Ihre Lese-Hardware vorbereiten.

Bitte beachten Sie bei der Verwendung der Lese-Software Adobe Digital Editions: wir empfehlen Ihnen unbedingt nach Installation der Lese-Software diese mit Ihrer persönlichen Adobe-ID zu autorisieren!

Weitere Informationen finden Sie in unserer E-Book Hilfe.


Download (sofort verfügbar)

117,99 €
inkl. 19% MwSt.
Download / Einzel-Lizenz
E-Book bestellen