Absolute Risk Methods and Applications in Clinical Management and Public Health

 Introduction
 Examples of risk models for disease incidence
 Breast cancer incidence
 A brief survey of models
 The National Cancer Institute’s (NCI’s) Breast Cancer Risk

 Assessment Tool, BCRAT
 Other models of cancer incidence
 Framingham Model for incidence of coronary heart disease
 Applications of risk models for disease incidence
 Prognosis after disease diagnosis
 Contents of book

 Definitions and basic concepts for survival data in a cohort without covariates
 Basic survival concepts
 Choice of time scale: age, time since diagnosis, time since accrual or counseling
 Censoring
 Right censoring
 Truncation
 Life-table estimator
 Kaplan–Meier survival estimate
 Counting processes and Markov methods

 Competing risks
 Concepts and definitions
 Pure versus cause-specific hazard functions
 Non-parametric estimation of absolute risk

 Regression models for absolute risk estimated from cohort data
 Cause-specific hazard regression
 Estimation of the hazard ratio parameters
 Non-parametric estimation of the baseline hazard
 Semi-parametric estimation of absolute risk rm
 Estimation of a piecewise exponential baseline hazard model
 Alternative hazard models
 Cumulative incidence regression
 Proportional sub-distribution hazards model
 Other cumulative incidence regression models
 Relationship between the cause-specific and the proportional sub-distribution hazards models
 Examples
 Absolute risk of breast cancer incidence
 Absolute risk of second primary thyroid cancer (SPTC) incidence
 Estimating cause-specific hazard functions from sub-samples from cohorts
 Case-cohort design
 Nested case-control design
 Estimating cause specific hazard functions from cohorts with complex survey designs
 Example of survey design
 Data
 Estimation of hazard ratio parameters and the baseline hazard function
 Example: absolute risk of cause-specific deaths from the NHANES I and II
 Variance estimation
 Approaches to variance estimation
 Influence function based variance of the absolute risk estimate from cohort data

 Estimating absolute risk by combining case-control or cohort data with disease registry data
 Relationship between attributable risk, composite age-specific incidence, and baseline hazard
 Estimating relative risk and attributable risk from case-control data
 Estimating relative risk and attributable risk from cohort data
 Estimating the cause-specific hazard of the competing causes of mortality, λ(t; z)
 Some strengths and limitations of using registry data
 Absolute risk estimate
 Example: estimating absolute risk of breast cancer incidence by combining cohort data with registry data
 Variance computations
 Relative risk parameters and attributable risk estimated from a case-control study
 Relative risk parameters and attributable risk estimated from a cohort study
 Variance computation when an external reference survey is used to obtain the risk factor distribution
 Resampling methods to estimate variance

 Assessment of risk model performance
 Introduction
 The risk distribution
 The predictiveness curve
 Calibration
 Definition of calibration and tests of calibration
 Reasons for poor calibration and approaches to recalibration
 Assessing calibration with right censored data
 Assessing calibration on the training data, that is, internal validation
 Accuracy measures
 Predictive accuracy: the Brier score and the logarithmic score
 Classification accuracy
 Distribution of risk in cases and non-cases
 Accuracy criteria
 Discriminatory accuracy
 Extensions of accuracy measures to functions of time and allowance for censoring
 Criteria for applications of risk models for screening or high-risk interventions
 Proportion of cases followed and proportion needed to follow
 Estimation of PCF and PNF
 Model assessment based on expected costs or expected utility specialized for a particular application
 Two health states and two intervention options
 More complex outcomes and interventions
 Example with four intervention choices
 Multiple outcomes in prevention trials
 Expected cost calculations for outcomes following disease diagnosis

 Comparing the performance of two models
 Use of external validation data for model comparison
 Data example
 Comparison of model calibration
 Model comparisons based on the difference in separate model-specific estimates of a criterion
 Comparisons of predictive accuracy using the Brier and logarithmic scores
 Classification accuracy criteria based on single risk threshold
 Comparisons based on the receiver operating characteristic (ROC) curve
 Integrated discrimination improvement (IDI) and mean risk difference
 Comparing two risk models based on PCF, PNF, iPCF, or iPNF
 Comparisons based on expected loss or expected benefit
 Joint distributions of risk
 Risk stratification tables and reclassification indices
 Net reclassification improvement (NRI)
 Extensions of NRI
 Concluding remarks

 Building and updating relative risk models
 Introductory remarks
 Selection of covariates
 Missing data
 Types of missing data
 Approaches to handling missing data
 Updating risk models with new risk factors
 Estimating an updated relative risk model, rr(X,Z), from case control data
 Estimating rr(X,Z) from new data only
 Incorporating information on rr(X) into rr(X,Z) via likelihood ratio (LR) updating
 Joint estimation of LRD(Z|X)
 Estimating LRD(Z|X) based on fitting separate models for cases (D = ) and non-cases (D = )
 LR updating assuming independence of Z and X (independence Bayes)
 LR updating with multiple markers
 Joint estimation, logistic model with offset
 Independence Bayes with shrinkage
 Updating using constrained maximum likelihood estimation (CML)
 Simulations
 Summary

 Risk estimates based on genetic variants and family studies
 Introduction
 Mendelian models: the autosomal dominant model for pure breast cancer risk
 Models that allow for residual familial aggregation to estimate pure breast cancer risk
 Polygenic risk
 Models with latent genetic effects: BOADICEA and IBIS
 Copula models
 Estimating genotype-specific absolute risk from family-based designs
 General considerations
 Combining relative-risks from family-based case-control studies with population-based incidence rates
 Kin-cohort design
 Families with several affected members (multiplex pedigrees)
 Comparisons of some models for projecting breast cancer risk
 Discussion

 Related topics
 Introduction
 Prognosis following disease onset
 Missing or misclassified information on event type
 Time varying covariates
 Fixed versus time-varying covariates and internal versus external time-varying covariates
 Joint modeling of covariates and health outcomes, including multistate models
 Landmark analysis
 Risk model applications for counseling individuals and for public health strategies for disease prevention
 Use of risk models in counseling individuals
 Providing realistic risk estimates and perspective
 More formal risk-benefit analysis for individual counseling
 Use of risk models in public health prevention
 Designing intervention trials to prevent disease
 Assessing absolute risk reduction in a population from interventions on modifiable risk factors
 Implementing a “high risk” intervention strategy for disease prevention
 Allocating preventive interventions under cost constraints

Biography

Ruth M. Pfeiffer is a mathematical statistician and Fellow of the American Statistical Association, with interests in risk modeling, dimension reduction, and applications in epidemiology. She developed absolute risk models for breast cancer, colon cancer, melanoma, and second primary thyroid cancer following a childhood cancer diagnosis.

Mitchell H. Gail developed the widely used "Gail model" for projecting the absolute risk of invasive breast cancer. He is a medical statistician with interests in statistical methods and applications in epidemiology and molecular medicine. He is a member of the National Academy of Medicine and former President of the American Statistical Association.

Both are Senior Investigators in the Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institutes of Health.

"Written by two leading experts in the field, this book provides a comprehensive overview of absolute risk, including both theoretical basis and clinical implications before and after the disease diagnosis. Equipped with sufficient technical details on the estimation and inference of absolute risk aswell as a range of real examples, this book is targeted toward a broad audience, including epidemiologists, clinicians, and statisticians. While a few other books on theoretical aspects of absolute risk are available in the literature, the book by Pfeiffer and Gail treats absolute risk from several new angles . . ."
~Journal of the American Statistical Association

"The book by Pfeiffer and Gail leads us into the higher statistical levels of predicting the medical future. The main focus is on the concept of the absolute risk of an event because this has a clinically meaningful interpretation for the individual person. The much more commonly reported hazard ratios of health research do not provide a directly useful number for the single subject...The examples are about the real world (mostly cancer research), and the mathematics provide all the formula for building a well‐calibrated absolute risk model and the validation study...The book contains a lot of material which is very difficult to find elsewhere, for example, on family studies, handling of missing data, and landmark analysis with time-dependent covariates. Overall, I found the book to provide a very complete documentation of a highly important subject. The authors are to be thanked for their thoroughness and congratulated for their work, which should be useful for many real‐world applications of absolute risk."
~Biometrics