Probability and statistics Books

Book SynopsisThe sixth edition of Meaningful Statistics introduces students to foundational concepts and demonstrates how statistics are an integral aspect of their everyday lives—from baseball batting averages to reports on the median cost of buying a home to the projected outcomes of an upcoming election.Each chapter begins with a question and scenario that is then explored through statistical concepts, demonstrating to students how research and statistics can help us to answer questions and solve problems. The opening chapter focuses on the process of collecting data and uses this information to explore whether multivitamins are a waste of money. Additional chapters explore linear regression and whether junk food is harmful to a child's IQ; normal distribution and the issue of a tie for Olympic downhill gold; confidence intervals and a simulation of the NBA draft lottery; and more.Students learn about descriptive measures for populations and samples; probability and random variables; and sampling distributions, with each concept corresponding to real-world examples. Closing chapters cover the testing of hypotheses, tests using the chi-square distribution; and inferences with two or more populations. For the sixth edition, exercises and examples have been updated throughout.Designed to bring key concepts to life, Meaningful Statistics is an ideal resource for courses in mathematics and statistics.

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Book SynopsisThis book examines non-Gaussian distributions. It addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series.Trade ReviewFrom the reviews: "Financial Modeling Under Non-Gaussian Distributions … is thus very welcome as it provides an accessible and easy-to-understand treatment of a broad range of topics, including core material to more advanced techniques on the subject of capturing non-Gaussian properties in the distributions of asset returns. … Financial Modeling Under Non-Gaussian Distributions is a very accessible textbook that covers a wide range of topics. … The authors define their target readers as specialized master and Ph.D. students, as well as financial industry practitioners." (Stephan Suess, Financial Markets and Portfolio Management, Vol. 22, 2008) "This book is written for non-mathematicians who want to model financial market prices. ... It targets practioners in the financial industry. It is suitable for use as core text for students in empirical finance, financial econometrics and financial derivatives. It is useful for mathematician who want to know more about their mathematical tools are applied in finance." (Klaus Ehemann, Zentralblatt MATH, Vol. 1138 (16), 2008)Table of ContentsFinancial Markets and Financial Time Series.- Statistical Properties of Financial Market Data.- Functioning of Financial Markets and Theoretical Models for Returns.- Econometric Modeling of Asset Returns.- Modeling Volatility.- Modeling Higher Moments.- Modeling Correlation.- Extreme Value Theory.- Applications of Non-Gaussian Econometrics.- Risk Management and VaR.- Portfolio Allocation.- Option Pricing with Non-Gaussian Returns.- Fundamentals of Option Pricing.- Non-structural Option Pricing.- Structural Option Pricing.- Appendices on Option Pricing Mathematics.- Brownian Motion and Stochastic Calculus.- Martingale and Changing Measure.- Characteristic Functions and Fourier Transforms.- Jump Processes.- Lévy Processes.

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Book SynopsisThis book examines the intelligent random walk algorithms based on learning automata: these versions of random walk algorithms gradually obtain required information from the nature of the application to improve their efficiency. The book also describes the corresponding applications of this type of random walk algorithm, particularly as an efficient prediction model for large-scale networks such as peer-to-peer and social networks. The book opens new horizons for designing prediction models and problem-solving methods based on intelligent random walk algorithms, which are used for modeling and simulation in various types of networks, including computer, social and biological networks, and which may be employed a wide range of real-world applications.Table of ContentsRandom walk algorithms: Definitions, weaknesses, and learning automata based approach.- Intelligent Models of Random Walk.- Applications.- Conclusions.

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Book SynopsisThis two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions.Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.Trade Review“The text is very well-written and can be used to study the theory on various levels. It develops systematically from the wealth of motivating examples and heuristical considerations, through the carefully chosen collection of in-depth explained preliminaries, to the extensive nontrivial theory explained in full detail. … The book is highly recommended for those interested in the foundations and the up-to-date development of MFGs, as well as in the general area of stochastic control and related issues of analysis and probability.” (Vassili, Mathematical Reviews, January, 2019)Table of ContentsPreface to Volume I.- Part I: The Probabilistic Approach to Mean Field Games.- Learning by Examples: What is a Mean Field Game?.- Probabilistic Approach to Stochastic Differential Games.- Stochastic Differential Mean Field Games.- FBSDEs and the Solution of MFGs without Common Noise.- Part II: Analysis on Wasserstein Space and Mean Field Control.- Spaces of Measures and Related Differential Calculus.- Optimal Control of SDEs of McKean-Vlasov Type.- Epologue to Volume I.- Extensions for Volume I. References.- Indices.

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Book Synopsis​This unique textbook presents the field of modern epidemiology as a whole; it does not restrict itself to particular aspects. It stresses the fundamental ideas and their role in any situation of epidemiologic practice. Its structure is largely determined by didactic viewpoints.Epidemiology is the art of defining and investigating the influence of factors on the health of populations. Hence the book starts by sketching the role of epidemiology in public health. It then treats the epidemiology of many particular diseases; mathematical modelling of epidemics and immunity; health information systems; statistical methods and sample surveys; clinical epidemiology including clinical trials; nutritional, environmental, social, and genetic epidemiology; and the habitual tools of epidemiologic studies. The book also reexamines the basic difference between the epidemiology of infectious diseases and that of non-infectious ones.The organization of the topics by didactic aspects makes the book ideal for teaching. All examples and case studies are situated in a single country, namely Vietnam; this provides a particularly vivid picture of the role of epidemiology in shaping the health of a population. It can easily be adapted to other developing or transitioning countries.This volume is well suited for courses on epidemiology and public health at the upper undergraduate and graduate levels, while its specific examples make it appropriate for those who teach these fields in developing or emerging countries. New to this edition, in addition to minor revisions of almost all chapters:• Updated data about infectious and non-infectious diseases• An expanded discussion of genetic epidemiology• A new chapter, based on recent research of the authors, on how to build a coherent system of Public Health by using the insights provided by this volume. Trade Review“It is best suited for physicians who will likely not need to perform large epidemiological studies. … It is most suitable as an introductory book, used in combination with a more in-depth textbook or practical experience.” (Allison Dykstra, Doody's Book Reviews, November 22, 2019)Table of Contents

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Book SynopsisThe second edition of this volume provides insight and practical illustrations on how modern statistical concepts and regression methods can be applied in medical prediction problems, including diagnostic and prognostic outcomes. Many advances have been made in statistical approaches towards outcome prediction, but a sensible strategy is needed for model development, validation, and updating, such that prediction models can better support medical practice.There is an increasing need for personalized evidence-based medicine that uses an individualized approach to medical decision-making. In this Big Data era, there is expanded access to large volumes of routinely collected data and an increased number of applications for prediction models, such as targeted early detection of disease and individualized approaches to diagnostic testing and treatment. Clinical Prediction Models presents a practical checklist that needs to be considered for development of a valid prediction model. Steps include preliminary considerations such as dealing with missing values; coding of predictors; selection of main effects and interactions for a multivariable model; estimation of model parameters with shrinkage methods and incorporation of external data; evaluation of performance and usefulness; internal validation; and presentation formatting. The text also addresses common issues that make prediction models suboptimal, such as small sample sizes, exaggerated claims, and poor generalizability. The text is primarily intended for clinical epidemiologists and biostatisticians. Including many case studies and publicly available R code and data sets, the book is also appropriate as a textbook for a graduate course on predictive modeling in diagnosis and prognosis. While practical in nature, the book also provides a philosophical perspective on data analysis in medicine that goes beyond predictive modeling. Updates to this new and expanded edition include:• A discussion of Big Data and its implications for the design of prediction models• Machine learning issues• More simulations with missing ‘y’ values• Extended discussion on between-cohort heterogeneity• Description of ShinyApp• Updated LASSO illustration• New case studies Trade ReviewTable of ContentsPreface viiAcknowledgements xiChapter 1 Introduction 11.1 Diagnosis, prognosis and therapy choice in medicine 11.1.1 Predictions for personalized evidence-based medicine 11.2 Statistical modeling for prediction 51.2.1 Model assumptions 51.2.2 Reliability of predictions: aleatory and epistemic uncertainty 61.2.3 Sample size 61.3 Structure of the book 81.3.1 Part I: Prediction models in medicine 81.3.2 Part II: Developing internally valid prediction models 81.3.3 Part III: Generalizability of prediction models 91.3.4 Part IV: Applications 9Part I: Prediction models in medicine 11Chapter 2 Applications of prediction models 132.1 Applications: medical practice and research 132.2 Prediction models for Public Health 142.2.1 Targeting of preventive interventions 14*2.2.2 Example: prediction for breast cancer 142.3 Prediction models for clinical practice 172.3.1 Decision support on test ordering 17*2.3.2 Example: predicting renal artery stenosis 172.3.3 Starting treatment: the treatment threshold 20*2.3.4 Example: probability of deep venous thrombosis 202.3.5 Intensity of treatment 21*2.3.6 Example: defining a poor prognosis subgroup in cancer 222.3.7 Cost-effectiveness of treatment 232.3.8 Delaying treatment 23*2.3.9 Example: spontaneous pregnancy chances 242.3.10 Surgical decision-making 26*2.3.11 Example: replacement of risky heart valves 272.4 Prediction models for medical research 282.4.1 Inclusion and stratification in a RCT 28*2.4.2 Example: selection for TBI trials 292.4.3 Covariate adjustment in a RCT 302.4.4 Gain in power by covariate adjustment 31*2.4.5 Example: analysis of the GUSTO-III trial 322.4.6 Prediction models and observational studies 322.4.7 Propensity scores 33*2.4.8 Example: statin treatment effects 342.4.9 Provider comparisons 35*2.4.10 Example: ranking cardiac outcome 352.5 Concluding remarks 35Chapter 3 Study design for prediction modeling 373.1 Studies for prognosis 373.1.1 Retrospective designs 37*3.1.2 Example: predicting early mortality in esophageal cancer 373.1.3 Prospective designs 38*3.1.4 Example: predicting long-term mortality in esophageal cancer 393.1.5 Registry data 39*3.1.6 Example: surgical mortality in esophageal cancer 393.1.7 Nested case-control studies 40*3.1.8 Example: perioperative mortality in major vascular surgery 403.2 Studies for diagnosis 413.2.1 Cross-sectional study design and multivariable modeling 41*3.2.2 Example: diagnosing renal artery stenosis 413.2.3 Case-control studies 41*3.2.4 Example: diagnosing acute appendicitis 423.3 Predictors and outcome 423.3.1 Strength of predictors 423.3.2 Categories of predictors 423.3.3 Costs of predictors 433.3.4 Determinants of prognosis 443.3.5 Prognosis in oncology 443.4 Reliability of predictors 453.4.1 Observer variability 45*3.4.2 Example: histology in Barrett’s esophagus 453.4.3 Biological variability 463.4.4 Regression dilution bias 46*3.4.5 Example: simulation study on reliability of a binary predictor 463.4.6 Choice of predictors 473.5 Outcome 473.5.1 Types of outcome 473.5.2 Survival endpoints 48*3.5.3 Examples: 5-year relative survival in cancer registries 483.5.4 Composite endpoints 49*3.5.5 Example: composite endpoints in cardiology 493.5.6 Choice of prognostic outcome 493.5.7 Diagnostic endpoints 49*3.5.8 Example: PET scans in esophageal cancer 503.6 Phases of biomarker development 503.7 Statistical power and reliable estimation 513.7.1 Sample size to identify predictor effects 513.7.2 Sample size for reliable modeling 533.7.3 Sample size for reliable validation 553.8 Concluding remarks 55Chapter 4 Statistical models for prediction 574.1 Continuous outcomes 57*4.1.1 Examples of linear regression 584.1.2 Economic outcomes 58*4.1.3 Example: prediction of costs 584.1.4 Transforming the outcome 584.1.5 Performance: explained variation 594.1.6 More flexible approaches 604.2 Binary outcomes 614.2.1 R2 in logistic regression analysis 624.2.2 Calculation of R2 on the log likelihood scale 634.2.3 Models related to logistic regression 654.2.4 Bayes rule 654.2.5 Prediction with Naïve Bayes 664.2.6 Calibration and Naïve Bayes 67*4.2.7 Logistic regression and Bayes 674.2.8 Machine learning: more flexible approaches 684.2.9 Classification and regression trees 69*4.2.10 Example: mortality in acute MI patients 694.2.11 Advantages and disadvantages of tree models 704.2.12 Trees versus logistic regression modeling 70*4.2.13 Other methods for binary outcomes 714.2.14 Summary on binary outcomes 724.3 Categorical outcomes 734.3.1 Polytomous logistic regression 734.3.2 Example: histology of residual masses 73*4.3.3 Alternative models 75*4.3.4 Comparison of modeling approaches 764.4 Ordinal outcomes 774.4.1 Proportional odds logistic regression 77* 4.4.2 Relevance of the proportional odds assumption in RCTs 784.5 Survival outcomes 804.5.1 Cox proportional hazards regression 804.5.2 Prediction with Cox models 814.5.3 Proportionality assumption 814.5.4 Kaplan-Meier analysis 81*4.5.5 Example: impairment after treatment of leprosy 824.5.6 Parametric survival 82*4.5.7 Example: replacement of risky heart valves 834.5.8 Summary on survival outcomes 834.6 Competing risks 844.6.1 Actuarial and actual risks 844.6.2 Absolute risk and the Fine&Gray model 844.6.3 Example: Prediction of coronary heart disease incidence 854.6.4 Multi-state modeling 864.7 Dynamic predictions 874.7.1 Multi-state models and landmarking 874.7.2 Joint models 874.8 Concluding remarks 88Chapter 5 Overfitting and optimism in prediction models 915.1 Overfitting and optimism 915.1.1 Example: surgical mortality in esophagectomy 925.1.2 Variability within one center 925.1.3 Variability between centers: noise vs. true heterogeneity 935.1.4 Predicting mortality by center: shrinkage 945.2 Overfitting in regression models 955.2.1 Model uncertainty and testimation bias 955.2.2 Other modeling biases 975.2.3 Overfitting by parameter uncertainty 975.2.4 Optimism in model performance 985.2.5 Optimism-corrected performance 995.3 Bootstrap resampling 1005.3.1 Applications of the bootstrap 1015.3.2 Bootstrapping for regression coefficients 1025.3.3 Bootstrapping for prediction: optimism correction 1025.3.4 Calculation of optimism-corrected performance 103*5.3.5 Example: Stepwise selection in 429 patients 1045.4 Cost of data analysis 105*5.4.1 Degrees of freedom of a model 1055.4.2 Practical implications 1055.5 Concluding remarks 106Chapter 6 Choosing between alternative models 1096.1 Prediction with statistical models 1096.1.1 Testing of model assumptions and prediction 1106.1.2 Choosing a type of model 1106.2 Modeling age – outcome relations 111*6.2.1 Age and mortality after acute MI 111*6.2.2 Age and operative mortality 112*6.2.3 Age – outcome relations in other diseases 1156.3 Head-to-head comparisons 1166.3.1 StatLog results 116*6.3.2 Cardiovascular disease prediction comparisons 117*6.3.3 Traumatic brain injury modeling results 1196.4 Concluding remarks 120Part II: Developing valid prediction models 123Checklist for developing valid prediction models 124Chapter 7 Missing values 1257.1 Missing values and prediction research 1257.1.1 Inefficiency of complete case analysis 1267.1.2 Interpretation of CC Analyses 1277.1.3 Missing data mechanisms 1277.1.4 Missing outcome data 1287.1.5 Summary points 1297.2 Prediction under MCAR, MAR and MNAR mechanisms 1307.2.1 Missingness patterns 1307.2.2 Missingness and estimated regression coefficients 1327.2.4 Missingness and estimated performance 1347.3 Dealing with missing values in regression analysis 1357.3.1 Imputation principle 1357.3.2 Simple and more advanced single imputation methods 1367.3.3 Multiple imputation 1377.4 Defining the imputation model 1387.4.1 Types of variables in the imputation model 138*7.4.2 Transformations of variables 1397.4.3 Imputation models for SI 1397.4.4 Summary points 1397.5 Success of imputation under MCAR, MAR and MNAR 1407.5.1 Imputation in a simple model 1407.5.2 Other simulation results 140* 7.5.3 Multiple predictors 1407.6 Guidance to dealing with missing values in prediction research 1427.6.1 Patterns of missingness 1427.6.2 Simple approaches 1437.6.3 More advanced approaches 1437.6.4 Maximum fraction of missing values before omitting a predictor 1437.6.5 Single or multiple imputation for predictor effects? 1447.6.6 Single or multiple imputation for deriving predictions? 1457.6.7 Missings and predictions for new patients 145*7.6.8 Performance across multiple imputed data sets 1467.6.9 Reporting of missing values in prediction research 1467.7 Concluding remarks 1487.7.1 Summary statements 148*7.7.2 Available software and challenges 149Chapter 8 Case study on dealing with missing values 1518.1 Introduction 1518.1.1 Aim of the IMPACT study 1518.1.2 Patient selection 1528.1.3 Potential predictors 1528.1.4 Coding and time dependency of predictors 1538.2 Missing values in the IMPACT study 1538.2.1 Missing values in outcome 1538.2.2 Quantification of missingness of predictors 1548.2.3 Patterns of missingness 1568.3 Imputation of missing predictor values 1598.3.1 Correlations between predictors 1598.3.2 Imputation model 1608.3.3 Distributions of imputed values 160*8.3.4 Multilevel imputation 1618.4 Predictor effect: adjusted analyses 1628.4.1 Adjusted analysis for complete predictors: age and motor score 1638.4.2 Adjusted analysis for incomplete predictors: pupils 1658.5 Predictions: multivariable analyses 165*8.5.1 Multilevel analyses 1668.6 Concluding remarks 166Chapter 9 Coding of categorical and continuous predictors 1699.1 Categorical predictors 1699.1.1 Examples of categorical coding 1709.2 Continuous predictors 171*9.2.1 Examples of continuous predictors 1719.2.2 Categorization of continuous predictors 1729.3 Non-linear functions for continuous predictors 1739.3.1. Polynomials 1739.3.2. Fractional polynomials (FP) 1749.3.3 Splines 175*9.3.4 Example: functional forms with RCS or FP 1769.3.5 Extrapolation and robustness 1769.3.5 Preference for FP or RCS? 1769.4 Outliers and winsorizing 1779.4.1 Example: glucose values and outcome of TBI 1789.5 Interpretation of effects of continuous predictors 180*9.5.1 Example: predictor effects in TBI 1819.6 Concluding remarks 1829.6.1 Software 183Chapter 10 Restrictions on candidate predictors 18510.1 Selection before studying the predictor – outcome relation 18510.1.1 Selection based on subject knowledge 185*10.1.2 Examples: too many candidate predictors 18510.1.3 Meta-analysis for candidate predictors 186*10.1.4 Example: predictors in testicular cancer 18610.1.5 Selection based on distributions 18610.2 Combining similar variables 18710.2.1 Subject knowledge for grouping 18710.2.2 Assessing the equal weights assumption 18810.2.3 Biologically motivated weighting schemes 18910.2.4 Statistical combination 18910.3 Averaging effects 190*10.3.1 Example: Chlamydia trachomatis infection risks 190*10.3.2 Example: acute surgery risk relevant for elective patients? 190*10.4 Case study: family history for prediction of a genetic mutation 19110.4.1 Clinical background and patient data 19110.4.2 Similarity of effects 19110.4.3 CRC and adenoma in a proband 19410.4.5 Full prediction model for mutations 19610.5 Concluding remarks 197Chapter 11 Selection of main effects 19911.1 Predictor selection 19911.1.1 Reduction before modeling 19911.1.2 Reduction while modeling 20011.1.3 Collinearity 20011.1.4 Parsimony 20011.1.5 Non-significant candidate predictors 20111.1.6 Summary points on predictor selection 20111.2 Stepwise selection 20211.2.1 Stepwise selection variants 20211.2.2 Stopping rules in stepwise selection 20211.3 Advantages of stepwise methods 20311.4 Disadvantages of stepwise methods 20411.4.1 Instability of selection 20411.4.2 Testimation: Biased in selected coefficients 206*11.4.3 Testimation: empirical illustrations 20711.4.4 Misspecification of variability and p-values 20811.5 Influence of noise variables 21011.6 Univariate analyses and model specification 21111.6.1 Pros and cons of univariate pre-selection 211*11.6.2 Testing of predictors in a domain 21211.7 Modern selection methods 212*11.7.1 Bootstrapping for selection 212*11.7.2 Bagging and boosting 212*11.7.3 Bayesian model averaging (BMA) 21311.7.4 Shrinkage of regression coefficients to zero 21311.8 Concluding remarks 214Chapter 12 Assumptions in regression models: Additivity and linearity 21712.1 Additivity and interaction terms 21712.1.1 Potential interaction terms to consider 21812.1.2 Interactions with treatment 21812.1.3 Other potential interactions 219*12.1.4 Example: time and survival after valve replacement 22012.2 Selection, estimation and performance with interaction terms 22012.2.1 Example: age interactions in GUSTO-I 22012.2.2 Estimation of interaction terms 22112.2.3 Better prediction with interaction terms? 22212.2.4 Summary points 22312.3 Non-linearity in multivariable analysis 22312.3.1 Multivariable restricted cubic splines (rcs) 22412.3.2 Multivariable fractional polynomials (FP) 22512.3.3 Multivariable splines in gam 22512.4 Example: non-linearity in testicular cancer case study 226*12.4.1 Details of multivariable FP and gam analyses 227*12.4.2 GAM in univariate and multivariable analysis 228*12.4.3 Predictive performance 229*12.4.4 R code for non-linear modeling in testicular cancer example 23012.5 Concluding remarks 23012.5.1 Recommendations 231Chapter 13 Modern estimation methods 23313.1 Predictions from regression and other models 233*13.1.1 Estimation with other modeling approaches 23413.2 Shrinkage 23413.2.1 Uniform shrinkage 23513.2.2 Uniform shrinkage: illustration 23613.3 Penalized estimation 236*13.3.1 Penalized maximum likelihood estimation 23713.3.2 Penalized ML: illustration 238*13.3.3 Optimal penalty by bootstrapping 23813.3.4 Firth regression 239*13.3.5 Firth regression: illustration 239*13.4.1 Estimation of a LASSO model 24013.5 Elastic net 241*13.5.1 Estimation of Elastic Net model 24113.6 Performance after shrinkage 24213.6.1 Shrinkage, penalization, and model selection 24213.7 Concluding remarks 244Chapter 14 Estimation with external information 247Background 24714.1 Combining literature and individual patient data (IPD) 24714.1.1 A global prediction model 248*14.1.2 A global model for traumatic brain injury 24914.1.3 Developing a local prediction model 24914.1.4 Adaptation of univariate coefficients 250*14.1.5 Adaptation method 1 250*14.1.6 Adaptation method 2 251*14.1.7 Estimation of adaptation factors 251*14.1.8 Simulation results 25214.1.9 Performance of the adapted model 25314.2 Case study: prediction model for AAA surgical mortality 25414.2.1 Meta-analysis 25414.2.2 Individual patient data analysis 25514.2.3 Adaptation and clinical presentation 25614.3 Alternative approaches 25714.3.1 Overall calibration 25714.3.2 Stacked regressions 25714.3.3 Bayesian methods: using data priors to regression modeling 25714.3.4 Example: predicting neonatal death 258*14.3.5 Example: aneurysm study 25814.4 Concluding remarks 258Chapter 15 Evaluation of performance 26115.1 Overall performance measures 26115.1.1 Explained variation: R2 26115.1.2 Brier score 26215.1.3 Performance of testicular cancer prediction model 26315.3.4 Assessment of moderate calibration 28315.3.5 Assessment of strong calibration 28315.3.6 Calibration of survival predictions 28415.3.7 Example: calibration in testicular cancer prediction model 285*15.3.8 R code for assessing calibration 28615.3.9 Calibration and discrimination 28615.4 Concluding remarks 28715.4.1 Bibliographic notes 287Chapter 16 Evaluation of clinical usefulness 28916.1 Clinical usefulness 28916.1.1 Intuitive approach to the cutoff 29016.1.2 Decision-analytic approach: benefit vs harm 29016.1.3 Accuracy measures for clinical usefulness 29116.1.4 Decision curve analysis 29216.1.5 Interpreting net benefit in decision curves 29316.1.6 Example: clinical usefulness of prediction in testicular cancer 29516.1.7 Decision curves for testicular cancer example 29616.1.8 Verification bias and clinical usefulness 297*16.1.9 R code 29816.2 Discrimination, calibration, and clinical usefulness 30016.2.1 Discrimination, calibration, and Net Benefit in the testicular cancer case study 30016.2.2 Aims of prediction models and performance measures 30116.2.2 Summary points 30216.3 From prediction models to decision rules 30316.3.1 Performance of decision rules 30316.3.2 Treatment benefit in prognostic subgroups 30516.3.3 Evaluation of classification systems 30516.4 Concluding remarks 306Chapter 17 Validation of prediction models 30917.1 Internal versus external validation, and validity 30917.1.1 Assessment of internal and external validity 31017.2 Internal validation techniques 31117.2.1 Apparent validation 31117.2.3 Cross-validation 31317.2.4 Bootstrap validation 31417.2.5 Internal validation combined with imputation 31517.3 External validation studies 31517.3.1 Temporal validation 316*17.3.2 Example: validation of a model for Lynch syndrome 31617.3.3 Geographic validation 31717.3.4 Fully independent validation 31917.3.5 Reasons for poor validation 32017.4 Concluding remarks 321Chapter 18 Presentation formats 32318.1 Prediction models versus decision rules 32318.2 Clinical prediction models 32518.2.1 Regression formulas 32518.2.2 Confidence intervals for predictions 32618.2.3 Nomograms 32718.2.4 Score chart 32918.2.5 Tables with predictions 33018.2.6 Specific formats 33118.2.7 Black box presentations 33118.3 Case study: clinical prediction model for testicular cancer model 33318.3.1 Regression formula from logistic model 33318.3.2 Nomogram 334*18.3.3 Score chart 33418.3.4 Summary points 33518.4 Clinical decision rules 33518.4.1 Regression tree 33518.4.2 Score chart rule 33518.4.3 Survival groups 33618.4.4 Meta-model 33718.5 Concluding remarks 338Part III: Generalizability of prediction models 341Chapter 19 Patterns of external validity 34319.1 Determinants of external validity 34319.1.1 Case-mix 34319.1.2 Differences in case-mix 34319.1.3 Differences in regression coefficients 34419.2.1 Simulation set-up 34519.2.2 Performance measures 34719.3 Distribution of predictors 34819.3.1 More or less severe case-mix according to X 348*19.3.2 Interpretation of testicular cancer validation 34919.3.3 More or less heterogeneous case-mix according to X 34919.3.4 More or less severe case-mix according to Z 35019.3.5 More or less heterogeneous case-mix according to Z 35119.4 Distribution of observed outcome y 35319.5 Coefficients β 35419.5.1 Coefficient of linear predictor < 1 35419.5.2 Coefficients β different 35519.6 Summary of patterns of invalidity 35619.6.1 Other scenarios of invalidity 35719.7 Reference values for performance 35819.7.1 Model-based performance: performance if the model is valid 35819.7.2 Performance with refitting 358*19.7.3 Examples: testicular cancer and TBI 359*19.7.4 R code 36019.8 Limited validation sample size 36119.8.1 Uncertainty in validation of performance 361*19.8.2 Estimating standard errors in validation studies 36319.8.3 Summary points 36319.9 Design of external validation studies 36319.9.1 Power of external validation studies 364*19.9.2 Calculating sample sizes for validation studies 36519.9.3 Rules for sample size of validation studies 36619.9.4 Summary points 36719.10 Concluding remarks 368Chapter 20 Updating for a new setting 37120.1 Updating only the intercept 37220.1.1 Simple updating methods 37220.2 Approaches to more extensive updating 37220.2.1 Eight updating methods for predicting binary outcomes 37320.3 Validation and updating in GUSTO-I 37520.3.1 Validity of TIMI-II model for GUSTO-I 37620.3.2 Updating the TIMI-II model for GUSTO-I 37720.3.3 Performance of updated models 378*20.3.4 R code for updating methods 37920.4 Shrinkage and updating 37920.4.1 Shrinkage towards recalibrated values in GUSTO-I 380*20.4.2 R code for shrinkage and penalization in updating 38120.4.4 Bayesian updating 38220.5 Sample size and updating strategy 383*20.5.1 Simulations of sample size, shrinkage, and updating strategy 38420.5.2 A closed test for the choice of updating strategy 38620.6 Validation and updating of tree models 38620.7 Validation and updating of survival models 388*20.7.1 Validation of a simple index for non-Hodgkin's lymphoma 38820.7.2 Updating the prognostic index 38920.7.3 Recalibration for groups by time points 38920.7.4 Recalibration with a Cox or Weibull regression model 39020.7.6 Summary points 39120.8 Continuous updating 392*20.8.1 Precision and updating strategy 392*20.8.2 Continuous updating in GUSTO-I 393*20.8.3 Other dynamic modeling approaches 39420.9 Concluding remarks 396*20.9.1 Further illustrations of updating 397Chapter 21 Updating for multiple settings 40121.1 Differences in outcome 40121.1.1 Testing for calibration-in-the large 401*21.1.2 Illustration of heterogeneity in GUSTO-I 40221.1.3 Updating for better calibration-in-the large 40321.1.4 Empirical Bayes estimates 403*21.1.5 Illustration of updating in GUSTO-I 40421.1.6 Testing and updating of predictor effects 405*21.1.7 Heterogeneity of predictor effects in GUSTO-I 405*21.1.8 R code for random effect analyses in GUSTO-I 40521.2 Provider profiling 40621.2.1 Ranking of centers: the expected rank 407*21.2.2 Example: provider profiling in stroke 408*21.2.4 Estimation and interpreting differences between centers 409*21.2.5 Ranking of centers 410*21.2.6 R code for provider profiling 41121.3 Concluding remarks 412*21.3.1 Further literature 413Part IV: Applications 415Chapter 22 Case study on a prediction of 30-day mortality 41722.1 GUSTO-I study 41722.1.1 Acute myocardial infarction 417*22.1.2 Treatment results from GUSTO-I 41822.1.3 Prognostic modeling in GUSTO-I 41822.2 General considerations of model development 42122.2.1 Research question and intended application 42122.2.2 Outcome and predictors 42122.2.3 Study design and analysis 42122.3 Seven modeling steps in GUSTO-I 42322.3.1 Preliminary 42322.3.2 Coding of predictors 42322.3.3 Model specification 42322.3.4 Model estimation 42322.3.5 Model performance 42422.3.6 Model validation 42422.3.7 Presentation 42522.3.8 Predictions 42622.4 Validity 42822.4.1 Internal validity: overfitting 42822.4.2 External validity: generalizability 42822.4.3 Summary points 42922.5 Translation into clinical practice 42922.5.1 Score chart for choosing thrombolytic therapy 42922.5.2 From predictions to decisions 43022.6 Concluding remarks 432Chapter 23 Case study on survival analysis: prediction of cardiovascular events 43523.1 Prognosis in the SMART study 435*23.1.1 Patients in SMART 43623.2 General considerations in SMART 43823.2.1 Research question and intended application 43823.2.2 Outcome and predictors 43823.2.3 Study design and analysis 43823.3 Preliminary modeling steps in the SMART cohort 44023.3.1 Patterns of missing values 44023.3.2 Imputation of missing values 44123.3.3 R code 44223.4 Coding of predictors 44323.4.1 Extreme values 44323.4.2 Transforming continuous predictors 44423.4.3 Combining predictors with similar effects 44523.4.4 R code 44623.5.1 A full model 44723.5.2 Impact of imputation 44923.5.3 R code for full model and imputation variants 44923.6 Model selection and estimation 45123.6.1 Stepwise selection 45123.6.2 LASSO for selection with imputed data 45223.7 Model performance and internal validation 45323.7.1 Estimation of optimism in performance 45323.7.2 Model presentation 45623.7.3 R code for presentations 45723.8 Concluding remarks 458Chapter 24 Overall lessons and data sets 46124.1 Sample size 46124.1.1 Model selection, estimation, and sample size 46224.1.2 Calibration improvement by penalization 46324.1.3 Poorer performance with more predictors 46424.1.4 Model selection with noise predictors 46524.1.5 Potential solutions 46624.1.6 R code for model selection and penalization 46624.2 Validation 46724.2.1 Examples of internal and external validation 46724.3 Subject matter knowledge versus machine learning 46824.3.1 Exploiting subject matter knowledge 46824.3.2 Machine learning and Big Data 47024.4 Reporting of prediction models and risk of bias assessments 47024.4.1 Reporting guidelines 47024.4.2 Risk of bias assessment 47224.5 Data sets 47324.5.1 GUSTO-I prediction models 47324.5.2 SMART case study 47524.5.3 Testicular cancer case study 47624.5.4 Abdominal aortic aneurysm case study 47824.6 Concluding remarks 481References 483

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This book gives a concise presentation of the mathematical foundations of Game Theory, with an emphasis on strategic analysis linked to information and dynamics. It is largely self-contained, with all of the key tools and concepts defined in the text.Combining the basics of Game Theory, such as value existence theorems in zero-sum games and equilibrium existence theorems for non-zero-sum games, with a selection of important and more recent topics such as the equilibrium manifold and learning dynamics, the book quickly takes the reader close to the state of the art. Applications to economics, biology, and learning are included, and the exercises, which often contain noteworthy results, provide an important complement to the text.Based on lectures given in Paris over several years, this textbook will be useful for rigorous, up-to-date courses on the subject. Apart from an interest in strategic thinking and a taste for mathematical formalism, the only prerequisite for reading the book is a solid knowledge of mathematics at the undergraduate level, including basic analysis, linear algebra, and probability.

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Book SynopsisFocussing on stochastic models for the spread of infectious diseases in a human population, this book is the outcome of a two-week ICPAM/CIMPA school on "Stochastic models of epidemics" which took place in Ziguinchor, Senegal, December 5–16, 2015. The text is divided into four parts, each based on one of the courses given at the school: homogeneous models (Tom Britton and Etienne Pardoux), two-level mixing models (David Sirl and Frank Ball), epidemics on graphs (Viet Chi Tran), and statistics for epidemic models (Catherine Larédo). The CIMPA school was aimed at PhD students and Post Docs in the mathematical sciences. Parts (or all) of this book can be used as the basis for traditional or individual reading courses on the topic. For this reason, examples and exercises (some with solutions) are provided throughout.Table of Contents- Part I Stochastic Epidemics in a Homogeneous Community. - Introduction. - Stochastic Epidemic Models. - Markov Models. - General Closed Models. - Open Markov Models. - Part II Stochastic SIR Epidemics in Structured Populations. - Introduction. - Single Population Epidemics. - The Households Model. - A General Two-Level Mixing Model. - Part III Stochastic Epidemics in a Heterogeneous Community. - Introduction. - Random Graphs. - The Reproduction Number R0. - SIR Epidemics on Configuration Model Graphs. - Statistical Description of Epidemics Spreading on Networks: The Case of Cuban HIV. - Part IV Statistical Inference for Epidemic Processes in a Homogeneous Community. - Introduction. - Observations and Asymptotic Frameworks. - Inference for Markov Chain Epidemic Models. - Inference Based on the Diffusion Approximation of Epidemic Models. - Inference for Continuous Time SIR models.

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Book SynopsisThis textbook provides a broad overview of the present state of insurance mathematics and some related topics in risk management, financial mathematics and probability. Both non-life and life aspects are covered. The emphasis is on probability and modeling rather than statistics and practical implementation. Aimed at the graduate level, pointing in part to current research topics, it can potentially replace other textbooks on basic non-life insurance mathematics and advanced risk management methods in non-life insurance. Based on chapters selected according to the particular topics in mind, the book may serve as a source for introductory courses to insurance mathematics for non-specialists, advanced courses for actuarial students, or courses on probabilistic aspects of risk. It will also be useful for practitioners and students/researchers in related areas such as finance and statistics who wish to get an overview of the general area of mathematical modeling and analysis in insurance.Table of ContentsBasics.- Experience Rating.- Sums and Aggregate Claims.- Ruin Theory.- Markov Models in Life Insurance.- Financial Mathematics in Life Insurance.- Special Studies in Life Insurance.- Orderings and Comparisons.- Extreme Value Theory.- Dependence and Further Topics in Risk Management.- Stochastic Control in Non-Life Insurance.- Stochastic Control in Life Insurance.- Selected Further Topics.

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Book SynopsisThis open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph.Table of ContentsOptimal transportation.- The Wasserstein space.- Fréchet means in the Wasserstein space.- Phase variation and Fréchet means.- Construction of Fréchet means and multicouplings.

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Book SynopsisThis book strikes a healthy balance between theory and applications, ensuring that it doesn’t offer a set of tools with no mathematical roots. It is intended as a comprehensive and largely self-contained introduction to probability and statistics for university students from various faculties, with accompanying implementations of some rudimentary statistical techniques in the language R. The content is divided into three basic parts: the first includes elements of probability theory, the second introduces readers to the basics of descriptive and inferential statistics (estimation, hypothesis testing), and the third presents the elements of correlation and linear regression analysis. Thanks to examples showing how to approach real-world problems using statistics, readers will acquire stronger analytical thinking skills, which are essential for analysts and data scientists alike. Table of ContentsElements of Probability Theory.- Descriptive and Inferential Statistics.- Linear Regression and Correlation.

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Book SynopsisThis book presents the principles and methods for the practical analysis and prediction of economic and financial time series. It covers decomposition methods, autocorrelation methods for univariate time series, volatility and duration modeling for financial time series, and multivariate time series methods, such as cointegration and recursive state space modeling. It also includes numerous practical examples to demonstrate the theory using real-world data, as well as exercises at the end of each chapter to aid understanding. This book serves as a reference text for researchers, students and practitioners interested in time series, and can also be used for university courses on econometrics or computational finance.Table of Contents1. Introduction.- I. Subject of Time Series.- 2. Random Processes.- II. Decomposition of Economic Time Series.- 3. Trend.- 4. Seasonality and Periodicity.- 5. Residual Component.- III. Autocorrelation Methods for Univariate Time Series.- 6. Box-Jenkins Methodology.- 7. Autocorrelation Methods in Regression Models.- IV. Financial Time Series.- 8. Volatility of Financial Time Series.- 9. Other Methods for Financial Time Series.- 10. Models of Development of Financial Assets.- 11. Value at Risk.- V. Multivariate Time Series.- 12. Methods for Multivariate Time Series.- 13. Multivariate Volatility Modeling.- 14. State Space Models of Time Series.- References.- Index.

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Book SynopsisThis textbook offers a unique compendium of measurement procedures for experimental data acquisition. After introducing readers to the basic theory of uncertainty evaluation in measurements, it shows how to apply it in practice to conduct a range of laboratory experiments with instruments and procedures operating both in the time and frequency domains. Offering extensive practical information and hands-on tips on using oscilloscopes, spectrum analyzers and reflectometric instrumentation, the book shows readers how to deal with e.g. filter characterization, operational amplifiers, digital and analogic spectral analysis, and reflectometry-based measurements. For each experiment, it describes the corresponding uncertainty evaluation in detail. Bridging the gap between theory and practice, the book offers a unique, self-contained guide for engineering students and professionals alike. It also provides university teachers and professors with a valuable resource for their laboratory courses on electric and electronic measurements.Table of ContentsBasic theory of uncertainty evaluation in measurements.- Time Domain Measurements.- Frequency Domain Measurements.- Reflectometric Measurements.- PCB scheme.

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This book provides readers with a systematic approach to quantitative investments and bridges the gap between theory and practice, equipping students to more seamlessly enter the world of industry. A successful quantitative investment strategy requires an individual to possess a deep understanding of the financial markets, investment theories and econometric modelings, as well as the ability to program and analyze real-world data sets. In order to connect finance theories and practical industry experience, each chapter begins with a real-world finance case study. The rest of the chapter introduces fundamental insights and theories, and teaches readers to use statistical models and R programming to analyze real-world data, therefore grounding the learning process in application. Additionally, each chapter profiles significant figures in investment and quantitative studies, so that readers can more fully understand the history of the discipline. This volume will be particularly useful to advanced students and practitioners in finance and investments.

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This book is specially designed to refresh and elevate the level of understanding of the foundational background in probability and distributional theory required to be successful in a graduate-level statistics program. Advanced undergraduate students and introductory graduate students from a variety of quantitative backgrounds will benefit from the transitional bridge that this volume offers, from a more generalized study of undergraduate mathematics and statistics to the career-focused, applied education at the graduate level. In particular, it focuses on growing fields that will be of potential interest to future M.S. and Ph.D. students, as well as advanced undergraduates heading directly into the workplace: data analytics, statistics and biostatistics, and related areas.

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Book SynopsisThis book provides a general introduction to Sequential Monte Carlo (SMC) methods, also known as particle filters. These methods have become a staple for the sequential analysis of data in such diverse fields as signal processing, epidemiology, machine learning, population ecology, quantitative finance, and robotics.The coverage is comprehensive, ranging from the underlying theory to computational implementation, methodology, and diverse applications in various areas of science. This is achieved by describing SMC algorithms as particular cases of a general framework, which involves concepts such as Feynman-Kac distributions, and tools such as importance sampling and resampling. This general framework is used consistently throughout the book.Extensive coverage is provided on sequential learning (filtering, smoothing) of state-space (hidden Markov) models, as this remains an important application of SMC methods. More recent applications, such as parameter estimation of these models (through e.g. particle Markov chain Monte Carlo techniques) and the simulation of challenging probability distributions (in e.g. Bayesian inference or rare-event problems), are also discussed.The book may be used either as a graduate text on Sequential Monte Carlo methods and state-space modeling, or as a general reference work on the area. Each chapter includes a set of exercises for self-study, a comprehensive bibliography, and a “Python corner,” which discusses the practical implementation of the methods covered. In addition, the book comes with an open source Python library, which implements all the algorithms described in the book, and contains all the programs that were used to perform the numerical experiments.Trade Review“The authors have written a comprehensive broad-audience treatment of sequential Monte Carlo (SMC) methods, covering all its major and diverse applications. … The book is structured as an advanced Ph.D.-level textbook.” (Michael Ludkovski, Mathematical Reviews, May, 2022)Table of Contents1 Preface.- 2 Introduction to state-space models.- 3 Beyond state-space models.- 4 Introduction to Markov processes.- 5 Feynman-Kac models: definition, properties and recursions.- 6 Finite state-spaces and hidden Markov models.- 7 Linear-Gaussian state-space models.- 8 Importance sampling.- 9 Importance resampling.- 10 Particle filtering.- 11 Convergence and stability of particle filters.- 12 Particle smoothing.- 13 Sequential quasi-Monte Carlo.- 14 Maximum likelihood estimation of state-space models.- 15 Markov chain Monte Carlo.- 16 Bayesian estimation of state-space models and particle MCMC.- 17 SMC samplers.- 18 SMC2, sequential inference in state-space models.- 19 Advanced topics and open problems.

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Book SynopsisThis book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.Table of Contents1.- Some Elements of Linear-Quadratic Optimal Controls.- 2. Linear-Quadratic Two-Person Differential Games.- 3. Mean-Field Linear-Quadratic Optimal Controls.

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Book SynopsisThis textbook offers an easy-to-follow, practical guide to modern data analysis using the programming language R. The chapters cover topics such as the fundamentals of programming in R, data collection and preprocessing, including web scraping, data visualization, and statistical methods, including multivariate analysis, and feature exercises at the end of each section. The text requires only basic statistics skills, as it strikes a balance between statistical and mathematical understanding and implementation in R, with a special emphasis on reproducible examples and real-world applications. This textbook is primarily intended for undergraduate students of mathematics, statistics, physics, economics, finance and business who are pursuing a career in data analytics. It will be equally valuable for master students of data science and industry professionals who want to conduct data analyses.Trade Review“It was very interesting to go through the pages of this book. The authors should be commended for writing a thorough book about complex concepts of data analysis in R that could, however, be read easily. I warmly recommend this book to students of statistics but also to professionals who would like to acquire advanced analytical skills or improve their competencies in R, especially nowadays with R very popular amongst data analysts.” (Georgios Nikolopoulos, ISCB News, iscb.info, Issue 71, June, 2021)Table of ContentsPreface.- 1 Introduction.- 2 Introduction to R.- 3 Databases in R.- 4 Visualization.- 5 Data Analysis with R.- R Packages and Funtions.

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Book SynopsisToday, information technology plays a pivotal role in financial control and audit: most financial data is now digitally recorded and dispersed among servers, clouds and networks over which the audited firm has no control. Additionally, a firm’s data—particularly in the case of finance, software, insurance and biotech firms— comprises most of the audited value of the firm. Financial audits are critical mechanisms for ensuring the integrity of information systems and the reporting of organizational finances. They help avoid the abuses that led to passage of legislation such as the Foreign Corrupt Practices Act (1977), and the Sarbanes-Oxley Act (2002). Audit effectiveness has declined over the past two decades as auditor skillsets have failed to keep up with advances in information technology. Information and communication technology lie at the core of commerce today and are integrated in business processes around the world. This book is designed to meet the increasing need of audit professionals to understand information technology and the controls required to manage it. The material included focuses on the requirements for annual Securities and Exchange Commission audits (10-K) for listed corporations. These represent the benchmark auditing procedures for specialized audits, such as internal, governmental, and attestation audits.Using R and RStudio, the book demonstrates how to render an audit opinion that is legally and statistically defensible; analyze, extract, and manipulate accounting data; build a risk assessment matrix to inform the conduct of a cost-effective audit program; and more.Table of Contents1. Fundamentals of Auditing Financial Statements.- 2. Foundations of Audit Analytics.- 3. Analysis of Accounting Transactions.- 4. Risk Assessment and Planning.- 5. Analytical Review: Technical Analysis.- 6. Analytical Review: Intelligence Scanning.- 7. Design of Audit Programs.- 8. Interim Compliance Tests.- 9. Substantive Tests.- 10. Sarbanes-Oxley Engagements.- 11. Blockchains, Cybercrime and Forensics.- 12. Special Engagements: Forecasts and Valuation.- 13. Simulated Transactions for Auditing Service Organizations.

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Book SynopsisThis book provides an extensive overview of the principles and methods of sample size calculation and recalculation in clinical trials. Appropriate calculation of the required sample size is crucial for the success of clinical trials. At the same time, a sample size that is too small or too large is problematic due to ethical, scientific, and economic reasons. Therefore, state-of-the art methods are required when planning clinical trials. Part I describes a general framework for deriving sample size calculation procedures. This enables an understanding of the common principles underlying the numerous methods presented in the following chapters. Part II addresses the fixed sample size design, where the required sample size is determined in the planning stage and is not changed afterwards. It covers sample size calculation methods for superiority, non-inferiority, and equivalence trials, as well as comparisons between two and more than two groups. A wide range of further topics is discussed, including sample size calculation for multiple comparisons, safety assessment, and multi-regional trials. There is often some uncertainty about the assumptions to be made when calculating the sample size upfront. Part III presents methods that allow to modify the initially specified sample size based on new information that becomes available during the ongoing trial. Blinded sample size recalculation procedures for internal pilot study designs are considered, as well as methods for sample size reassessment in adaptive designs that use unblinded data from interim analyses. The application is illustrated using numerous clinical trial examples, and software code implementing the methods is provided. The book offers theoretical background and practical advice for biostatisticians and clinicians from the pharmaceutical industry and academia who are involved in clinical trials. Covering basic as well as more advanced and recently developed methods, it is suitable for beginners, experienced applied statisticians, and practitioners. To gain maximum benefit, readers should be familiar with introductory statistics. The content of this book has been successfully used for courses on the topic.Trade Review“The R source code is shown by chapter, well-documented, and easy to find and follow as brief descriptions and necessary specifications for the function calls are given by means of comments. … a wide area of application fields is covered and exhaustive literature references for further reading are given. … The presentation of the material is very reader-friendly, easily accessible and pedagogical … . It is likewise highly recommended … . This is an effective and nicely written reference textbook.” (Oke Gerke, ISCB News, iscb.info, Vol. 72, December, 2021)Table of ContentsPart I Basics 1 Introduction 1.1 Background and outline 1.2 Examples 1.2.1 The ChroPac trial 1.2.2 The Parkinson trial 1.3 General considerations when calculating sample sizes 2 Statistical test and sample size calculation 2.1 The main principle of statistical testing 2.2 The main principle of sample size calculation Part II Sample size calculation 3 Comparison of two groups for normally distributed outcomes and test for difference or superiority 3.1 Background and notation 3.2 z-test 3.3 t-test 3.4 Analysis of covariance 3.5 Bayesian approach 3.5.1 Background 3.5.2 Methods 4 Comparison of two groups for continuous and ordered categorical outcomes and test for difference or superiority 4.1 Background and notation 4.2 Continuous outcomes 4.3 Ordered categorical outcomes 4.3.1 Assumption-free approach 4.3.2 Assuming proportional odds 5 Comparison of two groups for binary outcomes and test for difference and superiority 5.1 Background and notation 5.2 Asymptotic tests 5.2.1 Difference of rates as effect measure 5.2.2 Risk ratio as effect measure 5.2.3 Odds ratio as effect measure 5.2.4 Logistic regression 5.3 Exact unconditional tests 5.3.1 Background 5.3.2 Fisher-Boschloo test 6 Comparison of two groups for time-to-event outcomes and test for differences or superiority 6.1 Background and notation 6.1.1 Time-to-event data 6.1.2 Sample size calculation for time-to-event data 6.2 Exponentially distributed time-to-event data 6.3 Time-to-event data with proportional hazards 6.3.1 Approach of Schoenfeld 6.3.2 Approach of Freedman 7 Comparison of more than two groups and test for difference 7.1 Background and notation 7.2 Normally distributed outcomes 7.3 Continuous outcomes 7.4 Binary outcomes 7.4.1 Analysis with chi-square test 7.4.2 Analysis with Cochran-Armitage test 7.5 Time-to-event outcomes 8 Comparison of two groups and test for non-inferiority 8.1 Background and notation 8.2 Normally distributed outcomes 8.2.1 Difference of means 8.2.2 Ratio of means 8.3 Continuous and ordered categorical outcomes 8.4 Binary outcomes 8.4.1 Analysis with asymptotic tests 8.4.1.1 Difference of rates as effect measure 8.4.1.2 Risk ratio as effect measure 8.4.1.3 Odds ratio as effect measure 8.4.2 Exact unconditional tests 8.4.2.1 Background 8.4.2.2 Difference of rates as effect measure 8.4.2.3 Risk ratio as effect measure 8.4.2.4 Odds ratio as effect measure 8.5 Time-to-event outcomes 9 Comparison of three groups in the gold standard non-inferiority design 9.1 Background and notation 9.2 Net effect approach 9.3 Fraction effect approach 10 Comparison of two groups for normally distributed outcomes and test for equivalence 10.1 Background and notation 10.2 Difference of means 10.3 Ratio of means 11 Multiple comparisons 11.1 Background and notation 11.2 Generally applicable sample size calculation methods and applications 11.2.1 Methods 11.2.2 Applications 11.3 Multiple endpoints 11.3.1 Background and notation 11.3.2 Methods 11.4 More than two groups 11.4.1 Background and notation 11.4.2 Dunnett test 12 Assessment of safety 12.1 Background and notation 12.2 Testing hypotheses on the event probability 12.3 Estimating the occurrence probability of an event with specified precision 12.4 Observing at least one event 13 Cluster-randomized trials 13.1 Background and notation 13.2 Normally distributed outcomes 13.2.1 Cluster-level analysis 13.2.2 Individual-level analysis 13.2.3 Dealing with unequal cluster size 13.3 Other scale levels of the outcome 14 Multi-regional trials 14.1 Background and notation 14.2 Sample size calculation for demonstrating consistency of global results and results for a specified region 14.3 Sample size calculation for demonstrating a consistent trend across all regions 15 Integrated planning of phase II/III drug development programs 15.1 Background and notation 15.2 Optimizing phase II/III programs 16 Simulation-based sample size calculation Part III Sample size recalculation 17 Background Part IIIA Blinded sample size recalculation in internal pilot study designs 18 Background and notation 19 A general approach for controlling the type I error rate for blinded sample size recalculation 20 Comparison of two groups for normally distributed outcomes and test for difference or superiority 20.1 t-Test 20.1.1 Background and notation 20.1.2 Blinded variance estimation 20.1.3 Type I error rate 20.1.4 Power and sample size 20.2 Analysis of covariance 20.2.1 Background and notation 20.2.2 Blinded variance estimation 20.2.3 Type I error rate 20.2.4 Power and sample size 21 Comparison of two groups for binary outcomes and test for difference or superiority 21.1 Background and notation 21.2 Asymptotic tests 21.2.1 Difference of rates as effect measure 21.2.2 Risk ratio and odds ratio as effect measure 21.3 Fisher-Boschloo test 22 Comparison of two groups for normally distributed outcomes and test for non-inferiority 22.1 t-Test 22.1.1 Background and notation 22.1.2 Blinded variance estimation 22.1.3 Type I error rate 22.1.4 Power and sample size 22.2 Analysis of covariance 23 Comparison of two groups for binary outcomes and test for non-inferiority 23.1 Background and notation 23.2 Difference of rates as effect measure 23.3 Risk ratio and odds ratio as effect measure 24 Comparison of two groups for normally distributed outcomes and test for equivalence 25 Regulatory and operational aspects 26 Concluding remarks Part IIIB Unblinded sample size recalculation in adaptive designs 27 Background and notation 27.1 Group-sequential designs 27.2 Adaptive designs 27.2.1 Combination function approach 27.2.2 Conditional error function approach 28 Sample size recalculation based on conditional power 28.1 Background and notation 28.2 Using the interim estimate of the effect 28.3 Using the initially specified effect 28.4 Using prior information as well as the interim effect estimate 29 Sample size recalculation by optimization 30 Regulatory and operational aspects 31 Concluding remarks Appendix: Selected R software code References

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Book SynopsisThis book provides hands-on guidance for researchers and practitioners in criminal justice and criminology to perform statistical analyses and data visualization in the free and open-source software R. It offers a step-by-step guide for beginners to become familiar with the RStudio platform and tidyverse set of packages. This volume will help users master the fundamentals of the R programming language, providing tutorials in each chapter that lay out research questions and hypotheses centering around a real criminal justice dataset, such as data from the National Survey on Drug Use and Health, National Crime Victimization Survey, Youth Risk Behavior Surveillance System, The Monitoring the Future Study, and The National Youth Survey. Users will also learn how to manipulate common sources of agency data, such as calls-for-service (CFS) data. The end of each chapter includes exercises that reinforce the R tutorial examples, designed to help master the software as well as to provide practice on statistical concepts, data analysis, and interpretation of results. The text can be used as a stand-alone guide to learning R or it can be used as a companion guide to an introductory statistics textbook, such as Basic Statistics in Criminal Justice (2020).Table of Contents1. Getting started.2. Managing your data.3. Data visualization.4. Spatiotemporal data visualization and basic crime analysis.5. Descriptive statistics: measures of central tendency.6. Descriptive statistics: measures of dispersion.7. Statistical inference in criminal justice research.8. Defining the observed significance level of a test.9. Hypothesis testing using the binomial distribution.10. Chi-square: a test commonly used for nominal-level measures.11. The normal distribution and its application to tests of statistical significance.12. Comparing means in two samples.13. Analysis of variance.14. Measures of association for nominal and ordinal variables.15. Measuring association for interval data.16. Introduction to regression analysis.

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Book SynopsisThis book provides computational tools that readers can use to flourish in the retirement income industry. Each chapter describes recipe-like algorithms and explains how to implement them via simple scripts in the freely available R coding language. Students can use those skills to generate quantitative answers to the most common questions in retirement income planning, as well as to develop a deeper understanding of the finance and economics underlying the field itself. The book will be an excellent asset for experienced students who are interested in advanced wealth management, and specifically within courses that focus on holistic modeling of the retirement income process. The material will also be useful to current and future wealth management professionals within the financial services industry. Readers should have a solid understanding of financial principles, as well as a rudimentary background in economics and accounting. Table of Contents1 Setting Expectations and Deviations.- 2 Loading and Getting to Know R.- 3 Coding the (Simple) Financial Life-cycle Model.- 4 Data in R: The Family Balance Sheet.- 5 Portfolio Longevity: Deterministic & Stochastic.- 6 Modeling the Risk of Sequence-of-Returns.- 7 Modeling Human Longevity and Life Tables.- 8 Life & Death in Continuous Time: Gompertz 101.- 9 The Lifetime Ruin Probability (LRP).- 10 Life Annuities: From Immediate to Deferred.- 11 Intelligent Drawdown Rates.- 12 Pensionization: From Benefits to Utility.- 13 Biological (and other) Ages.- 14 Exotic Annuities for Longevity Risk.- 15 Very Last Thoughts.- Glossary of User Defined R-Functions.

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