This book provides a reference for people working in the design, development, and manufacturing of medical devices. While there are no statistical methods specifically intended for medical devices, there are methods that are commonly applied to various problems in the design, manufacturing, and quality control of medical devices. The aim of this book is not to turn everyone working in the medical device industries into mathematical statisticians; rather, the goal is to provide some help in thinking statistically, and knowing where to go to answer some fundamental questions, such as justifying a method used to qualify/validate equipment, or what information is necessary to support the choice of sample sizes.
While, there are no statistical methods specifically designed for analysis of medical device data, there are some methods that seem to appear regularly in relation to medical devices. For example, the assessment of receiver operating characteristic curves is fundamental to development of diagnostic tests, and accelerated life testing is often critical for assessing the shelf life of medical device products. Another example is sensitivity/specificity computations are necessary for in-vitro diagnostics, and Taguchi methods can be very useful for designing devices. Even notions of equivalence and noninferiority have different interpretations in the medical device field compared to pharmacokinetics. It contains topics such as dynamic modeling, machine learning methods, equivalence testing, and experimental design, for example.
This book is for those with no statistical experience, as well as those with statistical knowledgeable―with the hope to provide some insight into what methods are likely to help provide rationale for choices relating to data gathering and analysis activities for medical devices.
Author(s): Scott A. Pardo
Publisher: Springer
Year: 2023
Language: English
Pages: 383
City: Cham
Preface
Acknowledgments
Contents
Chapter 1: Some Fundamentals: Probability
1.1 The Basics
1.2 Summary
Reference
Chapter 2: Some Fundamentals: Estimation and Inference
2.1 Estimation
2.2 Inference
2.3 Model Building
2.4 Summary
Reference
Chapter 3: Confidence
3.1 What Does Confidence Mean?
3.2 What Confidence Does Not Mean
3.3 Some Consequences of Confidence Limits
3.4 Some Confidence Limit Formulas
3.4.1 Proportions
3.4.2 Means
3.4.3 Standard Deviations
3.5 Summary
References
Chapter 4: Power and Hypothesis Testing
4.1 Inductive Statistical Reasoning
4.2 Estimation
4.3 Inference and Hypothesis Tests
4.4 More Hypothesis Tests
4.5 Summary
Reference
Chapter 5: Least Squares: Regression and ANOVA
5.1 Motivation for Least Squares: Simple Linear Regression
5.2 Multiple Regression and ANOVA
5.3 Multiple Comparisons
5.4 Collinearity and Correlation of Regressors
5.4.1 Partial Least Squares
5.4.2 Ridge Regression
5.4.3 Least Absolute Shrinkage and Selection Operator (LASSO)
5.5 Summary
References
Chapter 6: Product Design: Factorial Experiments
6.1 General
6.2 Eliminating the ``Unimportant´´ Factors: First-Order Model
6.3 Assessing the Effect of Each Factor
6.4 Assessing the Cross-Product or Interaction Effects
6.5 A Three-Factor Example
6.6 Fractional Factorial Designs
6.7 Second-Order Models and Designs
6.7.1 Central Composite Design (CCD)
6.7.2 Box-Behnken Design (BBD)
6.8 Non-continuously Valued Input Factors and Multiple Comparisons
6.9 Matrix Form
6.10 The Taguchi Approach
6.10.1 The Quadratic Loss Function
6.10.2 Parameter Design: Noise Parameters, Control Parameters, and Inner and Outer Arrays
6.11 Summary
References
Chapter 7: Process Control
7.1 Introduction
7.2 The Chart
7.3 The S Chart
7.4 The CV Chart
7.5 The P Chart
7.6 Process Control
7.7 Summary
References
Chapter 8: Inspection and Acceptance Sampling
8.1 Inspection and Acceptance Sampling
8.2 Attribute Sampling Plans
8.2.1 Risk
8.2.2 Sample Size Considerations for Attribute Plans
8.3 Variable Sampling Plans and Cpk
8.3.1 The Population Cpk
8.3.2 Sample Cpk and Hypothesis Tests
8.3.3 Sample Size Considerations for Variable Plans
8.4 Confidence Limits for Cpk
8.5 Double Sampling Plans: Attributes
8.6 Sampling Plans for Precision Parameters
8.6.1 Introduction
8.6.2 Standard Deviation
8.6.3 Coefficient of Variation
8.7 Summary: A Final Word
References
Chapter 9: Reliability, Life Testing, and Shelf Life
9.1 The Reliability and Related Functions
9.2 Obtaining an Empirical Reliability Model
9.3 Relating the βi to Design Parameters
9.4 Censored Time-to-Failure
9.5 Accelerated Life Tests
9.6 Stability and Shelf Life
9.7 Summary
References
Chapter 10: Diagnostics: Sensitivity and Specificity
10.1 Receiver Operating Characteristic (ROC) Curves
10.2 Sensitivity and Specificity
10.3 Summary
Reference
Chapter 11: Equivalence and Noninferiority
11.1 Introduction
11.2 A Single Proportion
11.3 Comparing Two Proportions
11.4 Comparing Two Means
11.5 Comparing Two Standard Deviations
11.6 Summary of Equivalence and Noninferiority
References
Chapter 12: Nonparametrics
12.1 Introduction
12.2 Rank-Based Methods
12.2.1 The Mann-Whitney-Wilcoxon Test: Analogous to the T-Test
12.2.2 One-Way Nonparametric ANOVA: The Kruskal-Wallis Test
12.3 Resampling Methods: Bootstrap
12.4 Resampling Methods: Permutation Test
12.5 Summary
References
Chapter 13: Bayesian Methods
13.1 The Basic Idea of Bayesian Inference
13.2 The Markov Chain Monte Carlo (MCMC) Method
13.3 Summary
Reference
Chapter 14: Prediction, Classification, and Nonlinear Modeling
14.1 Introduction
14.2 Stepwise Regression
14.3 Bayesian Model Averaging
14.4 GLMULTI: An Automated Model Selection Procedure
14.5 Neural Networks
14.6 Classification and Regression Trees (CART)
14.7 Random Forests
14.8 Logistic Regression and Model Selection
14.9 Summary
References
Chapter 15: Variance Components and Precision
15.1 Introduction
15.2 The Mixed Model: Randomized Complete Block Design
15.3 Measures of Precision: Standard Deviation and Coefficient of Variation
15.4 Imprecision and Quality
15.5 Summary
References
Chapter 16: Time Series and Dynamic Systems
16.1 Introduction
16.2 Time Series
16.3 Identifying Time Series Model Types and Orders
16.4 The Box-Jenkins Approach
16.5 Non-stationarity and Differencing
16.6 An Example of a Time Series Analysis
16.7 Markov Chains
16.8 Steady-State, or ``Stationary,´´ Distribution
16.9 Extensions of Markov Chains
16.10 Summary
References
Chapter 17: Odds, Odds Ratios, and Comparing Proportions
17.1 Difference Between Proportions and Odds Ratios
17.2 Logistic Regression, Again
17.3 Summary
References
Untitled
Chapter 18: Afterword
Index
Appendix A: Some Mathematical Fundamentals
A.1 Basics of Calculus
A.2 Derivatives and Differentiation
A.3 Derivatives and Optima
A.4 Integrals and Integration
A.5 Matrix and Vector Algebra
A.6 Scalar Multiplication
A.7 Matrix and Vector Addition
A.8 Transposition
A.9 Matrix Multiplication
A.10 Dot or Scalar Product
A.11 Square Matrices, the Identity Matrix, and Matrix Inverses
A.12 Determinants
A.13 Eigenvalues and Eigenvectors
A.14 Diagonalization and Powers of Matrices
A.15 Least Squares and Variants
A.16 Taylor Series Expansions
A.17 Quadratic Solution and Vertices
A.18 Vertex
A.19 Inequalities and Absolute Value Expressions
A.20 Expressions with Absolute Values
A.21 Complex Numbers and Variables
A.22 Fourier Series
A.23 Spectral Analysis of Time Series
A.24 A Note on Importing Data
Reference
