Statistical Methods in Laboratory Medicine

Statistical Methods in Laboratory Medicine focuses on the application of statistics in laboratory medicine.

The book first ponders on quantitative and random variables, exploratory data analysis (EDA), probability, and probability distributions. Discussions focus on negative binomial distribution, non-random distributions, binomial distribution, fitting the binomial model to sample data, conditional probability and statistical independence, rules of probability, and Bayes' theorem. The text then examines inference, regression, and measurement and control. Topics cover analytical goals for assay precision, estimating the error variance components, indirect structural assays, functional assays, bivariate regression model, and least-squares estimates of the functional relation parameters.

The manuscript takes a look at assay method comparison studies, multivariate analysis, forecasting and control, and test interpretation. Concerns include time series structure and terminology, polynomial regression, assessing the performance of the classification rule, quantitative screening tests, sample correlation coefficient, and computer assisted diagnosis.

The book is a dependable reference for medical experts and statisticians interested in the employment of statistics in laboratory medicine.

Preface

1 Introduction

2 Getting the Picture

2.1 Quantitative Variables

2.3 Random Variables

2.4 Measures

2.5 Collecting the Right Data

2.6 Looking at Sample Data

2.7 The Histogram

2.8 Central Tendency

2.9 Scatter

2.10 Exploratory Data Analysis (EDA)

References

Software

3 Probability

3.1 Introduction

3.2 A State of Nature

3.3 A State of Mind

3.4 Axioms of Probability: Terminology

3.5 Axioms of Probability

3.6 Conditional Probability and Statistical Independence

3.7 Rules of Probability

3.8 Bayes’ Theorem

3.9 Odds and Ends

References

4 Probability Distributions I: Discrete Variables

4.1 Getting the Picture

4.2 The Binomial Distribution

4.3 Fitting the Binomial Model to Sample Data

4.4 The Poisson Distribution

4.5 Non-Random Distributions

4.6 The Negative Binomial Distribution

4.7 Final Thoughts

References

5 Probability Distributions II: Continuous Variables

5.1 The Normal Distribution

5.2 Probability Density

5.3 Fitting the Normal Distribution Function

5.4 Testing the Normal Model Assumption

5.5 Transformations of Non-Normal Data

5.6 Other Distributions

References

6 Inference I

6.1 Populations and Samples

6.2 Survey and Experiment

6.3 Sample Selection: Surveys

6.4 Sampling for Experiment

6.5 From Numbers to Knowledge

6.6 Hypothesis Testing

6.7 Sample Size: Inference on a Single Population Mean

6.8 Comparing Two Independent Samples

6.9 Paired Comparisons

6.10 Non-Parametric Tests

6.11 More than Two Samples

References

7 Regression I: Straight-Line Relationships

7.1 Introduction

7.2 The Nature of Relationships

7.3 Functional Relationships

7.4 Least-Squares Estimates Of The Functional Relation Parameters

7.5 From Arithmetic to Inference

7.6 Inference on the Linear Regression Model

7.7 The Calibration Problem

7.8 Weighted Regression

7.9 The Bivariate Regression Model

7.10 Through the Looking Glass

7.11 Rank Correlation

7.12 Looking Ahead

References

8 Measurement and Control

8.1 Introduction

8.2 Accuracy

8.3 Functional Assays

8.4 Structural Assays

8.5 Indirect Structural Assays

8.6 The Origins of Inaccuracy

8.7 Analytical Goals for Assay Accuracy

8.8 Precision

8.9 Estimating the Error Variance Components

8.10 Analytical Goals for Assay Precision

8.11 Control

8.12 Cumulative Sum Charts (CUSUMS)

8.13 Patient-Based Imprecision Studies

8.14 Patients' Daily Means

8.15 Qualitative Test Control

8.16 A Parting Thought

References

9 Assay Method Comparison Studies

9.1 Introduction

9.2 The Statistical Problem

9.3 A Little History

9.4 Calculations

9.5 Cautions

9.6 The Sample Correlation Coefficient

9.7 Final Thoughts

References

10 Test Interpretation

10.1 Introduction

10.2 A Quest for the Fabulous Norm

10.3 The 95% Reference Paradox

10.4 Multi Variate Reference Ranges

10.5 Screening

10.6 Qualitative Screening Tests

10.7 Quantitative Screening Tests

10.8 Assessing the Individual Patient

10.9 Kernel Density Estimation

10.10 Computer Assisted Diagnosis

References

11 Multivariate Analysis

11.1 Introduction

11.2 Linear Discriminant Function

11.3 Multivariate Normal Discrimination

11.4 Assessing the Performance of the Classification Rule

11.5 Assessing the Individual Patient

11.6 Quadratic Discrimination and Beyond

11.7 Variable Selection

11.8 Regression Revisited

11.9 Polynomial Regression

11.10 Is there a Pattern?

References

12 Forecasting And Control

12.1 Introduction

12.2 Time Series Structure and Terminology

12.3 Recursive Estimation

12.4 The Ewma Discount Coefficient W

12.5 Monitoring a Forecasting System

12.6 Following a Trend

12.7 Holt's Local Linear Trend Model

12.8 The Kaiman Filter

12.9 Following a Trend

Appendix 12.A GW-BASIC Program-Tracker

References

13 Inference II: Analysis of 2X2 Tables

13.1 Sampling Models for 2X2 Tables

13.2 The 2X2 Chi-Square Test

13.3 Fisher's Exact Probability Test

13.4 Estimation I: Comparing Proportions

13.5 Estimation I: The Odds-Ratio

13.6 Paired Comparisons

13.7 Combining 2X2 Tables

13.8 Multidimensional Problems

13.9 Regression with Counted Proportions

Note 13.A Derivation of a 2X2 X2 Statistic

A Note on Notation

References

Appendix A Statistical Tables A.1 to A.8

Table A.1 2000 Random Digits

Table A.2 Areas Under the Standard Normal Curve

Table A.3 Coefficients and Critical Values: Shapiro-Wilk Test

Table A.4 Percentiles of the t Distribution (Two-Sided)

Table A.5 Upper 100α Percentile Points of the Χ2 Distribution

Table A.6 Percentile Points of the F-Distribution (5%)

Table A.7 Critical Values of the Linear Correlation Coefficient

Table A.8 Random Numbers from a Specified Normal Distribution

Index