Introduction to Statistical Analysis of Laboratory Data

Alfred A. Bartolucci is Professor Emeritus in the Department of Biostatistics, School of Public Health, University of Alabama at Birmingham. He has over 300 peer-reviewed publications (manuscripts and book chapters) in the areas of original statistical methodologic research and clinical and laboratory statistical applications. An endowed scholarship in Biostatistics at UAB was established in his honor. Karan P. Singh is currently Professor of Medicine and serves as Director of the Biostatistics and Bioinformatics Shared Facility at the University of Alabama at Birmingham Comprehensive Cancer Center. He has authored or coauthored over 250 peer-reviewed articles, book chapters, and peer-reviewed congress or conference proceedings. He is a Fellow of the American Statistical association. Sejong Bae is Professor of Medicine and serves as Co-Director of the Biostatistics and Bioinformatics Shared Facility; Deputy Director of the Coronary Artery Risk Development in Young Adults Coordination Center; and Director of Data, Information, and Statistics Core in the Division of Preventive Medicine. In 2009, he was elected to International Statistical Institute.

• Preface xiAcknowledgments xv1 Descriptive Statistics 11.1 Measures of Central Tendency 11.2 Measures of Variation 41.3 Laboratory Example 71.4 Putting it All Together 81.5 Summary 10References 102 Distributions and Hypothesis Testing in Formal Statistical Laboratory Procedures 112.1 Introduction 112.2 Confidence Intervals (CT) 192.2.1 Confidence Interval (CI) for the Population Mean – The t-Distribution 202.2.2 Confidence Interval for the Variance and Standard Deviation 212.3 Inferential Statistics – Hypothesis Testing 232.3.1 t-Test for Means 252.3.2 Test for Variation: Coefficient of Variation (CV) 282.3.3 Two-Sample Test of the Population Means 292.3.4 One-Way Analysis of Variance (ANOVA) 342.3.5 Nonparametric Tests for Skewed Data 40References 413 Method Validation 433.1 Introduction 433.2 Accuracy 453.2.1 Method 1 453.2.2 Method 2 563.3 Brief Introduction to Bioassay 593.3.1 Direct Assay 593.3.2 Indirect Assay 613.4 Sensitivity, Specificity (Selectivity) 693.5 Method Validation and Method Agreement – Bland-Altman 73References 764 Methodologies in Outlier Analysis 794.1 Introduction 794.2 Some Outlier Determination Techniques 804.2.1 Grubb Statistic 824.2.2 Other Forms of the Grubb Statistic 844.2.3 Studentized Range Statistic 854.2.4 Sequential Test of Many Outliers 864.2.5 Mahalanobis Distance Measure 884.2.6 Dixon Q-Test for a Single Outlier 914.2.7 The Box Plot 944.2.8 Median Absolute Deviation 954.3 Combined Method Comparison Outlier Analysis 964.3.1 Further Outlier Considerations 964.3.2 Combined Method Comparison Outlier Analysis – Refined Method Comparisons Using Bland – Altman 984.4 Some Consequences of Outlier Removal 1034.5 Considering Outlier Variance 1044.5.1 The Cochran C test 1044.5.2 Cochran G Test 107References 1105 Statistical Process Control 1135.1 Introduction 1135.2 Control Charts 1155.2.1 Means (X-bar) Control Charts 1175.2.2 Range Control Charts 1225.2.3 The S-Chart 1245.2.4 The Median Chart 1265.2.5 Mean (X-bar) and S-Charts Based on the Median Absolute Deviation (MAD) 1285.3 Capability Analysis 1315.4 Capability Analysis – An Alternative Consideration 137References 1396 Limits of Calibration 1416.1 Calibration: Limit Strategies for Laboratory Assay Data 1416.1.1 Definition – Calibration 1416.2 Limit Strategies 1426.2.1 Example – Estimation of LoB and LoD for Drug Assay 1426.2.2 LoQ Results 1446.2.3 A Comparison of Empirical and Statistical Approaches to the LoD and LoQ 1456.2.4 Example – LoD/LoQ, GC – MS Approach 1456.2.5 LoD/LoQ, GC – MS Approach 1466.2.6 Explanation of the Difficulty of the Statistical Methodology for the LoD and LoQ 1476.2.7 Another LoQ Method 1516.3 Method Detection Limits (EPA) 1516.3.1 Method Detection Limits 1516.3.2 Example – Atrazine by Gas Chromatography (GC) 1526.3.3 LoD and LoQ Summary 1536.4 Data Near the Detection Limits 1546.4.1 Biased Estimators 1546.4.2 Computing Some Statistics with the LoD in the Data 1546.5 More on Statistical Management of Nondetects 1566.5.1 Model-Based Examples of Measuring Nondetects 1576.5.2 An Alternative Regression Approach with Improvements (Refer to the Box Cox Transformation in Chapter 5) 1606.5.3 Extension of the ROS Method for Multiple NDs in Various Positions 1636.5.4 Cohen’s Adjustment 1656.6 The Kaplan – Meier Method (Nonparametric Approach) for Analysis of Laboratory Data with Nondetects 170References 1747 Calibration Bias 1777.1 Error 1777.1.1 Types of Error 1797.2 Uncertainty 1807.3 Sources of Uncertainty 1807.4 Estimation Methods of Uncertainty 1817.4.1 Statistical Estimation Methods of Type A Uncertainty 1817.4.2 Estimation Methods of Type B Uncertainty 1837.4.3 Estimation Methods of Combined and Expanded Uncertainties (Normal Data) 1877.4.4 Estimation Methods of Combined and Expanded Uncertainties (Nonnormal Data) 1907.4.5 Another Method of Estimating Uncertainties for Nonnormal Data (Nonparametric) 1927.5 Calibration Bias 1947.5.1 Gas Chromatographic/Mass Spectrometric (GC – MS) Calibration Bias 1977.5.2 Discussion 2057.6 Multiple Instruments 2057.7 Crude Versus Precise Methodologies 208References 2108 Robustness and Ruggedness 2138.1 Introduction 2138.2 Robustness 2148.3 Ruggedness 2168.4 An Alternative Procedure for Ruggedness Determination 2248.5 Ruggedness and System Suitability Tests 2278.5.1 Determining the SST Limits from Replicated Experimentation 2288.5.2 Determining the SST Limits from Statistical Prediction 231References 233Index 235

"The book presents a detailed discussion of important statistical concepts and methods of data presentation and analysis. -Provides detailed discussions on statistical applications including a comprehensive package of statistical tools that are specific to the laboratory experiment process. - Introduces terminology used in many applications such as the interpretation of assay design and validation as well as fit for purpose" procedures including real world examples." (Zentralblatt MATH 2016)