Medical Biostatistics, Fourth Edition
Contents
Preface to Fourth
Edition |
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Summary Tables |
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Frequently Used
Notations |
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1 Medical Uncertainties |
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1.1 Uncertainties in Health
and Disease |
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1.1.1 Uncertainties due to Intrinsic Variation –
Biologic, Genetic, Behavioral and Other Host Factors, Environmental, Chance,
Sampling Fluctuations |
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1.1.2 Natural Variation in Assessment – Observer,
Treatment Strategies, Instrument and Laboratory, Imperfect Tools, Incomplete
Information on the Patient, Poor Compliance with the Regimen |
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1.1.3 Inadequate Knowledge – Epistemic
Uncertainties; Diagnostic, Therapeutic, and Prognostic Uncertainties;
Predictive and Other Uncertainties |
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1.2 Uncertainties in
Medical Research |
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1.2.1 Empiricism in Medical Research – Laboratory
Experiments, Clinical Trials, Surgical Procedures, Epidemiological Research |
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1.2.2 Elements of Minimizing the Impact of
Uncertainties on Research – Proper Design,
Improved Medical Methods, Analysis and Synthesis |
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1.2.3 Critique of a Report of a Medical Study –
Introduction, Methodology, Results, Discussion and Conclusions |
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1.3 Uncertainties in Health
Planning and Evaluation |
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1.3.1 Health Situation Analysis – Identification of
the Specifics of the Problem, Size of the Target Population, Magnitude of the
Problem, Health Infrastructure, Feasibility of Remedial Steps |
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1.3.2 Evaluation of Health Programs |
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1.4 Management of
Uncertainties: About This Book |
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1.4.1
Contents of the Book – Limitations and Strengths, New in Third Edition |
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1.4.2 Salient Features of the Text – System of
Notations, Guide Chart of the Biostatistical Methods |
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References |
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2 Basics of Medical
Studies |
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2.1 Study Protocol |
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2.1.1 The Problem, Objectives, and Hypotheses |
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2.1.2 Protocol Content |
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2.2 Types of Medical
Studies |
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2.2.1
Elements of Design |
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2.2.2
Basic Types of Study Design – Descriptive, Analytical, Basic Types of
Analytical Studies |
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2.2.3
Choosing a Design – Recommended Design for Particular Setups, Choice of
Design by Level of Evidence |
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2.3 Data Collection |
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2.3.1 Nature of Data – Factual, Knowledge-Based, and
Opinion-Based Data; Method of Obtaining the Data |
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2.3.2 Tools of Data Collection – Existing Records,
Questionnaires and Schedules, Likert Scale |
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2.3.3 Pretesting and Pilot Study |
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2.4 Nonsampling Errors and
Other Biases |
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2.4.1
Nonresponse |
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2.4.2
Variety of Biases to Guard Against – List of Biases, Steps for Minimizing
Bias |
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References |
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Exercises 3 Sampling Methods |
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3.1 Sampling Concepts |
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3.1.1 Advantages and Limitations of Sampling –
Sampling Fluctuations, Advantages and
Limitations |
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3.1.2 Some Special Terms Used in Sampling – Unit of
Enquiry and Sampling Unit, Sampling Frame, Parameters and Statistics, Sample
Size, Nonrandom and Random Sampling |
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3.2 Common Methods of Random
Sampling |
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3.2.1 Simple Random Sampling |
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3.2.2 Stratified Random Sampling |
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3.2.3 Multistage Random Sampling |
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3.2.4
Cluster Random Sampling |
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3.2.5
Systematic Random Sampling |
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3.2.6
Choice of Method of Random Sampling |
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3.3 Some Other Methods of Sampling |
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3.3.1 Other Random Methods of Sampling – Probability
Proportional to Size, Area Sampling, Inverse Sampling, Consecutive Subjects
Attending a Clinic, Sequential Sampling |
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3.3.2 Nonrandom Methods of Sampling – Convenience
Samples, Other Types of Purposive Samples |
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References |
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Exercises 4 Designs for
Observational Studies |
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4.1
Some Basic Concepts |
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4.1.1 Antecedent and Outcome |
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4.1.2 Confounders |
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4.1.3 Effect Size |
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4.2 Prospective Studies |
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4.2.1 Variations of Prospective Studies – Cohort
Study, Longitudinal Study, Repeated Measures Study |
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4.2.2 Selection of Subjects for a Prospective Study
– Comparison Group in a Prospective Study |
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4.2.3 Potential Biases in Prospective Studies –
Selection Bias, Bias due to Loss in Follow-Up, Assessment Bias and Errors,
Bias due to Change in the Status, Confounding Bias, Post Hoc Bias, Validity
Bias |
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4.2.4 Merits and Demerits of Prospective Studies |
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4.3 Retrospective Studies |
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4.3.1 Case-Control Design – Nested Case-Control
Design |
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4.3.2 Selection of Cases and Controls – Sampling
Methods in Retrospective Studies, Confounders and Matching |
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4.3.3 Merits and Demerits of Case-Control Studies |
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4.4 Cross-Sectional Studies |
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4.4.1
Selection of Subjects for a Cross-Sectional Study |
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4.4.2
Merits and Demerits of Cross-Sectional Studies |
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4.5 Comparative Performance of Prospective, Retrospective,
and Cross-Sectional Studies |
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4.5.1
Performance of Prospective Studies |
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4.5.2
Performance of Retrospective Studies |
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4.5.3
Performance of Cross-Sectional Studies |
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References |
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Exercises 5 Medical Experiments |
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5.1 Basic Features of
Medical Experiments |
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5.1.1 Statistical Principles of Experimentation –
Control Group, Randomization, Replication |
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5.1.2
Advantages and Limitations of Experiments |
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5.2 Design of Experiments |
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5.2.1 Classical Designs: One-Way Design, Two-Way
Design, Interaction, K-Way and Factorial Experiments |
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5.2.2 Some Unconventional Designs – Repeated
Measures Design, Crossover Design, Other Complex Designs |
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5.3 Choice and Sampling of
Units for Laboratory Experiments |
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5.3.1
Choice of Experimental Unit |
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5.3.2
Sampling Methods in Laboratory Experiments |
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5.3.3
Choosing a Design of Experiment |
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5.3.4
Pharmacokinetic Studies |
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References |
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Exercises 6 Clinical Trials |
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6.1 Therapeutic Trials |
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6.1.1
Phases of a Clinical Trial – Phases I to IV |
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6.1.2 Selection of Subjects – Selection of
Participants for RCT, Control Group in a Clinical Trial |
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6.1.3 Randomization and Matching |
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6.1.4 Methods of Random Allocation – Allocation out
of a Large Number of Available Subjects; Random Allocation of Consecutive
Patients Coming to a Clinic; Block, Cluster and Stratified Randomization |
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6.1.5 Blinding and Masking |
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6.2 Issues in Clinical
Trials |
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6.2.1 Outcome Assessment – Specification of
End-point or Outcome, Causal Inference, Side Effects, Efficacy versus
Effectiveness, Pragmatic Trials |
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6.2.2
Various Equivalences in Clinical Trials – Superiority, Equivalence, and
Noninferiority Trials; Therapeutic Equivalence and Bioequivalence |
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6.2.3
Designs for Clinical Trials – One-Way, Two-Way, and Factorial Designs;
Crossover and Repeated Measures Designs; N-of-1,
Up-and-Down, and Sequential Designs; Choosing a Design for a Clinical Trial |
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6.2.4 Designs
with Interim Appraisals – Design with Provision to Stop Early, Adaptive Designs |
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6.2.5
Biostatistical Ethics for Clinical Trials – Equipoise, Ethical Cautions,
Statistical Considerations in a Multicentric Trial, Multiple Treatments with
Different Outcomes in the Same Trial, Size of the Trial, Compliance |
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6.2.6
Reporting Results of a Clinical Trial – CONSORT, Open Access |
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6.3 Trials Other than for
Therapeutics |
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6.3.1 Clinical Trials for Diagnostic and
Prophylactic Modalities |
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6.3.2 Field Trials for Screening,
Prophylaxis, and Vaccines |
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6.3.3
Issues in Field Trials – Randomization and Blinding in Field Trials, Designs
for Field Trials |
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References |
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Exercises 7 Numerical Methods for
Representing Variation |
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7.1 Types of Measurement |
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7.1.1
Nominal, Metric, and Ordinal Scales |
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7.1.2
Other Classifications of the Types of Measurement – Discrete and Continuous
Variables, Qualitative and Quantitative Data, Stochastic and Deterministic
Variables |
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7.2 Tabular Presentation |
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7.2.1 Contingency Tables and Frequency Distribution
– Empty Cells, Problems in Preparing a Contingency Table on Metric Data |
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7.2.2
Multiple Response Tables and Other Features |
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7.2.3
Other Types of Statistical Tables – What is a Good Statistical Table? |
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7.3 Rates and Ratios |
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7.3.1
Proportion, Rate, and Ratio |
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7.4 Central and Other
Locations |
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7.4.1 Central Values: Mean, Median, and Mode –
Understanding Mean, Median, and Mode, Calculation in Case of Grouped Data,
Which Central Value to Use?, Geometric Mean, Harmonic Mean |
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7.4.2 Other Locations: Quantiles – Ungrouped and
Grouped Data, and Interpretation |
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7.5 Measuring Variability |
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7.5.1 Variance and Standard Deviation – Ungrouped
and Grouped Data, Variance of Sum or Difference of Two Measurements |
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7.5.2 Coefficient of Variation |
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References |
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Exercises 8 Presentation of Variation by Figures |
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8.1 Graphs for Frequency Distribution |
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8.1.1 Histogram and Its Variants – Histogram,
Stem-and-Leaf Plot, Line Histogram |
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8.1.2 Polygon and Its Variants – Frequency Polygon,
Area Diagram |
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8.1.3 Frequency Curve |
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8.2 Pie, Bar, and Line Diagrams |
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8.2.1 Pie Diagram – Useful Features, Donut Diagram |
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8.2.2 Bar Diagram |
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8.2.3 Scatter and Line Diagrams |
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8.2.4 Choice and Cautions in Visual Display of Data |
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8.2.5 Mixed and Three-Dimensional Diagrams – Mixed
Diagram, Box-and-Whiskers Plot, Three-Dimensional Diagram, Biplot, Nomogram |
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8.3 Special Diagrams in Health and Medicine |
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8.3.1 Diagrams Used in Public Health – Epidemic
Curve, Lexis Diagram |
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8.3.2 Diagrams Used in Individual Care and Research –
Growth Charts, Partogram, Dendrogram,
Area Under the Concentration Curve, Radar Graph |
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8.4 Charts and Maps |
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8.4.1 Charts – Schematic Chart, Pedigree Chart |
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8.4.2 Maps – Spot Map, Thematic Choroplethic Map,
Cartogram |
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References |
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Exercises 9 Some Quantitative Aspects of Medicine |
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9.1 Some Epidemiological Measures of Health and
Disease |
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9.1.1 Epidemiological Indicators of Neonatal Health
– Birth Weight, Apgar Score |
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9.1.2 Epidemiological Indicators of Growth in
Children – Weight-for-Age, Weight-for-Height and Height-for-Age, Z-Scores and Percent of Median, Growth
Velocity, Skinfold Thickness |
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9.1.3 Epidemiological Indicators of Adolescent
Health – Growth in Height and Weight in Adolescence, Sexual Maturity Rating |
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9.1.4 Epidemiological Indicators of Adult Health –
Obesity, Smoking, Physiological Functions, Quality of Life |
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9.1.5 Epidemiological Indicators of Geriatric Health
– Activities of Daily Living, Mental Health of the Elderly |
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9.2 Reference Values |
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9.2.1 Gaussian and Other Distributions – Checking
Gaussianity |
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9.2.2 Reference or Normal Values – Implications |
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9.2.3 Normal Range – Disease Threshold, Clinical
Threshold, Statistical Threshold |
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9.3 Measurement of Uncertainty: Probability |
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9.3.1 Elementary Laws of Probability – Law of
Multiplication, Law of Addition |
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9.3.2 Probability in Clinical Assessments –
Probabilities in Diagnosis, Assessment of Prognosis, Choice of Treatment, |
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9.3.3 Further on Diagnosis: Bayes Rule |
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9.4 Validity of Medical Tests |
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9.4.1 Sensitivity and Specificity – Features of
Sensitivity and Specificity, Likelihood Ratio |
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9.4.2 Predictivities – Positive and Negative
Predictivity, Predictivity and Prevalence, The Meaning of Prevalence for
Predictivity, Features of Positive and Negative Predictivities |
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9.4.3 Combination of Tests – Tests in Series, Tests
in Parallel, Gains from a Test, When Can a Test Be Avoided? |
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9.4.4 Gains from a Test – When can a Test be Avoided |
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9.5 Search for the Best Threshold of Continuous Test:
ROC Curve |
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9.5.1 Sensitivity–Specificity Based ROC Curve,
Methods to Find the ‘Optimal’ Threshold Point, Area Under the ROC Curve |
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9.5.2 Predictivities Based ROC Curve |
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References |
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Exercises 10 Clinimetrics and Evidence-Based Medicine |
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10.1 Indicators, Indexes, and Scores |
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10.1.1 Indicators – Merits and Demerits of
Indicators, Choice of Indicators |
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10.1.2 Indexes – Some Commonly Used Indexes,
Advantages and Limitations of Indexes |
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10.1.3 Scores – Scoring System for Diagnosis,
Scoring for Gradation of Severity |
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10.2 Clinimetrics |
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10.2.1 Method of Scoring – Method of Scoring for
Graded Characteristics, Method of Scoring for Diagnosis, Regression Method of
Scoring |
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10.2.2 Validity and Reliability of a Scoring System |
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10.3 Evidence-Based Medicine |
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10.3.1 Decision Analysis – Decision Tree |
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10.3.2 Other Statistical Tools for Evidence-Based
Medicine – Etiology Diagram, Expert System |
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References |
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Exercises 11 Measurement of Community Health |
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11.1 Indicators of Mortality |
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11.1.1 Crude and Standardized Death Rates – Crude
Death Rate, Age-Specific Death Rate, Standardized Death Rate, Comparative
Mortality Ratio |
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11.1.2 Specific Mortality Rates – Fetal Deaths and
Mortality in Children, Maternal Mortality, Adult Mortality, Other Measures of Mortality |
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11.1.3 Death Spectrum |
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11.2 Measures of Morbidity |
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11.2.1 Prevalence and Incidence – Point Prevalence,
Period Prevalence, Incidence, The Concept of Person-Time, Capture–Recapture
Methodology |
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11.2.2 Duration of Morbidity – Prevalence in
Relation to Duration of Morbidity, Incidence from Prevalence,
Epidemiologically Consistent Estimates |
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11.2.3 Morbidity Measures for Acute Conditions –
Attack Rates, Disease Spectrum |
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11.3 Indicators of Social and Mental Health |
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11.3.1 Indicators of Social Health – Education,
Income, Occupation, Socioeconomic Status, Dependency Ratio, Health Inequality |
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11.3.2 Indicators of Health Resources – Health
Infrastructure, Health Expenditure |
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11.3.3 Indicators of Lack of Mental Health – Smoking
and Other Addictions, Divorces, Vehicular Accidents and Crimes, Others
Measures of Lack of Mental Health |
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11.4 Composite Indexes of Health |
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11.4.1 Indexes of Status of Comprehensive Health –
Human Development Index, Physical Quality of Life Index |
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11.4.2 Indexes of Health Gap – DALYs Lost, Human
Poverty Index, Index of Need for Health Resources |
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References |
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Exercises 12 Confidence Intervals, Principles of Tests of
Significance, and Sample Size |
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12.1 Sampling Distributions |
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12.1.1 Basic Concepts – Sampling Error, Point
Estimate, Standard Error of p and |
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12.1.2 Sampling Distribution of p and – Gaussian
Conditions |
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12.1.3 Obtaining Probabilities from a Gaussian
Distribution – Gaussian Probability, Continuity Correction, Probabilities
Relating to the Mean and the Proportion |
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12.1.4 The Case of σ Not Known (t-Distribution) |
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12.2 Confidence Intervals |
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12.2.1 Confidence Interval for π, μ
and Median (Gaussian Conditions) – Confidence Interval for Proportion π
(Large n), Lower and Upper Bounds for π (Large n),
Confidence Interval for Mean μ (Large n), Confidence
Bounds for Mean μ (Large
n), CI for Median (Gaussian Distribution) |
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12.2.2 Confidence Interval for Differences (Large n)
– Two Independent Samples, Paired Samples |
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12.2.3 Confidence Interval for π, μ
and Median: NonGaussian Conditions – Confidence Interval for π
(Small n), Confidence Bound for π When the Success or the
Failure Rate in the Sample is Zero Percent, Confidence Interval for Median
(Small n): NonGaussian Conditions |
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12.3 P-Values and Statistical Significance |
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12.3.1 What Is Statistical Significance? – Court Judgment, Errors in Diagnosis, Null
Hypothesis, Philosophical Basis of Statistical Tests, Alternative Hypothesis,
One-Sided Alternatives: Which Tail is Wagging? |
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12.3.2 Errors, P-Values, and Power – Type-I
Error, Type-II Error, Power |
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12.3.3 General Procedure to Obtain P-value –
Subtleties of Statistical Significance |
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12.4 Assessing Gaussian Pattern |
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12.4.1 Significance Tests for Assessing Gaussianity |
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12.5 Initial Debate on Statistical Significance |
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12.5.1 Confidence Interval versus Test of H0 |
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12.5.2 Medical Significance versus Statistical
Significance |
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12.6 Sample Size Determination in Some Cases |
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12.6.1 Sample Size Required in Estimation Setup –
General Considerations in the Estimation Setup, General Procedure for
Determining Size of Sample for Estimation, Formulas for Sample Size
Calculation for Estimation in Simple Situations |
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12.6.2 Sample Size for Testing a Hypothesis with
Specified Power – General Considerations in a Testing-of-Hypothesis Setup,
Sample Size Formulas for Test of Hypothesis in Simple Situations, Nomograms
and Tables of Sample Size, Thumb Rules, Power Analysis |
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12.6.3 Sample Size Calculation in Clinical Trials –
Stopping Rules in Case of Early Evidence of Success or of Failure: Lan–deMets
Procedure, Sample Size Reestimation |
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References |
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Exercises 13 Inference from Proportions |
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13.1 One Qualitative Variable |
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13.1.1 Dichotomous Categories: Binomial Distribution
– Large n: Gaussian Approximation to Binomial |
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13.1.2 Poisson Distribution |
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13.1.3 Polytomous Categories (Large n):
Goodness-of-Fit Test – Chi-Square and Its Explanation, Degrees of Freedom,
Cautions in Using Chi-Square, Further Analysis: Partitioning of Table |
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13.1.4 Goodness of Fit to Assess Gaussianity |
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13.1.5 Polytomous Categories (Small n): Exact
Multinomial Test – Goodness-of-Fit in Small Samples |
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13.2 Proportions in 2×2 Tables |
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13.2.1 Structure of 2×2 Table in Different Types of
Study – Structure in Prospective Study, Structure in Retrospective
Study, Structure in Cross-Sectional
Study |
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13.2.2 Two Independent Samples (Large n):
Chi-Square Test and Proportion Test – Chi-square Test, Yates Correction for
Continuity, Z-Test for Proportions, Detecting a Medically Important
Difference in Proportions, Crossover Design with Binary Response (Large n) |
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13.2.3 Equivalence Tests – Superiority, Equivalence
and Noninferiority; Equivalence; Determining Inferiority Margin |
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13.2.4 Two Independent Samples (Small n):
Fisher Exact Test – Crossover Design (Small n) |
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13.2.5 Proportions in Matched Pairs: McNemar Test
(Large n) and Exact Test (Small n) – Large n: McNemar
Test, Small n: Exact Test (Matched Pairs), Comparison of Two Tests for
Sensitivity and Specificity: Paired Setup |
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13.3 Analysis of R × C Tables (Large n) |
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13.3.1 One Dichotomous and the Other Polytomous Variable
(2×C Table) – The Test Criterion, Trend in Proportions in Ordinal
Categories, Dichotomy in Repeated Measures: Cochran Q Test (Large n) |
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13.3.2 Two Polytomous Variables – Chi-square Test
for Large n, Matched Pairs: I×I
Tables |
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13.4 Three-Way Tables |
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13.4.1 Assessment of Association in Three-Way Tables |
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13.4.2 Log–Linear Models – Two-Way Tables, Three-Way
Tables |
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References |
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Exercises 14 Relative Risk and Odds Ratio |
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14.1 Relative and Attributable Risks (Large n) |
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14.1.1 Risk, Hazard, and Odds – Ratios of Risks and
Odds |
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14.1.2 Relative Risk – RR in Independent Samples,
Confidence Interval for RR (Independent Samples), Test of Hypothesis on RR
(Independent Samples), RR in the Case of Matched Pairs |
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14.1.3 Attributable Risk – AR in Independent
Samples, AR in Matched Pairs, Number Needed to Treat, Relative Risk
Reduction, Population Attributable Risk |
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14.2 Odds Ratio |
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14.2.1 OR in Two Independent Samples – CI for OR
(Independent Samples), Test of Hypothesis on OR (Independent Samples) |
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14.2.2 OR in Matched Pairs – Confidence Interval for
OR (Matched Pairs), Test of Hypothesis on OR (Matched Pairs), Multiple
Controls |
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14.3 Stratified Analysis, Sample Size and Meta-Analysis |
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14.3.1 Mantel–Haenszel Procedure – Pooled Odds Ratio
and Chi-square |
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14.3.2 Sample Size Requirement for Statistical Inference
on RR and OR |
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14.3.3 Meta-Analysis |
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References Exercises |
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15 Inference from Means |
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15.1 Comparison of Means in One and Two Groups (Gaussian
Conditions): Student t-Test |
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15.1.1 Comparison with a Prespecified Mean – Student
t-Test for One Sample, |
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15.1.2 Difference in Means in Two Samples – Paired
Samples Setup, Unpaired (Independent) Samples Setup, Some Features of Student
t, Effect of Unequal n,
Difference-in-Differences Approach |
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15.1.3 Analysis of Crossover Designs – Test for
Group Effect, Test for Carry-Over Effect, Test for Treatment Effect |
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15.1.4 Analysis of Data of Up-and-Down Trials |
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15.2 Comparison of Means in Three or More Groups
(Gaussian Conditions): ANOVA F-Test |
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15.2.1 One-Way ANOVA – The Procedure to Test H0,
Checking the Validity of the Assumptions of ANOVA |
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15.2.2 Two-Way ANOVA – Two-Factor Design, The
Hypotheses and Their Test, Main Effect and Interaction (Effect), Repeated
Measures |
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15.2.3 Repeated Measures – Random Effects versus
Fixed Effects, Sphericity and Hynh–Feldt Correction, Repeated Measures versus
Two-way ANOVA, Area Under the Concentration Curve |
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15.2.4 Multiple Comparisons: Bonferroni, Tukey and
Dunnett Tests – Intricacies of Multiple Comparisons |
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15.3 Non-Gaussian Conditions: Nonparametric Tests
for Location |
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15.3.1 Comparison of Two Groups: Wilcoxon Tests – Paired
Data, Independent Samples |
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15.3.2 Comparison of Three or More Groups:
Kruskal–Wallis Test |
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15.3.3 Two-Way Layout: Friedman Test |
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15.4 When Significant is Not Significant |
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15.4.1 The Nature of Statistical Significance |
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15.4.2 Testing for Presence of Medically Important
Difference in Means – Detecting Specified Difference in Mean, Equivalence
Tests for Means |
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15.4.3 Power and Level of Significance – Balancing
Type-I and Type-II Error |
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References Exercises |
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16 Relationships: Quantitative Data |
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16.1 Some General Features of a Regression Setup |
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16.1.1 Dependent and Independent Variables – Simple,
Multiple, and Multivariate Regression |
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16.1.2 Linear, Curvilinear, and Nonlinear
Regressions |
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16.1.3 The Concept of Residuals |
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16.1.4 General Method of Fitting a Regression |
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16.2 Linear Regression Models |
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16.2.1 Adequacy of a Regression Fit – 1 – Goodness
of Fit and η2, Multiple Correlation in Linear
Regression, Stepwise Procedure, Statistical Significance of Individual
Regression Coefficients |
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16.2.2 Adequacy of Regression – 2 – Validity of
Assumptions, Choice of Form of Regression, Outliers and Missing Values |
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16.2.3 Interpretation of the Regression Coefficients
– Standardized Coefficients, Other Implications of Regression Models |
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16.3 Some Issues in Linear Regression |
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16.3.1 Confidence Interval, Confidence Band, and
Tests – SEs and CIs for the Regression, Confidence Band for Simple Linear
Regression, Equality of Two Regression
Lines, Difference-in-Differences Approach with Regression |
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16.3.2 Some Variations of Regression – Ridge
Regression, Multilevel Regression, Regression Splines, Analysis of Covariance,
Some Generalizations |
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16.4 Measuring the Strength of Quantitative
Relationship |
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16.4.1 Product–Moment and Related Correlations –
Multiple Correlation, Product–Moment Correlation, Covariance, Statistical
Significance of r, Intraclass
Correlation, Serial Correlation |
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16.4.2 Rank Correlation – Spearman Rho, Kendall Tau |
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16.5 Assessment of Quantitative Agreement |
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16.5.1 Agreement in Quantitative Measurements |
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16.5.2 Approaches for Measuring Quantitative
Agreement – Limits of Disagreement Approach, Intraclass Correlation as a
Measure of Agreement, Relative Merits of the Two Methods, An Alternative
Simple Approach |
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References Exercises |
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17 Relationships: Qualitative Dependent |
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17.1 Binary Dependent: Logistic Regression (Large n) |
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17.1.1 Meaning of a Logistic Model |
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17.1.2 Assessing Overall Adequacy of a Logistic
Regression – Log Likelihood, Classification Accuracy, Hosmer–Lemeshow Test, |
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17.2 Inference from Logistic Coefficients |
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17.2.1 Interpretation of the Logistic Coefficients –
Dichotomous Predictors, Polytomous and Continuous Predictors |
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17.2.2 Confidence Interval and Test of Hypothesis on
Logistic Coefficients |
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17.3 Issues in Logistic Regression |
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17.3.1 Conditional Logistic for Matched Data |
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17.3.2 Polytomous Dependent – Nominal Categories:
Multinomial Logistic, Ordinal Categories |
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17.4 Some Models for Qualitative Data and
Generalizations |
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17.4.1 Cox Regression for Hazards |
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17.4.2 Classification and Regression Trees |
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17.4.3 Further Generalizations |
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17.5 Strength of Relationship in Qualitative
Variables |
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17.5.1 Both Variables Qualitative – Dichotomous
Categories, Polytomous Categories: Nominal, Proportional Reduction in Error,
Polytomous Categories: Ordinal Association |
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17.5.2 One Qualitative and the Other Quantitative
Variable |
|
17.5.3 Agreement in Qualitative Measurements (Matched
Pairs) – The Meaning of Qualitative Agreement, Cohen Kappa |
|
References Exercises |
|
18 Survival Analysis |
|
18.1 Life Expectancy |
|
18.1.1 Life Table |
|
18.1.2 Other Forms of Life Expectancy – Potential
Years of Life Lost, Healthy Life Expectancy, Application to Other Setups |
|
18.2 Analysis of Survival Data |
|
18.2.1 Nature of Survival Data – Types of Censoring,
Collection of Survival Time Data, Statistical Measures of Survival |
|
18.2.2 Survival Observed in Time Intervals: Life
Table Method |
|
18.2.3 Continuous Observation of Survival Time:
Kaplan–Meier Method – Using the Survival Curve, Standard Error of Survival
Rate, Hazard Function |
|
18.3 Issues in Survival Analysis |
|
18.3.1 Comparison of Survival in Two Groups –
Comparing Survival Rates, Comparing Survival Experience: Log-Rank Test |
|
18.3.2 Factors Affecting Survival: Cox Model –
Parametric Models, Cox Model for Survival, Proportional Hazards |
|
18.3.3 Sample Size for Survival Studies |
|
References Exercises |
|
19 Simultaneous Consideration of Several Variables |
|
19.1 Scope of Multivariate Methods |
|
19.1.1 The Essentials of a Multivariate Setup |
|
19.1.2 Statistical Limitation on the Number of
Variables |
|
19.2 Dependent and Independent Sets of Variables |
|
19.2.1 Dependents and Independents Both
Quantitative: Multivariate Multiple Regression |
|
19.2.2 Quantitative Dependents and Qualitative
Independents: Multivariate Analysis of Variance (MANOVA) – MANOVA for
Repeated Measures |
|
19.2.3 Classification of Subjects into Known Groups:
Discriminant Analysis – Discriminant Function, Classification Rule,
Classification Accuracy |
|
19.3 Identification of Structure in the Observations |
|
19.3.1 Identification of Clusters of Subjects:
Cluster Analysis – Measures of Similarity, Hierarchical Agglomerative
Algorithm, Deciding on the Number of Natural Clusters |
|
19.3.2 Identification of Unobservable Underlying
Factors: Factor Analysis – Steps for Factor Analysis, Features of a
Successful Factor Analysis, Factor Scores |
|
References Exercises |
|
20 Quality Considerations |
|
20.1 Statistical Quality Control in Medical Care |
|
20.1.1 Statistical Control of Medical Care Errors –
Adverse Patient Outcomes, Monitoring Fatality, Limits of Tolerance |
|
20.1.2 Quality of Lots – The Lot Quality Method,
LQAS in Health Assessment |
|
20.1.3 Quality Control in a Medical Laboratory –
Control Chart, Cusum Chart, Other Errors in Medical Laboratory, Six Sigma
Methodology, Nonstatistical Issues |
|
20.2 Quality of Measurements |
|
20.2.1 Validity of Instruments – Types of Validity |
|
20.2.2 Reliability of Instruments – Internal
Consistency, Cronbach Alpha, Test–Retest Reliability |
|
20.3 Quality of Statistical Models: Robustness |
|
20.3.1 External Validation – Split-Sample Method,
Another Sample Method |
|
20.3.2 Sensitivity Analysis and Uncertainty Analysis |
|
20.3.3 Resampling – Bootstrapping, Jackknife
Resampling |
|
20.4 Quality of Data |
|
20.4.1 Errors in Measurement – Lack of
Standardization in Definitions, Lack of Care in Obtaining or Recording
Information, Inability of the Observer to Get Confidence of the Respondent,
Bias of the Observer, Variable Competence of the Observers |
|
20.4.2 Missing Values – Approaches for Missing
Values, Handling Nonresponse, Imputations, Intention-to-Treat Analysis |
|
20.4.3 Lack of Standardization in Values –
Standardization Methods Already Described, Standardization for Calculating
Adjusted Rates, Standardized Mortality Ratio |
|
References Exercises |
|
21 Statistical Fallacies |
|
21.1 Problems with the Sample |
|
21.1.1 Biased Sample – Survivors, Volunteers,
Clinical Subjects, Publication Bias, Inadequate Specification of Sampling
Method, Abrupt Series |
|
21.1.2 Inadequate Size of the Sample – Problems with
Calculation of Sample Size |
|
21.1.3 Incomparable Groups – Differential in Group
Composition, Differential Definitions, Differential Compliance, Variable Periods of Exposure, Improper
Denominator |
|
21.1.4 Mixing of Distinct Groups – Effect on
Regression, Effect on Shape of the Distribution, Lack of Intragroup
Homogeneity |
|
21.2 Inadequate Analysis |
|
21.2.1 Ignoring Reality – Looking for Linearity, Overlooking
Assumptions, Selection of Inappropriate Variables, Area Under the Concentration
Curve, Further Problems with Statistical Analysis, Anomalous Person-Years,
Problems with Intention-to-Treat Analysis and Equivalence |
|
21.2.2 Choice of Analysis – Mean or Proportion?
Forgetting Baseline Values |
|
21.2.3 Misuse of Statistical Packages –
Over-Analysis, Data Dredging, Quantitative Analysis of Codes, Soft Data
versus Hard Data |
|
21.3 Errors in Presentation of Findings |
|
21.3.1 Misuse of Percentages and Means – Unnecessary
Decimals |
|
21.3.2 Problems in Reporting – Incomplete Reporting,
Over-Reporting, Selective Reporting, Self-Reporting versus Objective
Measurement, Misuse of Graphs |
|
21.4 Misinterpretation |
|
21.4.1 Misuse of P-Values – Magic Threshold
0.05, One-Tail or Two-Tail P-Values, Multiple Comparisons, Dramatic P-Values,
P-Values for Nonrandom Sample, “Normal” with Respect to Several
Parameters, Absence of Evidence is not Evidence of Absence |
|
21.4.2 Correlation versus Cause–Effect Relationship
– Criteria for Cause–Effect, Other Considerations |
|
21.4.3 Sundry Issues – Diagnostic Test is Only an
Additional Adjunct, Medical Significance versus Statistical Significance,
Interpretation of Standard Error of p, Univariate Analysis but
Multivariate Conclusions, Limitation of Relative Risk, Misinterpretation of Improvements |
|
21.4.4 Final Comments |
|
References Exercises Brief Solutions and Answers to the Selected
Exercises |
|
Appendix A: Statistical Software |
|
A.1 General Purpose Statistical Software |
|
A.2 Special Purpose Statistical Software |
|
Appendix B: Some Statistical Tables |
|
Appendix C: Software Illustrations |
|
C.1 ROC Curves |
|
C.2 Repeated Measures
ANOVA |
|
C.3 One-way ANOVA and
Tukey Test |
|
C.4 Stepwise Multiple
Linear Regression |
|
C.5 Curvilinear Regression |
|
C.6 Analysis of Covariance
(ANCOVA) |
|
C.7 Logistic Regression |
|
C.8 Survival Analysis
(Life Table Method) |
|
C.9 Cox Proportional
Hazards Model |
|
Index |
|
Data sets in the Examples in this text
are available in Excel for ready download at
http://MedicalBiostatistics.synthasite.com. Use these data sets to rework some
of the examples of your interest and to do further analysis where needed.