Clinical Biostatistics
Preface
Introduction
1
Binary diagnostic tests
1.1
Diagnostic accuracy studies
1.1.1
Study designs
1.1.2
Test integrity
1.2
Measures of diagnostic accuracy
1.2.1
Sensitivity and specificity
1.2.2
Predictive values
1.2.3
Likelihood ratios
1.2.4
Bayesian updating with likelihood ratios
1.2.5
Diagnostic odds ratio
1.3
Confidence intervals for measures of diagnostic accuracy
1.3.1
Proportions
1.3.2
Likelihood ratios
1.3.3
Diagnostic odds ratio
1.3.4
Predictive values
1.4
Comparing two diagnostic tests
1.5
Additional references
2
Continuous diagnostic tests
2.1
Diagnostic accuracy measures
2.1.1
ROC curve
2.1.2
Area under the curve (AUC)
2.1.3
Optimal cut-off
2.2
Comparing two diagnostic tests
2.3
Additional references
3
Clinical measurement and agreement
3.1
Precision of clinical measurements
3.1.1
Measurement error
3.1.2
Measurement error related to size
3.1.3
Repeatability
3.1.4
Reliability and the intraclass correlation coefficient
3.2
Agreement of two methods with continuous measurements
3.3
The method of Bland & Altman
3.3.1
Confidence intervals for limits of agreement
3.4
Agreement of two methods with binary variables
3.4.1
Cohen’s Kappa
3.4.2
Confidence Interval for Cohen’s Kappa
3.4.3
Weighted Kappa
3.5
Additional references
4
Randomized controlled trials
4.1
Study design
4.1.1
Historical context
4.1.2
Ethical issues of RCTs
4.1.3
Structure of RCTs
4.1.4
Eligibility criteria
4.1.5
The need for a control group
4.1.6
The importance of randomization
4.2
Bias in RCTs
4.2.1
Selection bias
4.2.2
Allocation bias
4.2.3
Assessment bias
4.2.4
Stopping bias
4.2.5
Publication bias
4.3
Target trials
4.4
Additional references
5
Statistical significance and sample size calculations
5.1
Statistical significance
5.1.1
Computation of the
\(P\)
-value for a continuous outcome
5.1.2
Confidence intervals and
\(P\)
-values
5.1.3
Error rates
5.1.4
Misinterpretation of Type I Error
5.2
Sample size calculations
5.2.1
Continuous outcomes
5.2.2
Binary outcomes
5.2.3
Adjusting for loss to follow-up
5.2.4
Study designs with unequal group sizes
5.2.5
Sample size based on precision
5.3
Additional references
6
Randomization and allocation, blinding and placebos
6.1
Methods of allocation
6.1.1
Simple randomization
6.1.2
Block randomization
6.1.3
Unequal randomization
6.1.4
Stratification
6.1.5
Minimization
6.2
Blinding
6.3
Placebos
6.3.1
The double-dummy technique
6.4
Reporting guidelines for Clinical Trials
6.4.1
The SPIRIT Statement
6.4.2
The CONSORT Statement
6.5
Reporting results
6.6
Additional references
7
Analysis of continuous outcomes
7.1
Comparison of follow-up measurements
7.1.1
\(t\)
-test
7.1.2
Welch’s test
7.2
Analysis of baseline and follow-up measurements
7.2.1
Change scores
7.2.2
Analysis of covariance
7.3
Additional references
8
Analysis of binary and ordinal outcomes
8.1
Comparison of two proportions
8.1.1
Statistical tests
8.1.2
Effect measures and confidence intervals
8.2
Adjusting for baseline observations
8.2.1
Logistic regression
8.3
Ordinal outcomes
8.4
Additional references
9
Survival analysis
9.1
Analysis of survival outcomes
9.1.1
Censoring
9.1.2
Survival function and curve
9.1.3
Median survival time
9.2
Comparison of survival curves
9.2.1
Log-rank test
9.2.2
Hazard function
9.2.3
Hazard ratio
9.3
Sample size in survival studies
9.3.1
Total number of events
9.3.2
Total number of patients
9.4
Time-varying explanatory variables
9.5
Additional references
10
Subgroup analysis and multiple outcomes
10.1
Subgroup analysis
10.1.1
Comparing subgroups
10.1.2
Selecting subgroups
10.1.3
Qualitative and quantitative interaction
10.2
Multiple outcomes
10.2.1
Adjusting for multiplicity
10.2.2
Multivariate methods
10.3
Additional references
11
Sequential methods and trial protocols
11.1
Monitoring accumulating data
11.1.1
Data monitoring committees
11.1.2
Group sequential methods
11.1.3
Problems of stopping at interim
11.2
The trial protocol
Designing and reporting trials
Protocol deviations
11.3
Additional references
12
Crossover trials
12.1
The AB/BA design
12.2
Continuous outcomes
12.2.1
Simple analysis
12.2.2
Analysis using mixed models
12.3
The issue of carryover
12.3.1
Analysis of carryover
12.3.2
Test for carryover
12.4
Sample size for AB/BA design
12.5
Binary outcomes
12.5.1
Naive analysis
12.5.2
Recommended analysis using Mainland-Gart test
12.5.3
Analysis with generalized linear mixed models
12.6
Additional references
13
Some special designs
13.1
Cluster-randomized trials
13.1.1
Analysis
13.1.2
Sample size calculation
13.2
Equivalence and non-inferiority trials
13.2.1
Equivalence trials
13.2.2
Non-inferiority trials
13.3
Additional references
14
Meta-analysis
14.1
Systematic review
14.2
Meta-analysis
14.2.1
Fixed effect model
14.2.2
Random effects model
14.2.3
Cumulative meta-analysis
14.2.4
Meta-regression
14.3
Reporting bias
14.3.1
Funnel plot
14.3.2
The trim-and-fill method
14.3.3
Tests for funnel plot asymmetry
14.4
Additional references
Appendix
A
Confidence intervals
A.1
Concepts
A.1.1
Standard error
A.1.2
Confidence interval
A.2
Methods
A.2.1
Normal approximation
A.2.2
Delta method
A.2.3
Difference
A.2.4
Substitution method
A.2.5
Bootstrap
A.3
Continuous outcome
A.3.1
One group
A.3.2
Two unpaired groups with equal variance
A.3.3
Two unpaired groups with unequal variance
A.3.4
Two paired groups
A.4
Binary outcome
A.4.1
One group
A.4.2
Two unpaired groups
A.4.3
Two paired groups
A.5
Confidence interval for a sample variance and standard deviation
B
Statistical tests and
\(P\)
-values
B.1
Concepts
B.1.1
\(P\)
-value
B.1.2
Hypothesis testing
B.1.3
Significance testing
B.2
Continuous outcome
B.2.1
\(z\)
-test
B.2.2
\(t\)
-test
B.3
Binary outcome
B.3.1
\(\chi^2\)
-test
B.3.2
Fisher’s exact test
B.4
Survival outcome
C
Some proofs on ROC curves
C.1
The ROC curve
C.2
AUC
D
Some theory on equivalence trials
D.1
Type I error in equivalence trials
D.2
Sample size calulations in equivalence trials
E
Expectation, Variance, Covariance and Correlation
E.1
Expectation
E.2
Variance
E.3
Moments
E.4
Conditional Expectation and Variance
E.5
Covariance
E.6
Correlation
F
The Linear Model
F.1
Concepts
F.1.1
Standard error
References
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Clinical Biostatistics
F
The Linear Model
F.1
Concepts
F.1.1
Standard error