Constructing Confidence Intervals for Sensitivity Under Controlled Specificity in Medical Tests Öffentlichkeit
Parakati, Isaac (2017)
Abstract
Abstract
Constructing Confidence Intervals for Sensitivity Under Controlled Specificity in Medical Tests
By: Isaac Parakati
Introduction: Medical tests frequently assist health care
workers with identifying individuals affected or not affected by a
disease. Although medical tests are supposed to correctly identify
diseased individuals as diseased and non-diseased individuals as
non-diseased, this does not always occur. The test's accuracy is
typically measured in terms of sensitivity and specificity. Fixing
the specificity of a test at a particular value, the test's
corresponding sensitivity can be determined. The goal of this paper
is to propose two new approaches for constructing confidence
intervals for sensitivity after fixing specificity.
Methods: To estimate sensitivity, both of the two
proposed approaches are based on a quadratic inference function but
differ by the procedure used to profile out a nuisance parameter.
The first approach minimizes the function with respect to the
nuisance parameter. The second approach determines an optimal
weighted average between two values for the nuisance parameter. To
demonstrate the two approaches, confidence intervals were
constructed for the sensitivity of a gene expression biomarker
using samples of cancerous and non-cancerous tissues, fixing
specificity. Simulations were conducted to evaluate the approaches
under different distributions with varying sample sizes. Coverage
probabilities and average confidence interval length were
determined for each simulation.
Results: In the simulations, the two new approaches
produced confidence intervals above or near the nominal
significance level. The first approach constructed very wide
intervals with conservative coverage. The second approach
constructed narrower intervals with coverage near the nominal
value; this approach performed similarly to the leading existing
BTII approach, whose simulation results were extracted from Zhou
and Qin's paper4. The BTII approach seemed to perform
slightly better when the diseased and non-diseased sample sizes
differed. With larger sample sizes, average confidence interval
length for all approaches narrowed.
Discussion: The second approach proposed in this paper appears to be a suitable non-bootstrap alternative to the BTII approach when constructing confidence intervals.
Table of Contents
Table of Contents
1. Introduction......................................................................................................................................... 1
1.1 Problem Statement and Notation........................................................................................................... 1
1.2 Purpose Statement.............................................................................................................................. 2
1.3 Significance Statement......................................................................................................................... 2
2. Background/Literature Review................................................................................................................. 2
2.1 Naive Interval..................................................................................................................................... 2
2.2 Linnet Interval.................................................................................................................................... 3
2.3 Bootstrap Intervals.............................................................................................................................. 4
3. Methods............................................................................................................................................... 6
4. Practical Application to Cancer Tissue....................................................................................................... 9
5. Simulations........................................................................................................................................... 9
5. Discussion............................................................................................................................................ 11
6. References........................................................................................................................................... 13
7. Appendix.............................................................................................................................................. 14
7.1 Bisection Method................................................................................................................................. 14
7.2 Tables & Figures.................................................................................................................................. 15
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