Constructing Confidence Intervals for Sensitivity Under Controlled Specificity in Medical Tests Open Access

Parakati, Isaac (2017)

Permanent URL: https://etd.library.emory.edu/concern/etds/6q182k88v?locale=en
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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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