Subtopic Deep Dive
Confidence Intervals for Proportions
Research Guide
What is Confidence Intervals for Proportions?
Confidence intervals for proportions construct probabilistic bounds around estimated proportions from binary medical data, ensuring coverage accuracy in clinical trials.
Methods compare Wald, Wilson, Newcombe, and exact intervals for single and multiple proportions (Newcombe, 1998; 4996 citations). Research targets small-sample bias and coverage shortfalls in binomial settings (Sakakibara, 2014; 6 citations). Over 5000 citations validate Newcombe's seven-method benchmark.
Why It Matters
Accurate intervals underpin binary outcome inference in vaccine efficacy trials and diagnostic test evaluation (Newcombe, 1998). Newcombe's methods correct Wald interval failures, enabling reliable 95% coverage for rare events like adverse reactions. Avdonina et al. (2019) applied them to measles immunity proportions among medical workers, informing public health policy.
Key Research Challenges
Small-sample coverage failure
Wald intervals undercover below nominal levels for n<30 or p near 0/1 (Sakakibara, 2014). Exact methods like Clopper-Pearson overcorrect, reducing precision. Newcombe (1998) scores seven alternatives on coverage and interval width.
Seven-method performance ranking
Newcombe (1998) ranks Wilson and Agresti-Coull superior to Wald for balanced coverage. Sakakibara (2014) confirms exact intervals' edge in tiny samples but wider bounds. Tradeoff complicates medical adoption.
Multiple proportion adjustments
Single-proportion fixes fail in multi-arm trials with correlated binaries. Avdonina et al. (2019) highlight collective immunity estimates needing simultaneous intervals. Bias correction lags for dependent proportions.
Essential Papers
Two-sided confidence intervals for the single proportion: comparison of seven methods
Robert G. Newcombe · 1998 · Statistics in Medicine · 5.0K citations
Simple interval estimate methods for proportions exhibit poor coverage and can produce evidently inappropriate intervals. Criteria appropriate to the evaluation of various proposed methods include:...
Collective Immunity to Virus Measles of Medical Workers and Students of Medical Colleges in the Republic of Tatarstan
L. G. Avdonina, М. А. Patyashina, Г. Ш. Исаева et al. · 2019 · Epidemiology and Vaccinal Prevention · 7 citations
Relevance. Within the framework of the state assignment in the, Kazan Scientific Research Institute of Epidemiology and Microbiology together with the Department of Rospotrebnadzor in the Republic ...
COMPARISON OF FIVE EXACT CONFIDENCE INTERVALS FOR THE BINOMIAL PROPORTION
Sakakibara · 2014 · Current Research in Biostatistics · 6 citations
The Wald interval is easy to calculate; it is often used as the confidence interval for binomial proportions. However, when using this confidence interval, the actual coverage probability often fal...
An Improved Confidence Interval
Rishi Raj Subedi · 2019 · American Review of Mathematics and Statistics · 1 citations
An Improved Confidence Interval Rishi Raj Subedi, James Issos Abstract For Interval estimation of a proportion the Wald procedure is almost universally used. This is because of its simplicity. A ne...
Trip Reporting and GPS-based Prompted Recall: Survey Design and Preliminary Analysis of Results
Josée Dumont · 2010 · Belarusian State Pedagogical University repository (Belarusian State Pedagogical University) · 1 citations
This trip reporting and GPS-based prompted-recall travel survey was undertaken to provide a better understanding of (a) demographic and behavioural differences between students with a home telephon...
Confidence Intervals Are a Programmer's Friend
Xinxin Guo, Zhaohui Su · 2015 · 0 citations
A confidence interval (CI) is a type of interval estimate of a population parameter and is one of the most common terms statistical programmers face in everyday practice. This paper will present a ...
Reading Guide
Foundational Papers
Start with Newcombe (1998) for seven-method benchmark and coverage criteria; read Sakakibara (2014) next for exact interval rankings in biostatistics.
Recent Advances
Subedi (2019) improved CI post-Wald; Avdonina et al. (2019) medical application to immunity proportions.
Core Methods
Wald (p±1.96√(p(1-p)/n)); Wilson score correction; Clopper-Pearson exact; Newcombe hybrid (1998).
How PapersFlow Helps You Research Confidence Intervals for Proportions
Discover & Search
Research Agent uses searchPapers('confidence intervals proportions medicine Newcombe') to retrieve 4996-cited benchmark (Newcombe, 1998), then citationGraph reveals Sakakibara (2014) and Subedi (2019) comparators. exaSearch('small sample binomial coverage') surfaces Avdonina et al. (2019) applications. findSimilarPapers expands to 250+ related works.
Analyze & Verify
Analysis Agent runs readPaperContent on Newcombe (1998) to extract seven-method coverage tables, then runPythonAnalysis simulates Wald vs. Wilson in NumPy for n=20, p=0.1 (95% coverage verification). verifyResponse (CoVe) with GRADE grading scores claims as 'high' evidence. Statistical tests confirm Sakakibara (2014) rankings.
Synthesize & Write
Synthesis Agent detects gaps like multiple-proportion extensions post-Newcombe, flags Wald contradictions across papers. Writing Agent uses latexEditText for interval formula tables, latexSyncCitations integrates 5 papers, latexCompile outputs PDF. exportMermaid diagrams seven-method comparison flowcharts.
Use Cases
"Simulate coverage of Newcombe intervals for n=15 successes=2 in vaccine trial"
Research Agent → searchPapers('Newcombe 1998') → Analysis Agent → runPythonAnalysis (NumPy binomial sim, 10k reps) → matplotlib coverage plot output.
"Write LaTeX section comparing Wald and Wilson for diagnostic test proportion"
Research Agent → citationGraph(Newcombe) → Synthesis → gap detection → Writing Agent → latexEditText('insert Wilson formula') → latexSyncCitations(3 papers) → latexCompile → arXiv-ready PDF.
"Find code for exact binomial intervals in medical stats papers"
Research Agent → searchPapers('binomial confidence code') → Code Discovery → paperExtractUrls → paperFindGithubRepo → githubRepoInspect → SAS/Python snippets from Guo (2015).
Automated Workflows
Deep Research scans 50+ proportion papers, chains searchPapers → citationGraph → GRADE summary on coverage methods (Newcombe benchmark). DeepScan's 7-steps verify small-sample claims: readPaperContent(Sakakibara) → runPythonAnalysis → CoVe checkpoint. Theorizer hypothesizes 'Agresti-Coull optimal for p<0.05' from lit synthesis.
Frequently Asked Questions
What defines confidence intervals for proportions?
Ranges estimating true binomial p with 95% coverage probability. Newcombe (1998) compares seven: Wald, Wilson, Jeffreys, etc.
Which methods outperform Wald?
Wilson and Agresti-Coull match nominal coverage best (Newcombe, 1998). Sakakibara (2014) ranks five exact versions superior for n<20.
Key papers on proportion intervals?
Newcombe (1998; 4996 cites) foundational comparison. Sakakibara (2014; 6 cites) exact methods. Subedi (2019) improved estimator.
Open problems in proportion CIs?
Multiple dependent proportions lack bias-corrected methods. Small-sample multi-arm trial coverage unoptimized post-Newcombe.
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