Dataset with 300 patients and very low disease prevalence (5%). Three tests with good characteristics (Sens: 0.80-0.75, Spec: 0.90-0.88).
Format
A data frame with 300 rows and 5 variables:
- patient_id
Character: Patient identifier (PT001-PT300)
- Test1
Factor: First test ("Negative", "Positive"), Sens=0.80, Spec=0.90
- Test2
Factor: Second test ("Negative", "Positive"), Sens=0.75, Spec=0.92
- Test3
Factor: Third test ("Negative", "Positive"), Sens=0.78, Spec=0.88
- screening_site
Factor: Screening site (Site_1 to Site_10)
Details
Rare disease setting (5% prevalence) typical of population screening. Tests stability of estimation with few positive cases.
Examples
data(nogoldstandard_rare)
nogoldstandard(data = nogoldstandard_rare,
test1 = "Test1", test1Positive = "Positive",
test2 = "Test2", test2Positive = "Positive",
test3 = "Test3", test3Positive = "Positive",
test4Positive = "", test5Positive = "")
#>
#> ANALYSIS WITHOUT GOLD STANDARD
#> Analysing 300 cases
#> All 300 cases have a result for every selected test.
#> Agreement Statistics (Cohen's Kappa)
#> ─────────────────────────────────────────────────────────
#> Test Pair Kappa p-value Agreement
#> ─────────────────────────────────────────────────────────
#> Test1 vs Test2 0.1767473 0.1003799 83.66667
#> Test1 vs Test3 0.1067762 0.3107576 80.66667
#> Test2 vs Test3 0.2679128 0.0062952 84.33333
#> ─────────────────────────────────────────────────────────
#> Note. Kappa standard errors and p-values use a
#> large-sample normal approximation rather than the
#> exact asymptotic SE (e.g. vcd::Kappa); interpret
#> p-values cautiously, especially in small samples.
#>
#>
#> <div class='clinical-summary' style='background: #f0f8ff; padding:
#> 15px; border-radius: 8px; margin: 10px 0;'><h4 style='color: #1565c0;
#> margin-top: 0;'> Clinical Summary
#>
#> Analysis: No gold standard analysis using latent_class method
#>
#> Tests analyzed: Test1, Test2, Test3 (N=3)
#>
#> Disease prevalence: 14.7%
#>
#> Test sensitivities: Range from 31.6% to 61.3%
#>
#> Clinical interpretation: Moderate prevalence setting - balanced
#> diagnostic performance
#>
#> <div style='background: #f8f9fa; padding: 20px; border-radius: 8px;
#> margin: 15px 0; border-left: 4px solid #007bff;'><h3 style='color:
#> #007bff; margin-top: 0;'> Method Selection Guide
#>
#> <div style='margin: 15px 0; padding: 15px; background: #e8f5e8;
#> border-radius: 5px;'><h4 style='color: #2e7d32; margin-top: 0;'>
#> Latent Class Analysis (Recommended)
#>
#> Description: Most robust method using mixture models. Estimates
#> disease prevalence and test parameters simultaneously.
#>
#> Best for: Diagnostic validation studies with 3+ tests and N>=100
#>
#> Strengths: The only method here that estimates accuracy rather than
#> agreement with a self-built reference; provides model fit statistics.
#> Assumes the tests are conditionally independent given true status --
#> it does NOT model conditional dependence
#>
#> <div style='margin: 15px 0; padding: 15px; background: #e3f2fd;
#> border-radius: 5px;'><h4 style='color: #1565c0; margin-top: 0;'>
#> Bayesian Analysis
#>
#> Description: Incorporates prior knowledge about test performance using
#> Bayesian methods.
#>
#> Best for: Studies where you have prior information about expected
#> sensitivity/specificity
#>
#> Strengths: Uses prior knowledge, handles uncertainty well, good for
#> smaller samples
#>
#> <div style='margin: 15px 0; padding: 15px; background: #fff3e0;
#> border-radius: 5px;'><h4 style='color: #ef6c00; margin-top: 0;'>
#> Composite Reference
#>
#> Description: Uses majority vote of available tests as pseudo-gold
#> standard.
#>
#> Best for: Inter-rater agreement studies with 3+ tests, exploratory
#> analysis
#>
#> Strengths: Simple and intuitive. Not an accuracy estimate: each test
#> helps build the standard it is judged against, which inflates its
#> apparent performance. Needs 3+ tests -- with 2 a tie counts as
#> diseased, making it identical to Any Test Positive
#>
#> <div style='margin: 15px 0; padding: 15px; background: #fce4ec;
#> border-radius: 5px;'><h4 style='color: #c2185b; margin-top: 0;'> All
#> Tests Positive
#>
#> Description: Conservative approach - disease present only if ALL tests
#> are positive.
#>
#> Best for: Highly specific diagnoses where false positives are very
#> costly
#>
#> Strengths: A deliberately strict reference. Sensitivity and NPV cannot
#> be estimated under this rule -- they are fixed at 100% by construction
#> -- so only specificity and PPV are shown, and both are inflated by the
#> same circularity
#>
#> <div style='margin: 15px 0; padding: 15px; background: #e8f5e8;
#> border-radius: 5px;'><h4 style='color: #388e3c; margin-top: 0;'> Any
#> Test Positive
#>
#> Description: Liberal approach - disease present if ANY test is
#> positive.
#>
#> Best for: Population screening scenarios where missing cases is costly
#>
#> Strengths: A deliberately permissive reference. Specificity and PPV
#> cannot be estimated under this rule -- they are fixed at 100% by
#> construction -- so only sensitivity and NPV are shown, and both are
#> inflated by the same circularity
#>
#> <div style='margin: 15px 0; padding: 10px; background: #fff8e1;
#> border-radius: 5px; border-left: 3px solid #ffb300;'><h4 style='color:
#> #e65100; margin-top: 0;'> Selection Tips
#>
#> Start with Latent Class Analysis for most diagnostic studiesUse
#> Composite Reference for quick exploratory analysisChoose All/Any Tests
#> Positive based on clinical consequences of errorsConsider Bayesian if
#> you have strong prior information
#>
#> Disease Prevalence
#> ───────────────────────────────────────
#> Estimate Lower CI Upper CI
#> ───────────────────────────────────────
#> 14.67025 10.66659 18.67390
#> ───────────────────────────────────────
#>
#>
#> Test Performance Metrics
#> ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Test Sensitivity Lower CI Upper CI Specificity Lower CI Upper CI PPV NPV
#> ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Test1 31.60863 17.87225 45.34501 92.15248 88.85823 95.44673 40.91527 88.68438
#> Test2 61.29889 46.90902 75.68875 97.64759 95.79097 99.50422 81.75180 93.62073
#> Test3 46.48314 31.74774 61.21853 92.36592 89.11301 95.61882 51.14393 90.94109
#> ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Note. 95% intervals are normal-approximation (Wald) intervals, using the estimated number of diseased cases as
#> the denominator for sensitivity and non-diseased for specificity. They treat the estimates as observed
#> proportions and so understate the uncertainty of a latent-variable model; enable Bootstrap for intervals that
#> account for the estimation itself.
#>
#>
#> Model Fit Statistics
#> ─────────────────────────────────────
#> Statistic Value
#> ─────────────────────────────────────
#> BIC 670.613231
#> AIC 644.686753
#> Log-Likelihood -315.343377
#> Degrees of Freedom 0.000000
#> ─────────────────────────────────────
#> Note. With three tests this
#> model has as many parameters as
#> the data can support (0
#> residual degrees of freedom),
#> so it reproduces the observed
#> table exactly. Goodness-of-fit
#> statistics are therefore
#> omitted: they cannot tell you
#> whether the
#> conditional-independence
#> assumption holds. Use four or
#> more tests if you need to test
#> the model's fit.
#>
#>
#> Conditional Independence Check (Bivariate Residuals)
#> ─────────────────────────────────────────────────────
#> Test Pair Bivariate Residual Interpretation
#> ─────────────────────────────────────────────────────
#> ─────────────────────────────────────────────────────
#> Note. Not computable with three tests: the
#> model has no residual degrees of freedom, so it
#> reproduces every observed table exactly and no
#> residual can detect conditional dependence. Add
#> a fourth test if you need to check this
#> assumption.
#>
#>
#> Test Cross-Tabulation
#> ─────────────────────────────────────────────────
#> Test Combination Count Percentage
#> ─────────────────────────────────────────────────
#> Test1-, Test2-, Test3- 219 73.00000
#> Test1-, Test2-, Test3+ 23 7.66667
#> Test1+, Test2-, Test3- 21 7.00000
#> Test1-, Test2+, Test3- 15 5.00000
#> Test1-, Test2+, Test3+ 9 3.00000
#> Test1+, Test2+, Test3- 5 1.66667
#> Test1+, Test2-, Test3+ 4 1.33333
#> Test1+, Test2+, Test3+ 4 1.33333
#> ─────────────────────────────────────────────────
#>
