Dataset with 150 patients including missing values in test results (~5-8% missingness per test). Three tests with good characteristics.
Format
A data frame with 150 rows and 5 variables:
- patient_id
Character: Patient identifier (PT001-PT150)
- Test1
Factor: First test ("Negative", "Positive"), ~7% missing, Sens=0.85, Spec=0.85
- Test2
Factor: Second test ("Negative", "Positive"), ~5% missing, Sens=0.80, Spec=0.88
- Test3
Factor: Third test ("Negative", "Positive"), ~8% missing, Sens=0.82, Spec=0.90
- age
Numeric: Patient age in years (mean 58, SD 12)
Details
Simulated with 30% prevalence. Missing data introduced randomly to test listwise deletion and missing data handling.
Examples
data(nogoldstandard_missing)
nogoldstandard(data = nogoldstandard_missing,
test1 = "Test1", test1Positive = "Positive",
test2 = "Test2", test2Positive = "Positive",
test3 = "Test3", test3Positive = "Positive",
test4Positive = "", test5Positive = "")
#>
#> ANALYSIS WITHOUT GOLD STANDARD
#> WARNING: Excluded 30 case(s) with missing test results
#> This analysis uses the 120 of 150 cases (80.0%) with a result recorded for every selected test. Latent class and composite estimates assume the excluded cases are missing at random; if a test is more often missing when it would have been positive, the estimates below are biased.
#> Agreement Statistics (Cohen's Kappa)
#> ──────────────────────────────────────────────────────────
#> Test Pair Kappa p-value Agreement
#> ──────────────────────────────────────────────────────────
#> Test1 vs Test2 0.5472441 < .0000001 80.83333
#> Test1 vs Test3 0.4512195 0.0000012 77.50000
#> Test2 vs Test3 0.3957704 0.0000343 75.00000
#> ──────────────────────────────────────────────────────────
#> 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: 31.9%
#>
#> Test sensitivities: Range from 64.8% to 82.8%
#>
#> Clinical interpretation: High prevalence setting - high PPV expected,
#> focus on confirming disease
#>
#> <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
#> ───────────────────────────────────────
#> 31.93134 23.58993 40.27275
#> ───────────────────────────────────────
#>
#>
#> Test Performance Metrics
#> ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Test Sensitivity Lower CI Upper CI Specificity Lower CI Upper CI PPV NPV
#> ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Test1 82.81741 70.87329 94.76153 94.77690 89.95188 99.60192 88.14903 92.16196
#> Test2 77.58385 64.37956 90.78814 91.09756 84.92178 97.27334 80.34669 89.65141
#> Test3 64.83313 49.71444 79.95183 90.01316 83.51109 96.51522 75.28032 84.51138
#> ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> 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 406.672567
#> AIC 387.160125
#> Log-Likelihood -186.580063
#> 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- 64 53.33333
#> Test1+, Test2+, Test3+ 16 13.33333
#> Test1+, Test2+, Test3- 9 7.50000
#> Test1-, Test2+, Test3- 8 6.66667
#> Test1-, Test2-, Test3+ 8 6.66667
#> Test1+, Test2-, Test3- 6 5.00000
#> Test1+, Test2-, Test3+ 5 4.16667
#> Test1-, Test2+, Test3+ 4 3.33333
#> ─────────────────────────────────────────────────
#>
