Co-Testing Analysis: Combining Diagnostic Tests for Better Clinical Decision Making

Introduction to Co-Testing Analysis

In clinical practice, physicians often use multiple diagnostic tests to improve diagnostic accuracy. The co-testing analysis function in ClinicoPath helps clinicians understand how combining two diagnostic tests affects post-test probabilities and clinical decision-making.

What is Co-Testing?

Co-testing refers to the simultaneous use of two diagnostic tests to improve diagnostic performance. This approach is common in:

Cancer screening (e.g., mammography + ultrasound)
Infectious disease diagnosis (e.g., antigen test + PCR)
Cardiac evaluation (e.g., troponin + ECG)
Neurological assessment (e.g., MRI + clinical examination)

Key Concepts

Post-Test Probability

The probability of disease after obtaining test results, calculated using Bayes’ theorem.

Test Independence

Whether the results of one test influence the results of another test, given the patient’s true disease status.

Likelihood Ratios

Positive Likelihood Ratio (PLR): How much more likely a positive result is in diseased vs. non-diseased patients
Negative Likelihood Ratio (NLR): How much more likely a negative result is in diseased vs. non-diseased patients

Understanding Test Independence vs. Dependence

Independent Tests

Tests are conditionally independent when the result of one test doesn’t affect the probability of the other test result, given the disease status.

Mathematical formulation for independent tests: - P(Test1+ and Test2+ | Disease+) = Sensitivity₁ × Sensitivity₂ - P(Test1+ and Test2+ | Disease-) = (1-Specificity₁) × (1-Specificity₂)

Dependent Tests

Tests are conditionally dependent when knowing one test result changes the probability of the other test result, even when disease status is known.

When tests are likely dependent: - Both tests measure similar biological phenomena - Tests use the same specimen or mechanism - Tests are affected by the same confounding factors

Clinical Examples

Example 1: COVID-19 Screening with Independent Tests

Let’s analyze a scenario where we use an antigen test and PCR test for COVID-19 screening, assuming they are independent.

# COVID-19 screening with antigen + PCR (independent)
covid_independent <- cotest(
  test1_sens = 0.68,    # Antigen test sensitivity
  test1_spec = 0.99,    # Antigen test specificity
  test2_sens = 0.95,    # PCR test sensitivity
  test2_spec = 0.99,    # PCR test specificity
  prevalence = 0.05,    # Community prevalence (5%)
  indep = TRUE,         # Assume independence
  fagan = TRUE,         # Show Fagan nomogram
  fnote = TRUE          # Show explanatory footnotes
)

print(covid_independent)

Interpretation

Pre-test probability: 5% (community prevalence)
Both tests positive: Dramatically increases disease probability
Both tests negative: Substantially decreases disease probability
Mixed results: Individual test probabilities apply

Example 2: COVID-19 Screening with Dependent Tests

Now let’s consider the same tests but account for potential dependence (e.g., both tests may be affected by viral load).

# COVID-19 screening with antigen + PCR (dependent)
covid_dependent <- cotest(
  test1_sens = 0.68,    # Antigen test sensitivity
  test1_spec = 0.99,    # Antigen test specificity
  test2_sens = 0.95,    # PCR test sensitivity
  test2_spec = 0.99,    # PCR test specificity
  prevalence = 0.05,    # Community prevalence (5%)
  indep = FALSE,        # Account for dependence
  cond_dep_pos = 0.15,  # Dependence in COVID+ patients
  cond_dep_neg = 0.05,  # Dependence in COVID- patients
  fagan = TRUE,         # Show Fagan nomogram
  fnote = TRUE          # Show explanatory footnotes
)

print(covid_dependent)

Key Differences

When accounting for dependence, the benefit of combined testing is typically reduced compared to the independence assumption. This is because: - Positive results are less surprising (tests tend to agree) - The tests provide less independent evidence

Example 3: Cancer Screening Scenario

Breast cancer screening using mammography and ultrasound in a high-risk population.

# Breast cancer screening in high-risk women
cancer_screening <- cotest(
  test1_sens = 0.88,    # Mammography sensitivity
  test1_spec = 0.92,    # Mammography specificity
  test2_sens = 0.95,    # Ultrasound sensitivity
  test2_spec = 0.85,    # Ultrasound specificity
  prevalence = 0.08,    # High-risk population (8% prevalence)
  indep = FALSE,        # Tests likely dependent
  cond_dep_pos = 0.25,  # High dependence in cancer patients
  cond_dep_neg = 0.15,  # Moderate dependence in non-cancer patients
  fagan = TRUE,
  fnote = TRUE
)

print(cancer_screening)

Clinical Decision Points

This analysis helps determine: - When to biopsy: High post-test probability after positive tests - When to reassure: Very low probability after negative tests - When to use additional testing: Intermediate probabilities

Example 4: Cardiac Biomarkers in Emergency Department

Evaluating chest pain patients using troponin and CK-MB.

# Cardiac biomarkers for myocardial infarction
cardiac_biomarkers <- cotest(
  test1_sens = 0.92,    # Troponin sensitivity
  test1_spec = 0.89,    # Troponin specificity
  test2_sens = 0.85,    # CK-MB sensitivity
  test2_spec = 0.94,    # CK-MB specificity
  prevalence = 0.25,    # ED chest pain patients (25% MI rate)
  indep = FALSE,        # Biomarkers likely correlated
  cond_dep_pos = 0.30,  # High correlation in MI patients
  cond_dep_neg = 0.20,  # Moderate correlation in non-MI patients
  fagan = TRUE,
  fnote = TRUE
)

print(cardiac_biomarkers)

Clinical Application

Both positive: Strong evidence for MI, immediate intervention
Both negative: Low MI probability, consider discharge protocols
Discordant results: May need additional testing or clinical correlation

Practical Guidelines for Co-Testing Analysis

When to Use Independent vs. Dependent Models

Use Independent Model when:

Tests measure completely different biological phenomena
Tests use different specimens or mechanisms
No evidence of correlation between test results
Limited information about test interactions

Use Dependent Model when:

Tests measure similar biological phenomena
Tests use the same specimen
Previous studies show correlation
Both tests affected by same confounding factors

Estimating Dependence Parameters

When dependence parameters are unknown:

Literature Review: Look for studies with paired testing data
Expert Opinion: Consult specialists familiar with the tests
Sensitivity Analysis: Test range of plausible values (0.05, 0.1, 0.2, 0.3)
Conservative Approach: Use moderate dependence (0.1-0.2) when uncertain

# Sensitivity analysis with different dependence levels
scenarios <- list(
  "Low Dependence" = 0.05,
  "Moderate Dependence" = 0.15,
  "High Dependence" = 0.30
)

sensitivity_results <- lapply(names(scenarios), function(scenario_name) {
  dep_value <- scenarios[[scenario_name]]
  
  result <- cotest(
    test1_sens = 0.85,
    test1_spec = 0.90,
    test2_sens = 0.80,
    test2_spec = 0.95,
    prevalence = 0.10,
    indep = FALSE,
    cond_dep_pos = dep_value,
    cond_dep_neg = dep_value
  )
  
  cat("\n", scenario_name, "(ρ =", dep_value, "):\n")
  print(result)
  
  return(result)
})

Impact of Ignoring Dependence

Ignoring conditional dependence when it exists typically leads to:

Overestimating the benefit of combined testing
Exaggerating post-test probabilities
Overly optimistic assessment of diagnostic accuracy
Unrealistic confidence intervals

Advanced Applications

Sequential vs. Simultaneous Testing

While this function models simultaneous testing, it can inform sequential testing strategies:

# First test: High sensitivity screening test
first_test <- cotest(
  test1_sens = 0.95,    # High sensitivity screening
  test1_spec = 0.80,    # Lower specificity acceptable
  test2_sens = 0.95,    # Dummy second test (same values)
  test2_spec = 0.80,
  prevalence = 0.05,
  indep = TRUE
)

# If first test positive, use confirmatory test
confirmatory_test <- cotest(
  test1_sens = 0.95,    # Original screening test
  test1_spec = 0.80,
  test2_sens = 0.85,    # Confirmatory test (different characteristics)
  test2_spec = 0.98,    # Higher specificity
  prevalence = 0.25,    # Higher prevalence after positive screen
  indep = FALSE,
  cond_dep_pos = 0.20,
  cond_dep_neg = 0.10
)

cat("Sequential Testing Strategy:\n")
cat("Step 1 - Screening Test Results:\n")
print(first_test)

cat("\nStep 2 - Confirmatory Testing (if screen positive):\n")
print(confirmatory_test)

Cost-Effectiveness Considerations

Co-testing analysis can inform cost-effectiveness decisions:

# High-cost, high-accuracy test combination
high_cost_scenario <- cotest(
  test1_sens = 0.98,    # Expensive, highly accurate test 1
  test1_spec = 0.99,
  test2_sens = 0.96,    # Expensive, highly accurate test 2
  test2_spec = 0.99,
  prevalence = 0.02,    # Low prevalence setting
  indep = TRUE,
  fagan = TRUE
)

# Moderate-cost, good-accuracy test combination
moderate_cost_scenario <- cotest(
  test1_sens = 0.85,    # Moderate cost, good accuracy test 1
  test1_spec = 0.90,
  test2_sens = 0.88,    # Moderate cost, good accuracy test 2
  test2_spec = 0.92,
  prevalence = 0.02,    # Same prevalence
  indep = TRUE,
  fagan = TRUE
)

cat("High-Cost Scenario:\n")
print(high_cost_scenario)

cat("\nModerate-Cost Scenario:\n")
print(moderate_cost_scenario)

Clinical Decision Thresholds

Understanding when co-testing changes clinical decisions:

Treatment Threshold Analysis

# Define clinical scenarios with different action thresholds
scenarios <- data.frame(
  Clinical_Setting = c("Screening", "Symptomatic", "High_Risk"),
  Prevalence = c(0.01, 0.15, 0.40),
  Treatment_Threshold = c(0.05, 0.20, 0.60),
  Test_Threshold = c(0.02, 0.08, 0.30)
)

for (i in 1:nrow(scenarios)) {
  setting <- scenarios[i, ]
  
  cat("\n", setting$Clinical_Setting, "Setting:\n")
  cat("Prevalence:", setting$Prevalence * 100, "%\n")
  cat("Treatment threshold:", setting$Treatment_Threshold * 100, "%\n")
  
  result <- cotest(
    test1_sens = 0.85,
    test1_spec = 0.90,
    test2_sens = 0.80,
    test2_spec = 0.95,
    prevalence = setting$Prevalence,
    indep = TRUE
  )
  
  print(result)
}

Summary and Best Practices

Key Takeaways

Co-testing can significantly improve diagnostic accuracy when used appropriately
Test dependence matters - ignoring it can lead to overoptimistic results
Clinical context is crucial - consider prevalence, thresholds, and consequences
Sensitivity analysis helps understand uncertainty in dependence parameters

Best Practices

Before Analysis

Understand the biological basis for potential test dependence
Gather accurate sensitivity and specificity data
Estimate realistic prevalence for your population
Define clinical decision thresholds

During Analysis

Start with independence assumption as baseline
Test dependence scenarios based on biological plausibility
Use sensitivity analysis for uncertain parameters
Consider both positive and negative test combinations

After Analysis

Interpret results in clinical context
Consider cost-effectiveness implications
Validate findings with clinical experience
Update analysis as new data becomes available

Limitations

Assumes binary test results (positive/negative)
Requires known test characteristics
Dependence parameters may be difficult to estimate
Does not account for test timing or sequence effects

Conclusion

Co-testing analysis provides a quantitative framework for understanding how multiple diagnostic tests interact to influence clinical decision-making. By properly accounting for test dependence and clinical context, this analysis can guide more informed use of diagnostic testing in clinical practice.

The cotest function in ClinicoPath makes these complex calculations accessible to clinicians, providing both numerical results and visual tools (Fagan nomograms) to support evidence-based medical decision-making.

This vignette demonstrates the use of the cotest function for analyzing combined diagnostic tests. For more information about ClinicoPath, visit our documentation or contact the development team.

ClinicoPath

2025-07-13