Result Page
Model Code : MODEL103
Model Name : The 3-tests in 1-population Model
(Simplified Interface)
Job ID : 20161217143450780
1. Summary Table
Prevalence, sensitivities and specificities, positive and negative predictive values (PPV and NPV) estimated by using gold standard model and Bayesian latent class model (LCM). (Hide)

Parameters Test A was assumed as a perfect gold standard (%)*  Bayesian latent class model (%) **
Prevalence 5.3 (3.6 - 7.7) 5.4 (3.8 - 7.6)
Test A
Sensitivity 100 98.7 (86.8 - 100)
Specificity 100 100 (99.5 - 100)
PPV 100 99.2 (90.8 - 100)
NPV 100 99.9 (99.2 - 100)
Test B
Sensitivity 71.4 (51.1 - 86.0) 70.3 (52.5 - 85.5)
Specificity 100 (99.0 - 100) 100 (99.5 - 100)
PPV 100 (80.0 - 100) 98.9 (88.4 - 100)
NPV 98.4 (96.8 - 99.3) 98.4 (96.9 - 99.3)
Test C
Sensitivity 100 (85.0 - 100) 99.3 (91.8 - 100)
Specificity 99.4 (98.1 - 99.8) 99.4 (98.4 - 99.9)
PPV 90.3 (73.1 - 97.5) 90.6 (76.0 - 98.8)
NPV 100 (99.0 - 100) 100 (99.5 - 100)

* Gold standard model assumed that test A is perfect (100% sensitivity and 100% specificity; all patients with gold standard test positive are diseased and all patients with gold standard test negative are non-diseased). Values shown are estimated means with 95% confidence interval.

** Bayesian latent class model assumed that all tests evaluated are imperfect. Values shown are estimated median with 95% credible interval.
THINGS TO BE AWARE OF!!!
1) Results estimated by Bayesian LCM are reliable only when the chains in Bayesian LCM converged properly. Therefore, please check for the convergence before considering the result in the summary table.

2) Results estimated by Bayesian LCM are reliable only when the frequencies predicted by Bayesian LCM do fit with the observed data. Therefore, please check for the fitness of the model before considering the result in the summary table.

3) Results estimated by Bayesian LCM here should be used as a preliminary statistical analysis ONLY. For further usage, please consult experienced Bayesian statisticians for thorough analysis and confirmation.

2. Checking for convergence of Bayesian LCM
Please carefully evaluate histogram and tracing plots of prevalence, sensitivities, specificities, PPVs and NPVs to check for convergence of two chains generated by Bayesian LCM. (Hide)

WARNING!!!
Please ensure that chains do CONVERGE!!! The follow two examples illustrate what kind of convergency is acceptable and what is not acceptable.

The black line represents chain 1 and red line represents chain 2. If the two chains do not converge (as in Example 1), the estimated parameters by the Bayesian model are UNRELIABLE.

There are many reasons for the chains not converged, please consult WinBUGS manual, standard textbooks of Bayesian statistics or experienced statisticians.


Prevalence (%)* = 5.4 (3.8 - 7.6)
Histogram Tracing plots

Sensitivity of Test A (%)* = 98.7 (86.8 - 100)
Histogram Tracing plots
Specificity of Test A (%)* =  100 (99.5 - 100)
Histogram Tracing plots

Sensitivity of Test B (%)* = 70.3 (52.5 - 85.5)
Histogram Tracing plots
Specificity of Test B (%)* = 100 (99.5 - 100)
Histogram Tracing plots

Sensitivity of Test C (%)* = 99.3 (91.8 - 100)
Histogram Tracing plots
Specificity of Test C (%)* = 99.3 (91.8 - 100)
Histogram Tracing plots
* Bayesian latent class model %

3. Checking for fitness of Bayesian LCM
Please carefully assess the agreement between "frequency observed" and "frequency predicted" using Bayesian p value and posterior predictive distribution of each profile. (Hide)

Profiles Test A Test B Test C Frequency observed Frequency predicted Bayesian
p value *
111 Positive Positive Positive 20 19 0.455
110 Positive Positive Negative 0 0 1.000
101 Positive Negative Positive 8 8 0.535
011 Negative Positive Positive 0 0 1.000
100 Positive Negative Negative 0 0 1.000
010 Negative Positive Negative 0 0 1.000
001 Negative Negative Positive 3 3 0.584
000 Negative Negative Negative 493 491 0.447
* Bayesian p-value is the probability that replicate data (predicted frequency) from the Bayesian model were more extreme than the observed data. A Bayesian p-value close to 0 or 1 indicates that the observed result would be unlikely to be seen in replication of the data if the mode was true. This means that when Bayesian p-value is close to 0.5 or exactly 0.5, the Bayesian model describes the observed data very well.

Histogram

Red line represents the observed frequency of each test result profile, while the histograms illustrate the predictive posterior distribution of predicted frequency.

In each of the figures, dataset was replicated for 20000 times and selected only 2000 time (thin sampling equals to 10) to assess the probability of observed frequencies, assuming the model was true.