9 - Diperkirakan prevalensi benar menggunakan satu tes dengan sampler Gibbs

Analisis ini menggunakanBayesian pendekatan dan Gibbs sampler to estimate the true animal-level prevalence of infection based on testing of individual (not pooled) samples using a test with imperfect sensitivity and/or specificity. The analysis requires prior estimates of true prevalence, test sensitivity and test specificity as Distribusi probabilitas beta, dan keluarandistribusi posterior untuk prevalensi, sensitivitas dan spesifisitas. LihatJoseph et al. (1995) untuk detail lebih lanjut.

Input yang diperlukan untuk analisis ini adalah:

• jumlah sampel yang diuji;
• jumlah sampel positif;
• parameter alfa dan beta untuk prior Distribusi beta untuk:
• diasumsikan benarprevalensi;
• taksiran tessensitivitas; dan
• taksiran tesspesifisitas.
• jumlahiterations untuk disimulasikan dalam sampler Gibbs;
• jumlah iterasi yang menjadidibuang untuk mengizinkan konvergensi model;
• lebih rendah dan atas probability (confidence) limits for summarising the output distributions; and
• nilai awal untuk jumlahtrue-positive dan false-negative test results (the numbers of truly infected individuals among the test-positive and test-negative groups, respectively).

The number of samples tested must be a positive integer and the number of positive samples must be an integer >=0 and <= the number of samples tested. Alpha and beta parameters for prevalence, sensitivity and specificity must be >0 and upper and lower confidence limits must be >0 and <1. Starting values for the numbers of true positives and false negatives must be integers >= zero and <= the number of positive samples and the number of negative samples, respectively. The number of iterations and the number discarded must both be positive integers (>0) and the number discarded must be less than the number of iterations.

TheGibbs sampler digunakan untuk memperkirakandistribusi probabilitas posterior of true prevalence, sensitivity and specificity that best fit the data and the prior distributions provided.

Prior estimates of the true prevalence and test sensitivity and specificity may be based on expert knowledge or on previous data. These estimates are specified as Distribusi probabilitas beta, dengan parameteralpha dan beta. Beta probability distributions are commonly used to express uncertainty about a proportion based on a random sample of individuals. In this situation, if x individuals are positive for a characteristic out of n examined, then the alpha and beta parameters can be calculated as alpha = x + 1 and beta = n - x + 1. Alternatively, alpha and beta can be calculated using the Utilitas distribusi beta, provided estimates of the mode and 5% or 95% confidence limits are available from expert opinion.

Keluaran dari sampler Gibbs adalah distribusi probabilitas posterior untuk:

• prevalensi tingkat hewan;
• uji sensitivitas;
• uji spesifisitas;
• positif dan nilai prediksi negatif untuk ujian;
• positif dan rasio kemungkinan negatif untuk ujian; dan
• angkatrue-positive dan false-negative hasil pengujian.

Distribusi ini dijelaskan oleh:

• minimum;
• batas probabilitas lebih rendah;
• median;
• batas probabilitas atas;
• maksimum;
• berarti;
• standar deviasi;
• histogram dan bagan kepadatan (unduh dengan mengklik ikon yang sesuai); dan
• text files of parameter estimates for all iterations of the Gibbs sampler (download by clicking on the appropriate icon).

Because the Gibbs sampler estimates prevalence iteratively, based on the data and the prior distributions, it may take a number of iterations for the model to converge on the true value. Therefore, a specified number of initial iterations must be dibuang (not used for estimation) to allow the model to converge on the true values. This number must be sufficient to allow convergence, and should be at least 2000 - 5000. It is also important to carry out an adequate number of iterations to support inference from the results. Suggested minimum values for the total number of iterations and the number to be discarded are provided, but can be varied if desired.

Analisis ini dapat memakan waktu beberapa menit untuk diselesaikan, tergantung pada jumlah iterasi yang diperlukan.