Module: Posterior probability of herd freedom from disease (Program: Bayesfreecalc1)
The calculations performed by the software program Bayesfreecalc1 (see Download Software). Determine the posterior probability that a population of size N, with a given number of positive reactors (test positive individuals) out of a sample of size n, truly exceeds some predetermined threshold/cut-off value. This is Hypergeometric sampling. The calculator can also be used for binomial sampling where N is assumed large relative to n. Each of the n individuals sampled is tested for a given agent and classified as test positive or test negative. The screening test used is usually imperfect and there may be false positive and negative results. Prior distributions reflecting the uncertainty about the diagnostic test sensitivity and specificity are incorporated into the calculation. Analytic results provide the posterior probability that prevalence in the overall population sampled exceeds a given cutoff/threshold value and the number of positive reactors expected out of the n individuals sampled.
The basic situation involves collecting a binomial or hypergeometric-like sample from a population of individuals. Each individual sampled is tested for a given agent and classified as test positive or test negative. The screening test used is usually imperfect and there may be false positive and negative results. Our goal is to determine if the prevalence of the agent in the population sampled either exceeds a given cutoff/threshold value. If the prevalence is below the threshold, the population is considered to be "disease free" and no action is regarded as necessary. Alternately, if the prevalence does exceed this value, an intervention may be considered imperative. Precise details associated with the calculations discussed below for both Bayesfreecalc1 and Bayesfreecalc2 are provided in the article "Johnson WO, Su CL, Gardner IA, Christensen R. Sample size calculations for surveys to substantiate freedom of populations from infectious agents. Biometrics. 2004 Mar;60(1):165-71".
The program Bayesfreecalc1 is designed to calculate the posterior probability of "herd infection status," given (a) prior knowledge about the prevalence of the population and the sensitivity and specificity of the diagnostic test used to sample the population, (b) information about the number of positive reactors (T+), the number of individuals sampled (n) and the overall population size (N). This program is consists of 3 "tabs": the "Determine Priors" tab, the "Options and Output" tab, and the "Extra Options" tab. The "Determine Priors" tab is used to specify prior knowledge about prevalence and the sensitivity and specificity of the diagnostic test; ultimately beta prior distributions are elicited from probability statements provided from either subjective expert opinion or previous studies. The "Options and Output" tab is used to supply information about the number sampled, the number in the population, and the number of reactors, and obtain a posterior probability of "herd infection status." The "Extra Options" tab is used to specify information about program algorithm itself (i.e., Monte Carlo sample size, maximum sample size, and the "burn-in").
Download Software with Worked Examples
The self-extracting Bayesfreecalc software (for Windows) includes a pair of programs: Bayesfreecalc1 (used to estimate the posterior probability of disease freedom) and Bayesfreecalc2 (used for sample size calculations). Bayesfreecalc is a GUI interface program that does not require other ancillary statistical software (such as S-plus or WinBUGS). Follow the steps below to install Bayesfreecalc1 and Bayesfreecalc2 on your computer.
Step1: Download the FreeBS self-extracting installation file (
FBSinst.zip). We suggest saving the file to your computer (e.g., into "C:\My Downloads\", or "C:\My Documents\", or onto the Desktop) and running the installation program from your local drive. File size is approx. 7MB.
Step 2: You should now be able to double click on the "FBSinst.exe" copy you just downloaded to your computer and install Bayesfreecalc into "C:\FreeBS".
Worked examples are provided in the Help file provided with the Program Bayesfreecalc1.