Assessing laboratory performance in Trichinella ring trials

Abstract

Trichinosis (Trichinellosis) is a zoonotic disease acquired by eating raw or not adequately processed pork or wild game infected with the larvae of the roundworm genus Trichinella. According to European regulations, animals susceptible to Trichinella have to be examined for infestation. To evaluate the performance of laboratories in Germany, inter-laboratory comparisons known as “ring trials” were introduced by the Federal Institute for Risk Assessment in 2004. The current method of analysis makes use of tolerance zones based on the number of larvae in the sample, but does not permit one to determine if a given lab can detect an infested sample reliably, as required by the quality assurance recommendations of the International Commission on Trichinellosis (ICT). A new way of analysing the ring trial data is presented here, which is based on Bayesian hierarchical models. The model implements the ICT requirement by providing an estimate for the probability that a given lab would fail to detect a sample containing, say, five larvae. When applied to the 87 labs that participated in Germany’s 2009 ring trials, it turns out this probability is greater than 10 % for 21 of them, although only 10 of these in fact returned a false negative result. Such a new method is required to abide by the ICT requirements and make ring trials effective.

Appendix

The top level of our model assumes that the labs can be considered to be drawn from a population (e.g. of all such labs in Germany or Europe). More specifically, we assume that the logit of the probability for the i-th lab of finding a Trichinella can be considered to be drawn from a normal distribution with (unknown) mean μ and standard deviation σ,

$$ \ln \left(\frac{\theta_i}{1-{\theta}_i}\right)\sim N\left(\mu, \sigma \right). $$

The next level in the hierarchy describes each lab individually and assumes that the total number of Trichinella observed, r _i , is described by the binomial distribution for the total number to be found, n,

$$ {r}_i\sim Bin\left(n,{\theta}_i\right). $$

However, we have more information at our disposal, since the total number of observed larvae was distributed amongst k probes, where s _ij represents the number observed in the j-th probe,

$$ {r}_i={\displaystyle \sum_{j=1}^k}{s}_{ij}. $$

We describe each probe by the binomial distribution

$$ {s}_{ij}\sim Bin\left({n}_j,{\tilde{\theta}}_{ij}\right), $$

having introduced a probability ${\tilde{\theta}}_{ij}$ for each lab and probe and where n _j denotes the number of Trichinella in the j-th probe. The bottom level in our hierarchical model assumes that the logit of the proportion of larvae found in each probe (for a given lab) follows a normal distribution with the mean given by logit θ _i and a standard deviation ${\tilde{\sigma}}_i$ specific to that lab,

$$ \ln \left(\frac{{\tilde{\theta}}_{ij}}{1-{\tilde{\theta}}_{ij}}\right)\sim N\left[ \ln \left(\frac{\theta_i}{1-{\theta}_i}\right),{\tilde{\sigma}}_i\right]. $$

Non-informative priors were chosen: a normal distribution for the global mean μ centred around zero and with a standard deviation of 1,000 and inverse gamma distributions for the global variance and those of individual labs.

The model was run with a burn-in of 1,000 steps and an update of 4,000 steps. Different parameters for the gamma distribution were shown to converge to the same results. A graphical display suggested that stationary solutions were approached for all variables and three chains with different initial values were used to calculate the Gelman Rubin statistic (Gelman and Rubin 1992; Brooks and Gelman 1998) which always converged to 1 generally to within 0.1 %. The MC error was also seen to be at least two orders of magnitude smaller than the value for the estimated parameter.

The corresponding author can provide the WINBUGS and R scripts upon request.