Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

Tuberculosis and latent tuberculosis in prison inmates

OBJECTIVE: To estimate the prevalences of tuberculosis and latent tuberculosis ill inmates. METHODS: Observational study was carried out with inmates of a prison and a jail in the State of Sao Paulo, Southeastern Brazil, between March and December of 2008. Questionnaires were used to collect sociodemographic and epidemiological data. Tuberculin skin testing was administered (PPD-RT23-2TU/0.1 mL), and the following laboratory tests were also performed: sputum smear examination, sputum culture, identification of strains isolated and drug susceptibility testing. The variables were compared using Pearson's chi-square (chi(2)) association test, Fisher's exact test and the proportion test. RESULTS: Of the 2,435 inmates interviewed, 2,237(91.9%) agreed to submit to tuberculin skin testing and of these, 73.0% had positive reactions. The prevalence of tuberculosis was 830.6 per 100,000 inmates. The coefficients of prevalence were 1,029.5/100,000 for inmates of the prison and 525.7/100,000 for inmates of the jail. The sociodemographic characteristics of the inmates in the two groups studied were similar; most of the inmates were young and single with little schooling. The epidemiological characteristics differed between the prison units, with the number of cases of previous tuberculosis and of previous contact with the disease greater in the prison and coughing, expectoration and smoking more common in the jail. Among the 20 Mycobacterium tuberculosis strains identified, 95.0% were sensitive to anti-tuberculosis drugs, and 5.0% were resistant to streptomycin. CONCLUSIONS: The prevalences of tuberculosis and latent tuberculosis were higher in the incarcerated population than in the general population, and they were also higher in the prison than in the jail.

A General Latent Class Model for Performance Evaluation of Diagnostic Tests in the Absence of a Gold Standard: An Application to Chagas Disease

We propose a new general Bayesian latent class model for evaluation of the performance of multiple diagnostic tests in situations in which no gold standard test exists based on a computationally intensive approach. The modeling represents an interesting and suitable alternative to models with complex structures that involve the general case of several conditionally independent diagnostic tests, covariates, and strata with different disease prevalences. The technique of stratifying the population according to different disease prevalence rates does not add further marked complexity to the modeling, but it makes the model more flexible and interpretable. To illustrate the general model proposed, we evaluate the performance of six diagnostic screening tests for Chagas disease considering some epidemiological variables. Serology at the time of donation (negative, positive, inconclusive) was considered as a factor of stratification in the model. The general model with stratification of the population performed better in comparison with its concurrents without stratification. The group formed by the testing laboratory Biomanguinhos FIOCRUZ-kit (c-ELISA and rec-ELISA) is the best option in the confirmation process by presenting false-negative rate of 0.0002% from the serial scheme. We are 100% sure that the donor is healthy when these two tests have negative results and he is chagasic when they have positive results.

Performance of six diagnostic tests to screen for Chagas disease in blood banks and prevalence of Trypanosoma cruzi infection among donors with inconclusive serology screening based on the analysis of epidemiological variables

OBJECTIVE: The frequent occurrence of inconclusive serology in blood banks and the absence of a gold standard test for Chagas'disease led us to examine the efficacy of the blood culture test and five commercial tests (ELISA, IIF, HAI, c-ELISA, rec-ELISA) used in screening blood donors for Chagas disease, as well as to investigate the prevalence of Trypanosoma cruzi infection among donors with inconclusive serology screening in respect to some epidemiological variables. METHODS: To obtain estimates of interest we considered a Bayesian latent class model with inclusion of covariates from the logit link. RESULTS: A better performance was observed with some categories of epidemiological variables. In addition, all pairs of tests (excluding the blood culture test) presented as good alternatives for both screening (sensitivity > 99.96% in parallel testing) and for confirmation (specificity > 99.93% in serial testing) of Chagas disease. The prevalence of 13.30% observed in the stratum of donors with inconclusive serology, means that probably most of these are non-reactive serology. In addition, depending on the level of specific epidemiological variables, the absence of infection can be predicted with a probability of 100% in this group from the pairs of tests using parallel testing. CONCLUSION: The epidemiological variables can lead to improved test results and thus assist in the clarification of inconclusive serology screening results. Moreover, all combinations of pairs using the five commercial tests are good alternatives to confirm results.