TY - JOUR

T1 - Logistic discrimination of mixtures of M. tuberculosis and non-specific tuberculin reactions

AU - Nagelkerke, Nico J.D.

AU - Borgdorff, Martien W.

AU - Kim, Sang Jae

PY - 2001/4/26

Y1 - 2001/4/26

N2 - Interpretation of the Mantoux test for tuberculous infection can be complicated by cross-reactions caused by infection with non-specific mycobacteria. Thus, the distribution of positive indurations is a mixture of two distributions. To estimate tuberculous infection prevalence, the marginal distribution of indurations needs to be separated into its component distributions. Observations from several populations with different mixes of the two types of infection are required. Homogeneity across populations of distributions of indurations for each type of infection is assumed. A logistic model is specified for the probability of having tuberculous infection conditional on the observed induration size. No other assumptions about the two distributions are made. Maximum likelihood is used to estimate the logistic function. Goodness-of-fit criteria are discussed. The method is applied to a series of tuberculin surveys carried out in (South) Korea. Estimated infection prevalence agrees reasonably well with several ad hoc criteria. The goodness-of-fit test rejects underlying assumptions of homogeneity. One reason appears to be a decline over time in induration sizes caused by tuberculous infection. However, not all reasons for this rejection are obvious. The proposed method of mixture analysis provides an additional tool for the interpretation of prevalence survey data where the diagnostic test lacks specificity as a result of cross-reactions.

AB - Interpretation of the Mantoux test for tuberculous infection can be complicated by cross-reactions caused by infection with non-specific mycobacteria. Thus, the distribution of positive indurations is a mixture of two distributions. To estimate tuberculous infection prevalence, the marginal distribution of indurations needs to be separated into its component distributions. Observations from several populations with different mixes of the two types of infection are required. Homogeneity across populations of distributions of indurations for each type of infection is assumed. A logistic model is specified for the probability of having tuberculous infection conditional on the observed induration size. No other assumptions about the two distributions are made. Maximum likelihood is used to estimate the logistic function. Goodness-of-fit criteria are discussed. The method is applied to a series of tuberculin surveys carried out in (South) Korea. Estimated infection prevalence agrees reasonably well with several ad hoc criteria. The goodness-of-fit test rejects underlying assumptions of homogeneity. One reason appears to be a decline over time in induration sizes caused by tuberculous infection. However, not all reasons for this rejection are obvious. The proposed method of mixture analysis provides an additional tool for the interpretation of prevalence survey data where the diagnostic test lacks specificity as a result of cross-reactions.

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U2 - 10.1002/sim.745

DO - 10.1002/sim.745

M3 - Article

C2 - 11276040

AN - SCOPUS:0035044513

VL - 20

SP - 1113

EP - 1124

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 7

ER -