This model links biological and epidemiological data related to heterosexual HIV-1 transmission. The model can be used to estimate transmission of HIV from men with high semen viral burden from inflammation, or reduced burden after antiretroviral therapy. The results offer a biological explanation for the magnitude of the HIV epidemic in places where earlier studies have shown men have high semen viral burden, such as in sub-Saharan Africa. The model can be used to develop and test HIV-1 prevention strategies.

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Estimating the correlation coefficient between two outcome variables is one of the most important aspects of epidemiological and clinical research. A simple Pearson's correlation coefficient method is usually employed when there are complete independent data points for both outcome variables. However, researchers often deal with correlated observations in a longitudinal setting with missing values where a simple Pearson's correlation coefficient method cannot be used. General linear mixed models (GLMM) techniques were used to estimate correlation coefficients in a longitudinal data set with missing values. A random regression mixed model with unstructured covariance matrix was employed to estimate correlation coefficients between concentrations of HIV-1 RNA in blood and seminal plasma. The effects of CD4 count and antiretroviral therapy were also examined. We used data sets from three different centres (650 samples from 238 patients) where blood and seminal plasma HIV-1 RNA concentrations were collected from patients; 137 samples from 90 different patients without antiviral therapy and 513 samples from 148 patients receiving therapy were considered for analysis. We found no significant correlation between blood and semen HIV-1 RNA concentration in the absence of antiviral therapy. However, a moderate correlation between blood and semen HIV-1 RNA was observed among subjects with lower CD4 counts receiving therapy. Our findings confirm and extend the idea that the concentrations of HIV-1 in semen often differ from the HIV-1 concentration in blood. Antiretroviral therapy administered to subjects with low CD4 counts result in sufficient concomitant reduction of HIV-1 in blood and semen so as to improve the correlation between these compartments. These results have important implications for studies related to the sexual transmission of HIV, and development of HIV prevention strategies.

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The paper considers estimation of β γ in the general regression model Y = Xj/Jj + e ^e ~ N(0, σ^Ι)^ where it is suspected that β^ = 0. Empirical Bayes estimators of β^ are proposed which shrink the unrestricted least squares estimator β j to the restricted least squares estimator β γ under the hypothesis HQ: β2 = 0. The empirical Bayes estimators serve as a compromise between β γ and βρ and lean more towards /3j if HQ is true, and towards β γ otherwise. Also these estimators when slightly modified, enjoy both Bayesian and frequentesl risk superiority over the preliminary test estimators. As an application, one may consider factorial experiments where the primary interest is to estimate the main effects, and one shrinks the unrestricted least squares estimators of the main effects towards the restricted least squares estimators under the hypothesis that higher order interactions are not significant.