Modelling HIV immune response and validation with clinical data

A system of ordinary differential equations is formulated to describe the pathogenesis of HIV infection, wherein certain features that have been shown to be important by recent experimental research are incorporated in the model. These include the role of CD4+memory cells that serve as a major reservoir of latently infected cells, a critical role for T-helper cells in the generation of CD8 memory cells capable of efficient recall response, and stimulation by antigens other than HIV. A stability analysis illustrates the capability of this model in admitting multiple locally asymptotically stable (locally a.s.) off-treatment equilibria. We show that this more biologically detailed model can exhibit the phenomenon of transient viremia experienced by some patients on therapy with viral load levels suppressed below the detection limit. We also show that the loss of CD4+T-cell help in the generation of CD8+memory cells leads to larger peak values for the viral load during transient viremia. Censored clinical data is used to obtain parameter estimates. We demonstrate that using a reduced set of 16 free parameters, obtained by fixing some parameters at their population averages, the model provides reasonable fits to the patient data and, moreover, that it exhibits good predictive capability. We further show that parameter values obtained for most clinical patients do not admit multiple locally a.s off-treatment equilibria. This suggests that treatment to move from a high viral load equilibrium state to an equilibrium state with a lower (or zero) viral load is not possible for these patients.     

Diversity and distribution of reptiles in Romania

The reptile fauna of Romania comprises 23 species, out of which 12 species reach here the limit of their geographic range. We compiled and updated a national database of the reptile species occurrences from a variety of sources including our own field surveys, personal communication from specialists, museum collections and the scientific literature. The occurrence records were georeferenced and stored in a geodatabase for additional analysis of their spatial patterns. The spatial analysis revealed a biased sampling effort concentrated in various protected areas, and deficient in the vast agricultural areas of the southern part of Romania. The patterns of species richness showed a higher number of species in the warmer and drier regions, and a relatively low number of species in the rest of the country. Our database provides a starting point for further analyses, and represents a reliable tool for drafting conservation plans.     

On Testing Equality of Means of Correlated Variates with Incomplete Data

A statistic is proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on one of the variates. Expressions for the second and fourth central moments of the statistic are obtained. These moments are used to approximate the distribution of the statistic by a Student's t distribution under the null hypothesis. The powers of the test are computed and compared with those of the conventional paired t and the other known statistics.     

On Comparing Correlated Means in the Presence of Incomplete Data

Two statistics are proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on both variates. One of the statistics reduces to the one proposed by Bhoj (1978, 1984) when the unpaired observations on the variates are equal. The distributions of the statistics are approximated by well known distributions under the null hypothesis. The empirical powers of the tests are computed and compared with those of some known statistics. The comparison supports the use of one of the statistics proposed in this paper.     

Abalone I: Analyzing Mark-Recapture-Recovery Data Incorporating Growth and Delayed Recovery

Abalone are semimobile marine gastropods that form the basis of Australia's second most valuable fishery. A site off the coast of Port Arthur, Tasmania, was visited on six occasions. On each occasion, any unmarked live abalone found were marked with a unique identification number and were recorded. Any previously marked abalone found had its identification number and whether or not it was still alive recorded. This results in integrated mark-recapture-recovery data, as in Catchpole et al. (1998, Biometrics 54, 33-46). During the study period, abalone grew in size, and we model the survival of individuals as a function of their size, estimated from a fitted growth curve. The shells of dead animals are long lasting, and we extend existing methodology to allow for the possibility that an animal found dead may have been dead but overlooked for several visits.     

Cervical screening in Luxembourg: 1990–1999

For quality assurance purposes, the results of the 1990's obtained by the National Cervical Cancer Screening Programme (NCCSP) launched in 1962 were reviewed. The positive cytodiagnosis, the histologically verified in situ and invasive cervical cancers and the mortality rates were reported.     

Describing Ordinal Odds Ratios for Stratified r × c Tables

For an r × ctable with ordinal responses, odds ratios are commonly used to describe the relationship between the row and column variables. This article shows two types of ordinal odds ratios where local‐global odds ratios are used to compare several groups on a c‐category ordinal response and a global odds ratio is used to measure the global association between a pair of ordinal responses. When there is a stratification factor, we consider Mantel‐Haenszel (MH) type estimators of these odds ratios to summarize the association from several strata. Like the ordinary MH estimator of the common odds ratio for several 2 × 2 contingency tables, the estimators are used when the association is not expected to vary drastically among the strata. Also, the estimators are consistent under the ordinary asymptotic framework in which the number of strata is fixed and also under sparse asymptotics in which the number of strata grows with the sample size. Compared to the maximum likelihood estimators, simulations find that the MH type estimators perform better especially when each stratum has few observations. This article provides variances and covariances formulae for the local‐global odds ratios estimators and applies the bootstrap method to obtain a standard error for the global odds ratio estimator. At the end, we discuss possible ways of testing the homogeneity assumption.