Volume 15, Issue 2 - Special issue: Biostatistics in Africa 2019

We propose a truncation model for the abundance distribution in species richness estimation. This model is inherently semiparametric and incorporates an unknown truncation threshold between rare and abundant observations. Using the conditional likelihood, we derive a class of estimators for the parameters in this model by stepwise maximization. The species richness estimator is given by the integer maximizing the binomial likelihood, given all other parameters in the model. Under regularity conditions, we show that our estimators of the model parameters are asymptotically efficient. We recover Chaos lower bound estimator of species richness when the parametric part of the model is single-component Poisson. Thus our class of estimators strictly generalized the latter. We illustrate the performance of the proposed method in a simulation study, and compare it favorably to other widely-used estimators. We also give an application to estimating the number of distinct vocabulary words in French playwright Molière’s Tartuffe.

A number of sophisticated estimators of longitudinal effects have been proposed for estimating the intervention-specific mean outcome. However, there is a relative paucity of research comparing these methods directly to one another. In this study, we compare various approaches to estimating a causal effect in a longitudinal treatment setting using both simulated data and data measured from a human immunodeficiency virus cohort. Six distinct estimators are considered: (i) an iterated conditional expectation representation, (ii) an inverse propensity weighted method, (iii) an augmented inverse propensity weighted method, (iv) a double robust iterated conditional expectation estimator, (v) a modified version of the double robust iterated conditional expectation estimator, and (vi) a targeted minimum loss-based estimator. The details of each estimator and its implementation are presented along with nuisance parameter estimation details, which include potentially pooling the observed data across all subjects regardless of treatment history and using data adaptive machine learning algorithms. Simulations are constructed over six time points, with each time point steadily increasing in positivity violations. Estimation is carried out for both the simulations and applied example using each of the six estimators under both stratified and pooled approaches of nuisance parameter estimation. Simulation results show that double robust estimators remained without meaningful bias as long as at least one of the two nuisance parameters were estimated with a correctly specified model. Under full misspecification, the bias of the double robust estimators remained better than that of the inverse propensity estimator under misspecification, but worse than the iterated conditional expectation estimator. Weighted estimators tended to show better performance than the covariate estimators. As positivity violations increased, the mean squared error and bias of all estimators considered became worse, with covariate-based double robust estimators especially susceptible. Applied analyses showed similar estimates at most time points, with the important exception of the inverse propensity estimator which deviated markedly as positivity violations increased. Given its efficiency, ability to respect the parameter space, and observed performance, we recommend the pooled and weighted targeted minimum loss-based estimator.

Many biomedical or epidemiological studies often aim to assess the association between the time to an event of interest and some covariates under the Cox proportional hazards model. However, a problem is that the covariate data routinely involve measurement error, which may be of classical type, Berkson type or a combination of both types. The issue of Cox regression with error-prone covariates has been well-discussed in the statistical literature, which has focused mainly on classical error so far. This paper considers Cox regression analysis when some covariates are possibly contaminated with a mixture of Berkson and classical errors. We propose a simulation extrapolation-based method to address this problem when two replicates of the mismeasured covariates are available along with calibration data for some subjects in a subsample only. The proposed method places no assumption on the mixture percentage. Its finite-sample performance is assessed through a simulation study. It is applied to the analysis of data from an AIDS clinical trial study.

In tropical regions, populations continue to suffer morbidity and mortality from malaria and arboviral diseases. In Kedougou (Senegal), these illnesses are all endemic due to the climate and its geographical position. The co-circulation of malaria parasites and arboviruses can explain the observation of coinfected cases. Indeed there is strong resemblance in symptoms between these diseases making problematic targeted medical care of coinfected cases. This is due to the fact that the origin of illness is not obviously known. Some cases could be immunized against one or the other of the pathogens, immunity typically acquired with factors like age and exposure as usual for endemic area. Thus, coinfection needs to be better diagnosed. Using data collected from patients in Kedougou region, from 2009 to 2013, we adjusted a multinomial logistic model and selected relevant variables in explaining coinfection status. We observed specific sets of variables explaining each of the diseases exclusively and the coinfection. We tested the independence between arboviral and malaria infections and derived coinfection probabilities from the model fitting. In case of a coinfection probability greater than a threshold value to be calibrated on the data, long duration of illness and age are mostly indicative of arboviral disease while high body temperature and presence of nausea or vomiting symptoms during the rainy season are mostly indicative of malaria disease.

This paper presents two approaches to smoothing time trends in prevalence and estimating the underlying incidence of remissible infections. In the first approach, we use second order segmented polynomials to smooth a curve in a bounded domain. In the second, incidence is modeled instead and the prevalence is reconstructed using the recovery rate which is assumed to be known. In both approaches, the number of knots and their positions are estimated, resulting in non-linear regressions. Akaike Information Criterion is used for model selection. The method is illustrated with Syphilis and Gonorrhea prevalence smoothing and incidence trend estimation in Guinea-Bissau and South Africa, respectively.

In this paper, we provide the ML (Maximum Likelihood) and the REML (REstricted ML) criteria for consistently estimating multivariate linear mixed-effects models with arbitrary correlation structure between the random effects across dimensions, but independent (and possibly heteroscedastic) residuals. By factorizing the random effects covariance matrix, we provide an explicit expression of the profiled deviance through a reparameterization of the model. This strategy can be viewed as the generalization of the estimation procedure used by Douglas Bates and his co-authors in the context of the fitting of one-dimensional linear mixed-effects models. Beside its robustness regarding the starting points, the approach enables a numerically consistent estimate of the random effects covariance matrix while classical alternatives such as the EM algorithm are usually non-consistent. In a simulation study, we compare the estimates obtained from the present method with the EM algorithm-based estimates. We finally apply the method to a study of an immune response to Malaria in Benin.

Biostatistic applications often require to collect and analyze a massive amount of data. Hence, it has become necessary to consider new statistical paradigms that perform well in characterizing complex data. Nonparametric Bayesian methods provide a widely used framework that offers the key advantages of a fully model-based probabilistic framework, while being highly flexible and adaptable. The goal of this paper is to provide a motivation of Bayesian nonparametrics (BNP) through a particular biomedical application, namely Positron Emission Tomography (PET) imaging reconstruction.

We study the asymptotic behavior of multiscale stochastic spatial gene networks. Multiscaling takes into account the difference of abundance between molecules, and captures the dynamic of rare species at a mesoscopic level. We introduce an assumption of spatial correlations for reactions involving rare species and a new law of large numbers is obtained. According to the scales, the whole system splits into two parts with different but coupled dynamics. The high scale component converges to the usual spatial model which is the solution of a partial differential equation, whereas the low scale component converges to the usual homogeneous model which is the solution of an ordinary differential equation. Comparisons are made in the supremum norm.

The development of new ways to probe samples for the three-dimensional (3D) structure of DNA paves the way for in depth and systematic analyses of the genome architecture. 3C-like methods coupled with high-throughput sequencing can now assess physical interactions between pairs of loci in a genome-wide fashion, thus enabling the creation of genome-by-genome contact maps. The spreading of such protocols creates many new opportunities for methodological development: how can we infer 3D models from these contact maps? Can such models help us gain insights into biological processes? Several recent studies applied such protocols to P. falciparum (the deadliest of the five human malaria parasites), assessing its genome organization at different moments of its life cycle. With its small genomic size, fairly simple (yet changing) genomic organization during its lifecyle and strong correlation between chromatin folding and gene expression, this parasite is the ideal case study for applying and developing methods to infer 3D models and use them for downstream analysis. Here, I review a set of methods used to build and analyse three-dimensional models from contact maps data with a special highlight on P. falciparum ’s genome organization.