Denis Heng Yan Leung

In missing data problems, missing not at random is difficult to handle since the response probability or propensity score is confounded with the outcome data model in the likelihood. Existing works often assume the propensity score is known up to a finite dimensional parameter. We relax this assumption and consider an unspecified single index model for the propensity score. A pseudo-likelihood based on the complete data is constructed by profiling out a synthetic distribution function that involves the unknown propensity score. The pseudo-likelihood gives asymptotically normal estimates. Simulations show the method compares favourably with existing methods.

The outbreak of Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) that originated in the city of Wuhan, China has now spread to every inhabitable continent, but now theattention has shifted from China to other epicenters, especially Italy. This study explored the influence of spatial proximities and travel patterns from Italy on the further spread of SARS-CoV-2 around the globe. We showed that as the epicenter changes, the dynamics of SARS-CoV-2 spread change to reflect spatial proximities.

Non-response is a commonly encountered problem in many population-based surveys. Broadly speaking, non-response can be due to refusal or failure to contact the sample units. Although both types of non-response may lead to bias, there is much evidence to indicate that it is much easier to reduce the proportion of non-contacts than to do the same with refusals. In this article, we use data collected from a nationally representative survey under the Demographic and Health Surveys program to study non-response due to refusals to HIV testing in Malawi. We review existing estimation methods and propose novel approaches to the estimation of HIV prevalence that adjust for refusal behaviour. We then explain the data requirement and practical implications of the conventional and proposed approaches. Finally, we provide some general recommendations for handling non-response due to refusals and we highlight the challenges in working with Demographic and Health Surveys and explore different approaches to statistical estimation in the presence of refusals. Our results show that variation in the estimated HIV prevalence across different estimators is due largely to those who already know their HIV test results. In the case of Malawi, variations in the prevalence estimates due to refusals for women are larger than those for men.

Summary: Spatial statistical analyses are often used to study the link between environmental factors and the incidence of diseases. In modelling spatial data, the existence of spatial correlation between observations must be considered. However, in many situations, the exact form of the spatial correlation is unknown. This paper studies environmental factors that might influence the incidence of malaria in Afghanistan. We assume that spatial correlation may be induced by multiple latent sources. Our method is based on a generalized estimating equation of the marginal mean of disease incidence, as a function of the geographical factors and the spatial correlation. Instead of using one set of generalized estimating equations, we embed a series of generalized estimating equations, each reflecting a particular source of spatial correlation, into a larger system of estimating equations. To estimate the spatial correlation parameters, we set up a supplementary set of estimating equations based on the correlation structures that are induced from the various sources. Simultaneous estimation of the mean and correlation parameters is performed by alternating between the two systems of equations.

This paper is motivated by spatio-temporal pattern in the occurrence of Leishmaniasis in Afghanistan and the relatively high number of zero counts. We hold the view that correlations that arise from spatial and temporal sources are inherently distinct. Our method decouples these two sources of correlations, there are at least two advantages in taking this approach. First, it circumvents the need to inverting a large correlation matrix, which is a commonly encountered problem in spatio-temporal analyses. Second, it simplifies the modelling of complex relationships such as anisotropy, which would have been extremely difficult or impossible if spatio-temporal correlations were simultaneously considered. We identify three challenges in the modelling of a spatio-temporal process: (1) accommodation of covariances that arise from spatial and temporal sources; (2) choosing the correct covariance structure and (3) extending to situations where a covariance is not the natural measure of association. Moreover, because the data covers a period that overlaps with the US invasion of Afghanistan, the high number of zero counts may be the result of no disease incidence or lapse of data collection. To resolve this issue, a model truncated at zero built on a foundation of the generalized estimating equations was proposed.

When analyzing data with missing data, a commonly used method is the inverse probability weighting (IPW) method, which reweights estimating equations with propensity scores. The popularity of the IPW method is due to its simplicity. However, it is often being criticized for being inefficient because most of the information from the incomplete observations is not used. Alternatively, the regression method is known to be efficient but is nonrobust to the misspecification of the regression function. In this article, we propose a novel way of optimally combining the propensity score function and the regression model. The resulting estimating equation enjoys the properties of robustness against misspecification of either the propensity score or the regression function, as well as being locally semiparametric efficient. We demonstrate analytically situations where our method leads to a more efficient estimator than some of its competitors. In a simulation study, we show the new method compares favorably with its competitors in finite samples. Supplementary materials for this article are available online.

Malaria and leishmaniasis are among the two most important health problems of many developing countries especially in the Middle East and North Africa. It is common for vector-borne infectious diseases to have similar hotspots which may be attributed to the overlapping ecological distribution of the vector. Hotspot analyses were conducted to simultaneously detect the location of local hotspots and test their statistical significance. Spatial scan statistics were used to detect and test hotspots of malaria and cutaneous leishmaniasis (CL) in Afghanistan in 2009. A multivariate negative binomial model was used to simultaneously assess the effects of environmental variables on malaria and CL. In addition to the dependency between malaria and CL disease counts, spatial and temporal information were also incorporated in the model. Results indicated that malaria and CL incidence peaked at the same periods. Two hotspots were detected for malaria and three for CL. The findings in the current study show an association between the incidence of malaria and CL in the studied areas of Afghanistan. The incidence of CL disease in a given month is linked with the incidence of malaria in the previous month. Co-existence of malaria and CL within the same geographical area was supported by this study, highlighting the presence and effects of environmental variables such as temperature and precipitation. People living in areas with malaria are at increased risk for leishmaniasis infection. Local healthcare authorities should consider the co-infection problem by recommending systematic malaria screening for all CL patients.