A Simultaneous Equation Approach to Estimating HIV Prevalence with Non-Ignorable Missing Responses

Estimates of HIV prevalence are important for policy in order to establish the health status of a country's population and to evaluate the effectiveness of population-based interventions and campaigns. However, participation rates in testing for surveillance conducted as part of household surveys, on which many of these estimates are based, can be low. HIV positive individuals may be less likely to participate because they fear disclosure, in which case estimates obtained using conventional approaches to deal with missing data, such as imputation-based methods, will be biased. We develop a Heckman-type simultaneous equation approach which accounts for non-ignorable selection, but unlike previous implementations, allows for spatial dependence and does not impose a homogeneous selection process on all respondents. In addition, our framework addresses the issue of separation, where for instance some factors are severely unbalanced and highly predictive of the response, which would ordinarily prevent model convergence. Estimation is carried out within a penalized likelihood framework where smoothing is achieved using a parametrization of the smoothing criterion which makes estimation more stable and efficient. We provide the software for straightforward implementation of the proposed approach, and apply our methodology to estimating national and sub-national HIV prevalence in Swaziland, Zimbabwe and Zambia.

Maximum likelihood estimation of higher-order integer-valued autoregressive processes

In this article, we extend the earlier work of Freeland and McCabe [Journal of time Series Analysis (2004) Vol. 25, pp. 701–722] and develop a general framework for maximum likelihood (ML) analysis of higher-order integer-valued autoregressive processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is binomial. A recursive representation of the transition probability of the model is proposed. Based on this transition probability, we derive expressions for the score function and the Fisher information matrix, which form the basis for ML estimation and inference. Similar to the results in Freeland and McCabe (2004), we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. Using the INAR(2) speci?cation with binomial thinning and Poisson innovations, we examine both the asymptotic e?ciency and ?nite sample properties of the ML estimator in relation to the widely used conditional least
squares (CLS) and Yule–Walker (YW) estimators. We conclude that, if the Poisson assumption can be justi?ed, there are substantial gains to be had from using ML especially when the thinning parameters are large.

Maximum likelihood estimation of higher-order integer-valued autoregressive processes

Corrigendum Vol. 30, Issue 2, 259, Article first published online: 15 MAR 2009 to correct the order of authors names: Bu R., K. Hadri, and B. McCabe.

Predicting the likelihood of carrying a BRCA1 or BRCA2 mutation: validation of BOADICEA, BRCAPRO, IBIS, Myriad and the Manchester scoring system using data from UK genetics clinics

Objectives: Genetic testing for the breast and ovarian cancer susceptibility genes BRCA1 and BRCA2 has important implications for the clinical management of people found to carry a mutation. However, genetic testing is expensive and may be associated with adverse psychosocial effects. To provide a cost-efficient and clinically appropriate genetic counselling service, genetic testing should be targeted at those individuals most likely to carry pathogenic mutations. Several algorithms that predict the likelihood of carrying a BRCA1 or a BRCA2 mutation are currently used in clinical practice to identify such individuals.

Predator diversity enhances secondary production and decreases the likelihood of trophic cascades

We manipulated the diversity of top predators in a three trophic level marine food web. The food web included four top benthic marine fish predators (black goby, rock goby, sea scorpion and shore rockling), an intermediate trophic level of small fish, and a lower trophic level of benthic invertebrates. We kept predator density constant and monitored the response of the lower trophic levels. As top predator diversity increased, secondary production increased. We also observed that in the presence of the manipulated fish predators, the density of small gobiid fish (intermediate consumers) was suppressed, releasing certain groups of benthic invertebrates (caprellid amphipods, copepods, nematodes and spirorbid worms) from heavy intermediate predation pressure. We attribute the mechanism responsible for this trophic cascade to a trait-mediated indirect interaction, with the small gobiid fish changing their use of space in response to altered predator diversity. In the absence of top fish predators, a full-blown trophic cascade occurs. Therefore the diversity of predators reduces the likelihood of trophic cascades occurring and hence provides insurance against the loss of an important ecosystem function (i.e. secondary production).

Social support and the likelihood of maintaining and improving levels of physical activity:the Whitehall II Study

Background: Evidence on the association between social support and leisure time physical activity (LTPA) is scarce and mostly based on cross-sectional data with different types of social support collapsed into a single index. The aim of this study was to investigate whether social support from the closest person was associated with LTPA.

Nonresident Father Involvement with Children and Divorced Women's Likelihood of Remarriage

Although remarriage is a relatively common transition, little is known about how nonresident fathers affect divorced mothers’ entry into remarriage. Using the 1979–2010 rounds of the National Longitudinal Study of Youth 1979, the authors examined the likelihood of remarriage for divorced mothers (N = 882) by nonresident father contact with children and payment of child support. The findings suggest that maternal remarriage is positively associated with nonresident father contact but not related to receiving child support.

Nonresident Father Involvement with Children and Divorced Women's Likelihood of Remarriage

Although remarriage is a relatively common transition, we know little about how nonresident fathers affect divorced mothers’ entry into remarriage. Using the 1979-2010 rounds of the National Longitudinal Study of Youth 1979, we examined the likelihood of remarriage for divorced mothers (n=882) by nonresident father contact with children and payment of child support. The findings suggest that maternal remarriage is positively associated with nonresident father contact but not related to receiving child support.

Efficient Marginal Likelihood Computation for Gaussian Process Regression

In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional hyperparameters which need to be tuned in order to achieve optimum predictive performance; this operation can be efficiently performed in an Empirical Bayes fashion by maximizing the posterior marginal likelihood of the observed data. Since the score function of this optimization problem is in general characterized by the presence of local optima, it is necessary to resort to global optimization strategies, which require a large number of function evaluations. Given that the evaluation is usually computationally intensive and badly scaled with respect to the dataset size, the maximum number of observations that can be treated simultaneously is quite limited. In this paper, we consider the case of hyperparameter tuning in Gaussian process regression. A straightforward implementation of the posterior log-likelihood for this model requires O(N^3) operations for every iteration of the optimization procedure, where N is the number of examples in the input dataset. We derive a novel set of identities that allow, after an initial overhead of O(N^3), the evaluation of the score function, as well as the Jacobian and Hessian matrices, in O(N) operations. We prove how the proposed identities, that follow from the eigendecomposition of the kernel matrix, yield a reduction of several orders of magnitude in the computation time for the hyperparameter optimization problem. Notably, the proposed solution provides computational advantages even with respect to state of the art approximations that rely on sparse kernel matrices.

Improving parameter learning of Bayesian nets from incomplete data

This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood estimate. We argue that choosing the maximum log-likelihood estimate (as well as the maximum penalized log-likelihood and the maximum a posteriori estimate) has severe drawbacks, being affected both by overfitting and model uncertainty. Two ideas are discussed to overcome these issues: a maximum entropy approach and a Bayesian model averaging approach. Both ideas can be easily applied on top of EM, while the entropy idea can be also implemented in a more sophisticated way, through a dedicated non-linear solver. A vast set of experiments shows that these ideas produce significantly better estimates and inferences than the traditional and widely used maximum (penalized) log-likelihood and maximum a posteriori estimates. In particular, if EM is adopted as optimization engine, the model averaging approach is the best performing one; its performance is matched by the entropy approach when implemented using the non-linear solver. The results suggest that the applicability of these ideas is immediate (they are easy to implement and to integrate in currently available inference engines) and that they constitute a better way to learn Bayesian network parameters.

An evaluation of portion size estimation aids precision, ease of use and likelihood of future use

OBJECTIVE: The present study aimed to evaluate the precision, ease of use and likelihood of future use of portion size estimation aids (PSEA).

DESIGN: A range of PSEA were used to estimate the serving sizes of a range of commonly eaten foods and rated for ease of use and likelihood of future usage.

SETTING: For each food, participants selected their preferred PSEA from a range of options including: quantities and measures; reference objects; measuring; and indicators on food packets. These PSEA were used to serve out various foods (e.g. liquid, amorphous, and composite dishes). Ease of use and likelihood of future use were noted. The foods were weighed to determine the precision of each PSEA.

SUBJECTS: Males and females aged 18-64 years (n 120).

RESULTS: The quantities and measures were the most precise PSEA (lowest range of weights for estimated portion sizes). However, participants preferred household measures (e.g. 200 ml disposable cup) - deemed easy to use (median rating of 5), likely to use again in future (all scored either 4 or 5 on a scale from 1='not very likely' to 5='very likely to use again') and precise (narrow range of weights for estimated portion sizes). The majority indicated they would most likely use the PSEA preparing a meal (94 %), particularly dinner (86 %) in the home (89 %; all P<0·001) for amorphous grain foods.

CONCLUSIONS: Household measures may be precise, easy to use and acceptable aids for estimating the appropriate portion size of amorphous grain foods.