Traditional kinship foster care in northern Ghana: the experiences and views of children, carers and adults in Tamale

Surveys were employed to explore the experiences of children in care and their carers about traditional fostering. They also examined the perspectives of randomly selected adults in the community about the practice of traditional foster care in the Tamale area of northern Ghana. The 74 participants responded to closed- and open-ended interview questions about traditional foster care. Frequencies and thematic grouping of qualitative responses showed that the need to keep family ties alive was the key reason for placement of children with family and kin. Majority of the children expressed satisfaction with living in foster care, even though they had experienced physical and emotional abuse and intimidation. Although most carers were not formally employed and had little personal income, they were positive about having the care role, but faced challenges in providing for many children in a difficult economic situation. The report highlights the role of reciprocity, altruistic and socio-cultural factors in quality of care, and the potential for the traditional kinship foster care to provide suitable avenues of placement for children as recommended by the Ghana child rights law. It also identifies the need for education for carers around children's needs and Ghana's child rights law.     

A joint marginalized multilevel model for longitudinal outcomes

The shared-parameter model and its so-called hierarchical or random-effects extension are widely used joint modeling approaches for a combination of longitudinal continuous, binary, count, missing, and survival outcomes that naturally occurs in many clinical and other studies. A random effect is introduced and shared or allowed to differ between two or more repeated measures or longitudinal outcomes, thereby acting as a vehicle to capture association between the outcomes in these joint models. It is generally known that parameter estimates in a linear mixed model (LMM) for continuous repeated measures or longitudinal outcomes allow for a marginal interpretation, even though a hierarchical formulation is employed. This is not the case for the generalized linear mixed model (GLMM), that is, for non-Gaussian outcomes. The aforementioned joint models formulated for continuous and binary or two longitudinal binomial outcomes, using the LMM and GLMM, will naturally have marginal interpretation for parameters associated with the continuous outcome but a subject-specific interpretation for the fixed effects parameters relating covariates to binary outcomes. To derive marginally meaningful parameters for the binary models in a joint model, we adopt the marginal multilevel model (MMM) due to Heagerty [13] and Heagerty and Zeger [14] and formulate a joint MMM for two longitudinal responses. This enables to (1) capture association between the two responses and (2) obtain parameter estimates that have a population-averaged interpretation for both outcomes. The model is applied to two sets of data. The results are compared with those obtained from the existing approaches such as generalized estimating equations, GLMM, and the model of Heagerty [13]. Estimates were found to be very close to those from single analysis per outcome but the joint model yields higher precision and allows for quantifying the association between outcomes. Parameters were estimated using maximum likelihood. The model is easy to fit using available tools such as the SAS NLMIXED procedure.     

The Combined Model: A Tool for Simulating Correlated Counts with Overdispersion

The combined model as introduced by Molenberghs et al. (2007 Molenberghs, G., Verbeke, G., Demétrio, C. (2007). An extended random-effects approach to modeling repeated, overdispersed count data. Lifetime Data Analysis 13:513–531.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar], 2010 Molenberghs, G., Verbeke, G., Demétrio, C., Vieira, A. (2010). A family of generalized linear models for repeated measures with normal and conjugate random effects. Statistical Science 25:325–347.[Crossref], [Web of Science ®] , [Google Scholar]) has been shown to be an appealing tool for modeling not only correlated or overdispersed data but also for data that exhibit both these features. Unlike techniques available in the literature prior to the combined model, which use a single random-effects vector to capture correlation and/or overdispersion, the combined model allows for the correlation and overdispersion features to be modeled by two sets of random effects. In the context of count data, for example, the combined model naturally reduces to the Poisson-normal model, an instance of the generalized linear mixed model in the absence of overdispersion and it also reduces to the negative-binomial model in the absence of correlation. Here, a Poisson model is specified as the parent distribution of the data conditional on a normally distributed random effect at the subject or cluster level and/or a gamma distribution at observation level. Importantly, the development of the combined model and surrounding derivations have relevance well beyond mere data analysis. It so happens that the combined model can also be used to simulate correlated data. If a researcher is interested in comparing marginal models via Monte Carlo simulations, a necessity to generate suitable correlated count data arises. One option is to induce correlation via random effects but calculation of such quantities as the bias is then not straightforward. Since overdispersion and correlation are simultaneous features of longitudinal count data, the combined model presents an appealing framework for generating data to evaluate statistical properties, through a pre-specification of the desired marginal mean (possibly in terms of the covariates and marginal parameters) and a marginal variance-covariance structure. By comparing the marginal mean and variance of the combined model to the desired or pre-specified marginal mean and variance, respectively, the implied hierarchical parameters and the variance-covariance matrices of the normal and Gamma random effects are then derived from which correlated Poisson data are generated. We explore data generation when a random intercept or random intercept and slope model is specified to induce correlation. The data generator, however, allows for any dimension of the random effects although an increase in the random-effects dimension increases the sensitivity of the derived random effects variance-covariance matrix to deviations from positive-definiteness. A simulation study is carried out for the random-intercept model and for the random intercept and slope model, with or without the normal and Gamma random effects. We also pay specific attention to the case of serial correlation.     

Empirical Bayes estimates for correlated hierarchical data with overdispersion

An extension of the generalized linear mixed model was constructed to simultaneously accommodate overdispersion and hierarchies present in longitudinal or clustered data. This so‐called combined model includes conjugate random effects at observation level for overdispersion and normal random effects at subject level to handle correlation, respectively. A variety of data types can be handled in this way, using different members of the exponential family. Both maximum likelihood and Bayesian estimation for covariate effects and variance components were proposed. The focus of this paper is the development of an estimation procedure for the two sets of random effects. These are necessary when making predictions for future responses or their associated probabilities. Such (empirical) Bayes estimates will also be helpful in model diagnosis, both when checking the fit of the model as well as when investigating outlying observations. The proposed procedure is applied to three datasets of different outcome types. Copyright © 2014 John Wiley & Sons, Ltd.     

A Marginalized Combined Gamma Frailty and Normal Random-effects Model for Repeated,Overdispersed, Time-to-event Outcomes

This article proposes a marginalized model for repeated or otherwise hierarchical, overdispersed time-to-event outcomes, adapting the so-called combined model for time-to-event outcomes of Molenberghs et al. (in press Molenberghs, G., Verbeke, G., Efendi, A., Braekers, R., Demétrio, C. G.B. (in press). A combined gamma frailty and normal random-effects model for repeated, overdispersed time-to-event data. In press. [Google Scholar]), who combined gamma and normal random effects. The two sets of random effects are used to accommodate simultaneously correlation between repeated measures and overdispersion. The proposed version allows for a direct marginal interpretation of all model parameters. The outcomes are allowed to be censored. Two estimation methods are proposed: full likelihood and pairwise likelihood. The proposed model is applied to data from a so-called comet assay and to data from recurrent asthma attacks in children. Both estimation methods perform very well. From simulation results, it follows that the marginalized combined model behaves similarly to the ordinary combined model in terms of point estimation and precision. It is also observed that the pairwise likelihood required more computation time on the one hand but is less sensitive to starting values and stabler in terms of bias with increasing sample size and censoring percentage than full likelihood, on the other, leaving room for both in practice.