ESTIMATING WITHIN-HOUSEHOLD CONTACT NETWORKS FROM EGOCENTRIC DATA

Acute respiratory diseases are transmitted over networks of social contacts. Large-scale simulation models are used to predict epidemic dynamics and evaluate the impact of various interventions, but the contact behavior in these models is based on simplistic and strong assumptions which are not informed by survey data. These assumptions are also used for estimating transmission measures such as the basic reproductive number and secondary attack rates. Development of methodology to infer contact networks from survey data could improve these models and estimation methods. We contribute to this area by developing a model of within-household social contacts and using it to analyze the Belgian POLYMOD data set, which contains detailed diaries of social contacts in a 24-hour period. We model dependency in contact behavior through a latent variable indicating which household members are at home. We estimate age-specific probabilities of being at home and age-specific probabilities of contact conditional on two members being at home. Our results differ from the standard random mixing assumption. In addition, we find that the probability that all members contact each other on a given day is fairly low: 0.49 for households with two 0-5 year olds and two 19-35 year olds, and 0.36 for households with two 12-18 year olds and two 36+ year olds. We find higher contact rates in households with 2-3 members, helping explain the higher influenza secondary attack rates found in households of this size.     

ESTIMATING THE NUMBER OF VISITS TO THE DOCTOR

The frequency of doctor consultations has direct consequences for health care budgets, yet little statistical analysis of the determinants of doctor visits has been reported. We consider the distribution of the number of visits to the doctor and, in particular, we model its dependence on a number of demographic factors. Examination of the Australian 1995 National Health Survey data reveals that generalized linear Poisson or negative binomial models are inadequate for modelling the mean as a function of covariates, because of excessive zero counts, and a mean‐variance relationship that varies enormously over covariate values. A negative binomial model is used, with parameter values estimated in subgroups according to the discrete combinations of the covariate values. Smoothing splines are then used to smooth and interpolate the parameter values. In effect the mean and the shape parameters are each modelled as (different) functions of gender, age and geographical factors. The estimated regressions for the mean have simple and intuitive interpretations. However, the dependence of the (negative binomial) shape parameter on the covariates is more difficult to interpret and is subject to influence by extreme observations. We illustrate the use of the model by estimating the distribution of the number of doctor consultations in the Statistical Local Area of Ryde, based on population numbers from the 1996 census.     

ESTIMATING BAYESIAN NETWORKS FOR HIGH‐DIMENSIONAL DATA WITH COMPLEX MEAN STRUCTURE AND RANDOM EFFECTS

The estimation of Bayesian networks given high‐dimensional data, in particular gene expression data, has been the focus of much recent research. Whilst there are several methods available for the estimation of such networks, these typically assume that the data consist of independent and identically distributed samples. It is often the case, however, that the available data have a more complex mean structure, plus additional components of variance, which must then be accounted for in the estimation of a Bayesian network. In this paper, score metrics that take account of such complexities are proposed for use in conjunction with score‐based methods for the estimation of Bayesian networks. We propose first, a fully Bayesian score metric, and second, a metric inspired by the notion of restricted maximum likelihood. We demonstrate the performance of these new metrics for the estimation of Bayesian networks using simulated data with known complex mean structures. We then present the analysis of expression levels of grape‐berry genes adjusting for exogenous variables believed to affect the expression levels of the genes. Demonstrable biological effects can be inferred from the estimated conditional independence relationships and correlations amongst the grape‐berry genes.     

ASYMPTOTIC PROPERTIES OF AN OPTIMAL ESTIMATING FUNCTION APPROACH TO THE ANALYSIS OF MARK RECAPTURE DATA

ABSTRACT

A drawback of non parametric estimators of the size of a closed population in the presence of heterogeneous capture probabilities has been their lack of analytic tractability. Here we show that the martingale estimating function/sample coverage approach to estimating the size of a closed population with heterogeneous capture probabilities is mathematically tractable and develop its large sample properties.     

ESTIMATING PROCESSES OF COUNTS FROM CROSS-SECTIONAL AGGREGATE DATA, WITH AN APPLICATION TO MULTISTATE LIFE TABLES AND HEALTH EXPECTANCIES

This paper discusses the estimation of time‐dependent probabilities of a finite state‐space discrete‐time process using aggregate cross‐sectional data. A large‐sample version of multistate logistic regression is described and shown to be useful for analysing multistate life tables. The technique is applied to the estimation of disability‐free, severely disabled and other disabled survival curves and health expectancies in Australia, based on data from national health surveys in 1988, 1993 and 1998. A conclusion is that there has been a general upward trend in the future time expected to be spent in a state of disability, the picture being more pessimistic for males than females. For example, during 1988‐1998 the estimated increase in male life expectancy at birth of 2.7 years is decomposed as a decrease of 1.2 years in disability‐free health (life) expectancy and increases of 1.3 and 2.6 years, respectively, in states of severe disability and other disability.