BIC extensions for order-constrained model selection.

The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC however is not suitable for evaluating models with order constraints on the parameters of interest. This paper explores two extensions of the BIC for evaluating order constrained models, one where a truncated unit information prior is used under the order-constrained model, and the other where a truncated local unit information prior is used. The first prior is centered around the maximum likelihood estimate and the latter prior is centered around a null value. Several analyses show that the order-constrained BIC based on the local unit information prior works better as an Occam's razor for evaluating order-constrained models and results in lower error probabilities. The methodology based on the local unit information prior is implemented in the R package 'BFpack' which allows researchers to easily apply the method for order-constrained model selection. The usefulness of the methodology is illustrated using data from the European Values Study.

Consistency for the tree bootstrap in respondent-driven sampling.

Respondent-driven sampling is an approach for estimating features of populations that are difficult to access using standard survey tools, e.g., the fraction of injection drug users who are HIV positive. Baraff et al. (2016) introduced an approach to estimating uncertainty in population proportion estimates from respondent-driven sampling using the tree bootstrap method. In this paper we establish the consistency of this tree bootstrap approach in the case of [Formula: see text]-trees.

Predicting relapse prior to transplantation in chronic myeloid leukemia by integrating expert knowledge and expression data.

MOTIVATION: Selecting a small number of signature genes for accurate classification of samples is essential for the development of diagnostic tests. However, many genes are highly correlated in gene expression data, and hence, many possible sets of genes are potential classifiers. Because treatment outcomes are poor in advanced chronic myeloid leukemia (CML), we hypothesized that expression of classifiers of advanced phase CML when detected in early CML [chronic phase (CP) CML], correlates with subsequent poorer therapeutic outcome. RESULTS: We developed a method that integrates gene expression data with expert knowledge and predicted functional relationships using iterative Bayesian model averaging. Applying our integrated method to CML, we identified small sets of signature genes that are highly predictive of disease phases and that are more robust and stable than using expression data alone. The accuracy of our algorithm was evaluated using cross-validation on the gene expression data. We then tested the hypothesis that gene sets associated with advanced phase CML would predict relapse after allogeneic transplantation in 176 independent CP CML cases. Our gene signatures of advanced phase CML are predictive of relapse even after adjustment for known risk factors associated with transplant outcomes.

Bayesian melding for estimating uncertainty in national HIV prevalence estimates.

OBJECTIVE: To construct confidence intervals for HIV prevalence in countries with generalised epidemics. METHODS: In the Bayesian melding approach, a sample of country-specific epidemic curves describing HIV prevalence over time is derived based on time series of antenatal clinic prevalence data and general information on the parameters that describe the HIV epidemic. The prevalence trends at antenatal clinics are calibrated to population-based HIV prevalence estimates from national surveys. For countries without population based estimates, a general calibration method is developed. Based on the sample of calibrated epidemic curves, we derive annual 95% confidence intervals for HIV prevalence. The curve that best represents the data at antenatal clinics and population-based surveys, as well as general information about the epidemic, is chosen to represent the best estimates and predictions. RESULTS: We present results for urban areas in Haiti and Namibia to illustrate the estimates and confidence intervals that are derived with the methodology.

Progress and challenges in modelling country-level HIV/AIDS epidemics: the UNAIDS Estimation and Projection Package 2007.

The UNAIDS Estimation and Projection Package (EPP) was developed to aid in country-level estimation and short-term projection of HIV/AIDS epidemics. This paper describes advances reflected in the most recent update of this tool (EPP 2007), and identifies key issues that remain to be addressed in future versions. The major change to EPP 2007 is the addition of uncertainty estimation for generalised epidemics using the technique of Bayesian melding, but many additional changes have been made to improve the user interface and efficiency of the package. This paper describes the interface for uncertainty analysis, changes to the user interface for calibration procedures and other user interface changes to improve EPP's utility in different settings. While formal uncertainty assessment remains an unresolved challenge in low-level and concentrated epidemics, the Bayesian melding approach has been applied to provide analysts in these settings with a visual depiction of the range of models that may be consistent with their data. In fitting the model to countries with longer-running epidemics in sub-Saharan Africa, a number of limitations have been identified in the current model with respect to accommodating behaviour change and accurately replicating certain observed epidemic patterns. This paper discusses these issues along with their implications for future changes to EPP and to the underlying UNAIDS Reference Group model.

Variable selection and Bayesian model averaging in case-control studies.

Covariate and confounder selection in case-control studies is often carried out using a statistical variable selection method, such as a two-step method or a stepwise method in logistic regression. Inference is then carried out conditionally on the selected model, but this ignores the model uncertainty implicit in the variable selection process, and so may underestimate uncertainty about relative risks. We report on a simulation study designed to be similar to actual case-control studies. This shows that p-values computed after variable selection can greatly overstate the strength of conclusions. For example, for our simulated case-control studies with 1000 subjects, of variables declared to be 'significant' with p-values between 0.01 and 0.05, only 49 per cent actually were risk factors when stepwise variable selection was used. We propose Bayesian model averaging as a formal way of taking account of model uncertainty in case-control studies. This yields an easily interpreted summary, the posterior probability that a variable is a risk factor, and our simulation study indicates this to be reasonably well calibrated in the situations simulated. The methods are applied and compared in the context of a case-control study of cervical cancer.

Model-based clustering and data transformations for gene expression data.

MOTIVATION: Clustering is a useful exploratory technique for the analysis of gene expression data. Many different heuristic clustering algorithms have been proposed in this context. Clustering algorithms based on probability models offer a principled alternative to heuristic algorithms. In particular, model-based clustering assumes that the data is generated by a finite mixture of underlying probability distributions such as multivariate normal distributions. The issues of selecting a 'good' clustering method and determining the 'correct' number of clusters are reduced to model selection problems in the probability framework. Gaussian mixture models have been shown to be a powerful tool for clustering in many applications. RESULTS: We benchmarked the performance of model-based clustering on several synthetic and real gene expression data sets for which external evaluation criteria were available. The model-based approach has superior performance on our synthetic data sets, consistently selecting the correct model and the number of clusters. On real expression data, the model-based approach produced clusters of quality comparable to a leading heuristic clustering algorithm, but with the key advantage of suggesting the number of clusters and an appropriate model. We also explored the validity of the Gaussian mixture assumption on different transformations of real data. We also assessed the degree to which these real gene expression data sets fit multivariate Gaussian distributions both before and after subjecting them to commonly used data transformations. Suitably chosen transformations seem to result in reasonable fits. AVAILABILITY: MCLUST is available at http://www.stat.washington.edu/fraley/mclust. The software for the diagonal model is under development. CONTACT: kayee@cs.washington.edu. SUPPLEMENTARY INFORMATION: http://www.cs.washington.edu/homes/kayee/model.

Bayesian information criterion for censored survival models.

We investigate the Bayesian Information Criterion (BIC) for variable selection in models for censored survival data. Kass and Wasserman (1995, Journal of the American Statistical Association 90, 928-934) showed that BIC provides a close approximation to the Bayes factor when a unit-information prior on the parameter space is used. We propose a revision of the penalty term in BIC so that it is defined in terms of the number of uncensored events instead of the number of observations. For a simple censored data model, this revision results in a better approximation to the exact Bayes factor based on a conjugate unit-information prior. In the Cox proportional hazards regression model, we propose defining BIC in terms of the maximized partial likelihood. Using the number of deaths rather than the number of individuals in the BIC penalty term corresponds to a more realistic prior on the parameter space and is shown to improve predictive performance for assessing stroke risk in the Cardiovascular Health Study.

Are births underreported in rural China? Manipulation of statistical records in response to China's population policies.

Under the current family planning policy in China, the criterion for evaluating all parties involved in the birth planning system provides an incentive for everyone to see that the policy is met, either in reality through strict enforcement of family planning regulations, or statistically through manipulation of statistical records. We investigate underreporting of births in four rural counties of northern China, using data from a 1992 sample survey featuring a reproductive history. To clarify the mechanisms of underreporting, we focus on the ways in which reporting errors may affect the distribution of first births by time since marriage. The results of our investigation suggest that in three of the four counties, first-birth intervals are lengthened by underreporting of girl babies and by replacing them with second births reported as first births.

Demand or ideation? Evidence from the Iranian marital fertility decline.

Is the onset of fertility decline caused by structural socioeconomic changes or by the transmission of new ideas? The decline of marital fertility in Iran provides a quasi-experimental setting for addressing this question. Massive economic growth started in 1955; measurable ideational changes took place in 1967. We argue that the decline is described more precisely by demand theory than by ideation theory. It began around 1959, just after the onset of massive economic growth but well before the ideational changes. It paralleled the rapid growth of participation in primary education, and we found no evidence that the 1967 events had any effect on the decline. More than one-quarter of the decline can be attributed to the reduction in child mortality, a key mechanism of demand theory. Several other findings support this main conclusion.

Industrial accidents are produced by social relations of work: a sociological theory of industrial accidents.

Industrial accidents are produced by social relations work. This sociological explanation of accidents differs from the hypotheses on which the majority of modern safety practices are based, which reduce accident causes to unsafe acts and unsafe conditions. Accidents are seen as produced at each of three levels of social relations of work (rewards, command and organisation), and also non-socially at the individual-member level. The resulting hypotheses were tested using data collected according to a semi-experimental design in seven plants in which shift (day/night), shift type (rotating/fixed), technological type and management styles were the factors controlled for. Because of the design, machines, materials and, in most cases, workers were the same across shifts and social relations varied. The sociological theory proved capable of explaining most of the variation in inter-shift differences in accident rates, and, when tested statistically, appeared to have greater explanatory power than competing hypotheses. It is concluded that accidents can be prevented by workers who exercise auto-control at all levels and by management which, in the absence of worker orientations favourable to auto-control, engages in safety management as defined sociologically. A practical consequence for ergonomics is that when plant, equipment and processes are to be modified, an attempt to understand their interaction with the social relations of work should be made. A theoretical consequence is that sociological insights should be incorporated into the perspective of the ergonomics discipline.

Forecasting spore concentrations: a time series approach.

Fungal basidiospores and Cladosporium spores are the two most numerous spore types in the air of Dublin and its surroundings. They are known to have allergenic components, and the aim of the study described here is to develop a predictive model for these spores. A very simple model, which combines an estimated diurnal rhythm with a simple, one-parameter time series model, provided good short-term forecasts. The one-step prediction error variance was reduced by 88% for Cladosporium spores and by 98% for basidiospores.