A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

Understanding public response to a congestion charge : a random-effects ordered logit approach

Public acceptance is consistently listed as having an enormous impact on the implementation and success of a congestion charge scheme. This paper investigates public acceptance of such a scheme in Australia. Surveys were conducted in Brisbane and Melbourne, the two fastest growing Australian cities. Using an ordered logit modeling approach, the survey data including stated preferences were analyzed to pinpoint the important factors influencing people’s attitudes to a congestion charge and, in turn, to their transport mode choices. To accommodate the nature of, and to account for the resulting heterogeneity of the panel data, random effects were considered in the models. As expected, this study found that the amount of the congestion charge and the financial benefits of implementing it have a significant influence on respondents’ support for the charge and on the likelihood of their taking a bus to city areas. However, respondents’ current primary transport mode for travelling to the city areas has a more pronounced impact. Meanwhile, respondents’ perceptions of the congestion charge’s role in protecting the environment by reducing vehicle emissions, and of the extent to which the charge would mean that they travelled less frequently to the city for shopping or entertainment, also have a significant impact on their level of support for its implementation. We also found and explained notable differences across two cities. Finally, findings from this study have been fully discussed in relation to the literature.

Comparing multilevel and Bayesian spatial random effects survival models to assess geographical inequalities in colorectal cancer survival: a case study

Background Multilevel and spatial models are being increasingly used to obtain substantive information on area-level inequalities in cancer survival. Multilevel models assume independent geographical areas, whereas spatial models explicitly incorporate geographical correlation, often via a conditional autoregressive prior. However the relative merits of these methods for large population-based studies have not been explored. Using a case-study approach, we report on the implications of using multilevel and spatial survival models to study geographical inequalities in all-cause survival. Methods Multilevel discrete-time and Bayesian spatial survival models were used to study geographical inequalities in all-cause survival for a population-based colorectal cancer cohort of 22,727 cases aged 20–84 years diagnosed during 1997–2007 from Queensland, Australia. Results Both approaches were viable on this large dataset, and produced similar estimates of the fixed effects. After adding area-level covariates, the between-area variability in survival using multilevel discrete-time models was no longer significant. Spatial inequalities in survival were also markedly reduced after adjusting for aggregated area-level covariates. Only the multilevel approach however, provided an estimation of the contribution of geographical variation to the total variation in survival between individual patients. Conclusions With little difference observed between the two approaches in the estimation of fixed effects, multilevel models should be favored if there is a clear hierarchical data structure and measuring the independent impact of individual- and area-level effects on survival differences is of primary interest. Bayesian spatial analyses may be preferred if spatial correlation between areas is important and if the priority is to assess small-area variations in survival and map spatial patterns. Both approaches can be readily fitted to geographically enabled survival data from international settings

Modeling random effect and excess zeros in road traffic accident prediction

Poisson distribution has often been used for count like accident data. Negative Binomial (NB) distribution has been adopted in the count data to take care of the over-dispersion problem. However, Poisson and NB distributions are incapable of taking into account some unobserved heterogeneities due to spatial and temporal effects of accident data. To overcome this problem, Random Effect models have been developed. Again another challenge with existing traffic accident prediction models is the distribution of excess zero accident observations in some accident data. Although Zero-Inflated Poisson (ZIP) model is capable of handling the dual-state system in accident data with excess zero observations, it does not accommodate the within-location correlation and between-location correlation heterogeneities which are the basic motivations for the need of the Random Effect models. This paper proposes an effective way of fitting ZIP model with location specific random effects and for model calibration and assessment the Bayesian analysis is recommended.

Systematic review and meta-analysis of the effects of exercise for those with cancer-related lymphedema

Objective: To evaluate the effects of exercise on cancer-related lymphedema and related symptoms, and to determine the need for those with lymphedema to wear compression during exercise. Data Sources: CINAHL, Cochrane, Ebscohost, MEDLINE, Pubmed, ProQuest Health and Medical Complete, ProQuest Nursing and Allied Health Source, Science Direct and SPORTDiscus databases were searched for trials published prior to 1 January, 2015. Study Selection: Randomised and non-randomised, controlled trials, and single group pre-post studies published in English-language were included. Twenty-one (exercise) and four (compression and exercise) studies met inclusion criteria. Data Extraction: Data was extracted into tabular format using predefined data fields by one reviewer and assessed for accuracy by a second reviewer. Study quality was evaluated using the Effective Public Health Practice Project assessment tool. Data Synthesis: Data was pooled using a random effects model to assess the effects of acute and long-term exercise on lymphedema and lymphedema-associated symptoms, with subgroup analyses for exercise mode and intervention length. There was no effect of exercise (acute or intervention) on lymphedema or associated symptoms with standardised mean differences from all analyses ranging between −0.2 and 0.1 (p-values ≥0.22). Findings from subgroup analyses for exercise mode (aerobic, resistance, mixed, other) and intervention duration (>12 weeks or ≤12 weeks) were consistent with these findings; that is, no effect on lymphedema or associated symptoms. There were too few studies evaluating the effect of compression during regular exercise to conduct a meta-analysis. Conclusions: Individuals with secondary lymphedema can safely participate in progressive, regular exercise without experiencing a worsening of lymphedema or related-symptoms. However, the results also do not suggest any improvements will occur in lymphedema. At present, there is insufficient evidence to support or refute the current clinical recommendation to wear compression garments during regular exercise.

Difference-based meta-analytic procedures for between-participant and/or within-participant designs : a tutorial review for sports and exercise scientists

The aim of this paper is to provide a contemporary summary of statistical and non-statistical meta-analytic procedures that have relevance to the type of experimental designs often used by sport scientists when examining differences/change in dependent measure(s) as a result of one or more independent manipulation(s). Using worked examples from studies on observational learning in the motor behaviour literature, we adopt a random effects model and give a detailed explanation of the statistical procedures for the three types of raw score difference-based analyses applicable to between-participant, within-participant, and mixed-participant designs. Major merits and concerns associated with these quantitative procedures are identified and agreed methods are reported for minimizing biased outcomes, such as those for dealing with multiple dependent measures from single studies, design variation across studies, different metrics (i.e. raw scores and difference scores), and variations in sample size. To complement the worked examples, we summarize the general considerations required when conducting and reporting a meta-analysis, including how to deal with publication bias, what information to present regarding the primary studies, and approaches for dealing with outliers. By bringing together these statistical and non-statistical meta-analytic procedures, we provide the tools required to clarify understanding of key concepts and principles.

An analysis of the determinants of job satisfaction when individuals' baseline satisfaction levels may differ.

A growing literature seeks to explain differences in individuals' self-reported satisfaction with their jobs. The evidence so far has mainly been based on cross-sectional data and when panel data have been used, individual unobserved heterogeneity has been modelled as an ordered probit model with random effects. This article makes use of longitudinal data for Denmark, taken from the waves 1995-1999 of the European Community Household Panel, and estimates fixed effects ordered logit models using the estimation methods proposed by Ferrer-i-Carbonel and Frijters (2004) and Das and van Soest (1999). For comparison and testing purposes a random effects ordered probit is also estimated. Estimations are carried out separately on the samples of men and women for individuals' overall satisfaction with the jobs they hold. We find that using the fixed effects approach (that clearly rejects the random effects specification), considerably reduces the number of key explanatory variables. The impact of central economic factors is the same as in previous studies, though. Moreover, the determinants of job satisfaction differ considerably between the genders, in particular once individual fixed effects are allowed for.

Persistence of income inequality : does child mortality matter?

Many developing countries are afflicted by persistent inequality in the distribution of income. While a growing body of literature emphasizes differential fertility as a channel through which income inequality persists, this paper investigates differential child mortality – differences in the incidence of child mortality across socioeconomic groups – as a critical link in this regard. Using evidence from cross-country data to evaluate this linkage, we find that differential child mortality serves as a stronger channel than differential fertility in the transmission of income inequality over time. We use random effects and generalized estimating equations techniques to account for temporal correlation within countries. The results are robust to the use of an alternate definition of fertility that reflects parental preference for children instead of realized fertility.

Empirical Bayes method in the study of traffic safety via heterogeneous negative multinomial model

In the study of traffic safety, expected crash frequencies across sites are generally estimated via the negative binomial model, assuming time invariant safety. Since the time invariant safety assumption may be invalid, Hauer (1997) proposed a modified empirical Bayes (EB) method. Despite the modification, no attempts have been made to examine the generalisable form of the marginal distribution resulting from the modified EB framework. Because the hyper-parameters needed to apply the modified EB method are not readily available, an assessment is lacking on how accurately the modified EB method estimates safety in the presence of the time variant safety and regression-to-the-mean (RTM) effects. This study derives the closed form marginal distribution, and reveals that the marginal distribution in the modified EB method is equivalent to the negative multinomial (NM) distribution, which is essentially the same as the likelihood function used in the random effects Poisson model. As a result, this study shows that the gamma posterior distribution from the multivariate Poisson-gamma mixture can be estimated using the NM model or the random effects Poisson model. This study also shows that the estimation errors from the modified EB method are systematically smaller than those from the comparison group method by simultaneously accounting for the RTM and time variant safety effects. Hence, the modified EB method via the NM model is a generalisable method for estimating safety in the presence of the time variant safety and the RTM effects.

Combining expert opinions in prior elicitation

A method of eliciting prior distributions for Bayesian models using expert knowledge is proposed. Elicitation is a widely studied problem, from a psychological perspective as well as from a statistical perspective. Here, we are interested in combining opinions from more than one expert using an explicitly model-based approach so that we may account for various sources of variation affecting elicited expert opinions. We use a hierarchical model to achieve this. We apply this approach to two problems. The first problem involves a food risk assessment problem involving modelling dose-response for Listeria monocytogenes contamination of mice. The second concerns the time taken by PhD students to submit their thesis in a particular school.

Severity of driver injury and vehicle damage in traffic crashes at intersections: A Bayesian hierarchical analysis

Most crash severity studies ignored severity correlations between driver-vehicle units involved in the same crashes. Models without accounting for these within-crash correlations will result in biased estimates in the factor effects. This study developed a Bayesian hierarchical binomial logistic model to identify the significant factors affecting the severity level of driver injury and vehicle damage in traffic crashes at signalized intersections. Crash data in Singapore were employed to calibrate the model. Model fitness assessment and comparison using Intra-class Correlation Coefficient (ICC) and Deviance Information Criterion (DIC) ensured the suitability of introducing the crash-level random effects. Crashes occurring in peak time, in good street lighting condition, involving pedestrian injuries are associated with a lower severity, while those in night time, at T/Y type intersections, on right-most lane, and installed with red light camera have larger odds of being severe. Moreover, heavy vehicles have a better resistance on severe crash, while crashes involving two-wheel vehicles, young or aged drivers, and the involvement of offending party are more likely to result in severe injuries.

Prevalence of hallux valgus in the general population : a systematic review and meta-analysis

BACKGROUND: Hallux valgus (HV) is a foot deformity commonly seen in medical practice, often accompanied by significant functional disability and foot pain. Despite frequent mention in a diverse body of literature, a precise estimate of the prevalence of HV is difficult to ascertain. The purpose of this systematic review was to investigate prevalence of HV in the overall population and evaluate the influence of age and gender. METHODS: Electronic databases (Medline, Embase, and CINAHL) and reference lists of included papers were searched to June 2009 for papers on HV prevalence without language restriction. MeSH terms and keywords were used relating to HV or bunions, prevalence and various synonyms. Included studies were surveys reporting original data for prevalence of HV or bunions in healthy populations of any age group. Surveys reporting prevalence data grouped with other foot deformities and in specific disease groups (e.g. rheumatoid arthritis, diabetes) were excluded. Two independent investigators quality rated all included papers on the Epidemiological Appraisal Instrument. Data on raw prevalence, population studied and methodology were extracted. Prevalence proportions and the standard error were calculated, and meta-analysis was performed using a random effects model. RESULTS: A total of 78 papers reporting results of 76 surveys (total 496,957 participants) were included and grouped by study population for meta-analysis. Pooled prevalence estimates for HV were 23% in adults aged 18-65 years (CI: 16.3 to 29.6) and 35.7% in elderly people aged over 65 years (CI: 29.5 to 42.0). Prevalence increased with age and was higher in females [30% (CI: 22 to 38)] compared to males [13% (CI: 9 to 17)]. Potential sources of bias were sampling method, study quality and method of HV diagnosis. CONCLUSIONS: Notwithstanding the wide variation in estimates, it is evident that HV is prevalent; more so in females and with increasing age. Methodological quality issues need to be addressed in interpreting reports in the literature and in future research.

Characteristics of foot structure and footwear associated with hallux valgus : a systematic review

Objective Factors associated with the development of hallux valgus (HV) are multifactorial and remain unclear. The objective of this systematic review and meta-analysis was to investigate characteristics of foot structure and footwear associated with HV. Design Electronic databases (Medline, Embase, and CINAHL) were searched to December 2010. Cross-sectional studies with a valid definition of HV and a non-HV comparison group were included. Two independent investigators quality rated all included papers. Effect sizes and 95% confidence intervals (CIs) were calculated (standardized mean differences (SMDs) for continuous data and risk ratios (RRs) for dichotomous data). Where studies were homogeneous, pooling of SMDs was conducted using random effects models. Results A total of 37 papers (34 unique studies) were quality rated. After exclusion of studies without reported measurement reliability for associated factors, data were extracted and analysed from 16 studies reporting results for 45 different factors. Significant factors included: greater first intermetatarsal angle (pooled SMD = 1.5, CI: 0.88–2.1), longer first metatarsal (pooled SMD = 1.0, CI: 0.48–1.6), round first metatarsal head (RR: 3.1–5.4), and lateral sesamoid displacement (RR: 5.1–5.5). Results for clinical factors (e.g., first ray mobility, pes planus, footwear) were less conclusive regarding their association with HV. Conclusions Although conclusions regarding causality cannot be made from cross-sectional studies, this systematic review highlights important factors to monitor in HV assessment and management. Further studies with rigorous methodology are warranted to investigate clinical factors associated with HV.

Spatial modelling of population health screening : the role of accessibility in predicting expected patient flows

This paper describes a generalised linear mixed model (GLMM) approach for understanding spatial patterns of participation in population health screening, in the presence of multiple screening facilities. The models presented have dual focus, namely the prediction of expected patient flows from regions to services and relative rates of participation by region- service combination, with both outputs having meaningful implications for the monitoring of current service uptake and provision. The novelty of this paper lies with the former focus, and an approach for distributing expected participation by region based on proximity to services is proposed. The modelling of relative rates of participation is achieved through the combination of different random effects, as a means of assigning excess participation to different sources. The methodology is applied to participation data collected from a government-funded mammography program in Brisbane, Australia.

A meta-analysis of pigmentary characteristics, sun sensitivity, freckling and melanocytic nevi and risk of basal cell carcinoma of the skin

Objective: To calculate pooled risk estimates of the association between pigmentary characteristics and basal cell carcinoma (BCC) of the skin. Methods: We searched three electronic databases and reviewed the reference lists of the retrieved articles until July 2012 to identify eligible epidemiologic studies. Eligible studies were those published in between 1965 and July 2012 that permitted quantitative assessment of the association between histologically-confirmed BCC and any of the following characteristics: hair colour, eye colour, skin colour, skin phototype, tanning and burning ability, and presence of freckling or melanocytic nevi. We included 29 studies from 2236 initially identified. We calculated summary odds ratios (ORs) using weighted averages of the log OR, using random effects models. Results: We found strongest associations with red hair (OR 2.02; 95% CI: 1.68, 2.44), fair skin colour (OR 2.11; 95% CI: 1.56, 2.86), and having skin that burns and never tans (OR 2.03; 95% CI: 1.73, 2.38). All other factors had weaker but positive associations with BCC, with the exception of freckling of the face in adulthood which showed no association. Conclusions: Although most studies report risk estimates that are in the same direction, there is significant heterogeneity in the size of the estimates. The associations were quite modest and remarkably similar, with ORs between about 1.5 and 2.5 for the highest risk level for each factor. Given the public health impact of BCC, this meta-analysis will make a valuable contribution to our understanding of BCC.