Asymptotic normality in mixtures of power series distributions

The problem of estimating the individual probabilities of a discrete distribution is considered. The true distribution of the independent observations is a mixture of a family of power series distributions. First, we ensure identifiability of the mixing distribution assuming mild conditions. Next, the mixing distribution is estimated by non-parametric maximum likelihood and an estimator for individual probabilities is obtained from the corresponding marginal mixture density. We establish asymptotic normality for the estimator of individual probabilities by showing that, under certain conditions, the difference between this estimator and the empirical proportions is asymptotically negligible. Our framework includes Poisson, negative binomial and logarithmic series as well as binomial mixture models. Simulations highlight the benefit in achieving normality when using the proposed marginal mixture density approach instead of the empirical one, especially for small sample sizes and/or when interest is in the tail areas. A real data example is given to illustrate the use of the methodology.

Meta-analysis: a unifying meta-likelihood approach framing unobserved heterogeneity, study covariates, publication bias, and study quality

OBJECTIVES: This contribution provides a unifying concept for meta-analysis integrating the handling of unobserved heterogeneity, study covariates, publication bias and study quality. It is important to consider these issues simultaneously to avoid the occurrence of artifacts, and a method for doing so is suggested here. METHODS: The approach is based upon the meta-likelihood in combination with a general linear nonparametric mixed model, which lays the ground for all inferential conclusions suggested here. RESULTS: The concept is illustrated at hand of a meta-analysis investigating the relationship of hormone replacement therapy and breast cancer. The phenomenon of interest has been investigated in many studies for a considerable time and different results were reported. In 1992 a meta-analysis by Sillero-Arenas et al. concluded a small, but significant overall effect of 1.06 on the relative risk scale. Using the meta-likelihood approach it is demonstrated here that this meta-analysis is due to considerable unobserved heterogeneity. Furthermore, it is shown that new methods are available to model this heterogeneity successfully. It is argued further to include available study covariates to explain this heterogeneity in the meta-analysis at hand. CONCLUSIONS: The topic of HRT and breast cancer has again very recently become an issue of public debate, when results of a large trial investigating the health effects of hormone replacement therapy were published indicating an increased risk for breast cancer (risk ratio of 1.26). Using an adequate regression model in the previously published meta-analysis an adjusted estimate of effect of 1.14 can be given which is considerably higher than the one published in the meta-analysis of Sillero-Arenas et al. In summary, it is hoped that the method suggested here contributes further to a good meta-analytic practice in public health and clinical disciplines.

Bayesian decision procedures for binary and continuous bivariate dose-escalation studies

In this paper, Bayesian decision procedures are developed for dose-escalation studies based on binary measures of undesirable events and continuous measures of therapeutic benefit. The methods generalize earlier approaches where undesirable events and therapeutic benefit are both binary. A logistic regression model is used to model the binary responses, while a linear regression model is used to model the continuous responses. Prior distributions for the unknown model parameters are suggested. A gain function is discussed and an optional safety constraint is included. Copyright (C) 2006 John Wiley & Sons, Ltd.

A practical approach to a multi-level analysis with a sparse binary outcome within a large surgical trial

Objectives: To assess the potential source of variation that surgeon may add to patient outcome in a clinical trial of surgical procedures. Methods: Two large (n = 1380) parallel multicentre randomized surgical trials were undertaken to compare laparoscopically assisted hysterectomy with conventional methods of abdominal and vaginal hysterectomy; involving 43 surgeons. The primary end point of the trial was the occurrence of at least one major complication. Patients were nested within surgeons giving the data set a hierarchical structure. A total of 10% of patients had at least one major complication, that is, a sparse binary outcome variable. A linear mixed logistic regression model (with logit link function) was used to model the probability of a major complication, with surgeon fitted as a random effect. Models were fitted using the method of maximum likelihood in SAS((R)). Results: There were many convergence problems. These were resolved using a variety of approaches including; treating all effects as fixed for the initial model building; modelling the variance of a parameter on a logarithmic scale and centring of continuous covariates. The initial model building process indicated no significant 'type of operation' across surgeon interaction effect in either trial, the 'type of operation' term was highly significant in the abdominal trial, and the 'surgeon' term was not significant in either trial. Conclusions: The analysis did not find a surgeon effect but it is difficult to conclude that there was not a difference between surgeons. The statistical test may have lacked sufficient power, the variance estimates were small with large standard errors, indicating that the precision of the variance estimates may be questionable.

Bergmann's rule and body size in mammals

Aim: To describe the geographical pattern of mean body size of the non-volant mammals of the Nearctic and Neotropics and evaluate the influence of five environmental variables that are likely to affect body size gradients. Location: The Western Hemisphere. Methods: We calculated mean body size (average log mass) values in 110 × 110 km cells covering the continental Nearctic and Neotropics. We also generated cell averages for mean annual temperature, range in elevation, their interaction, actual evapotranspiration, and the global vegetation index and its coefficient of variation. Associations between mean body size and environmental variables were tested with simple correlations and ordinary least squares multiple regression, complemented with spatial autocorrelation analyses and split-line regression. We evaluated the relative support for each multiple-regression model using AIC. Results: Mean body size increases to the north in the Nearctic and is negatively correlated with temperature. In contrast, across the Neotropics mammals are largest in the tropical and subtropical lowlands and smaller in the Andes, generating a positive correlation with temperature. Finally, body size and temperature are nonlinearly related in both regions, and split-line linear regression found temperature thresholds marking clear shifts in these relationships (Nearctic 10.9 °C; Neotropics 12.6 °C). The increase in body sizes with decreasing temperature is strongest in the northern Nearctic, whereas a decrease in body size in mountains dominates the body size gradients in the warmer parts of both regions. Main conclusions: We confirm previous work finding strong broad-scale Bergmann trends in cold macroclimates but not in warmer areas. For the latter regions (i.e. the southern Nearctic and the Neotropics), our analyses also suggest that both local and broad-scale patterns of mammal body size variation are influenced in part by the strong mesoscale climatic gradients existing in mountainous areas. A likely explanation is that reduced habitat sizes in mountains limit the presence of larger-sized mammals.

Multivariate analysis of the Fugl-Meyer outcome measures assessing the effectiveness of GENTLE/S robot-mediated stroke therapy

Background: Robot-mediated therapies offer entirely new approaches to neurorehabilitation. In this paper we present the results obtained from trialling the GENTLE/S neurorehabilitation system assessed using the upper limb section of the Fugl-Meyer ( FM) outcome measure. Methods: We demonstrate the design of our clinical trial and its results analysed using a novel statistical approach based on a multivariate analytical model. This paper provides the rational for using multivariate models in robot-mediated clinical trials and draws conclusions from the clinical data gathered during the GENTLE/S study. Results: The FM outcome measures recorded during the baseline ( 8 sessions), robot-mediated therapy ( 9 sessions) and sling-suspension ( 9 sessions) was analysed using a multiple regression model. The results indicate positive but modest recovery trends favouring both interventions used in GENTLE/S clinical trial. The modest recovery shown occurred at a time late after stroke when changes are not clinically anticipated. Conclusion: This study has applied a new method for analysing clinical data obtained from rehabilitation robotics studies. While the data obtained during the clinical trial is of multivariate nature, having multipoint and progressive nature, the multiple regression model used showed great potential for drawing conclusions from this study. An important conclusion to draw from this paper is that this study has shown that the intervention and control phase both caused changes over a period of 9 sessions in comparison to the baseline. This might indicate that use of new challenging and motivational therapies can influence the outcome of therapies at a point when clinical changes are not expected. Further work is required to investigate the effects arising from early intervention, longer exposure and intensity of the therapies. Finally, more function-oriented robot-mediated therapies or sling-suspension therapies are needed to clarify the effects resulting from each intervention for stroke recovery.

Identification of nonlinear systems using generalized kernel models

Nonlinear system identification is considered using a generalized kernel regression model. Unlike the standard kernel model, which employs a fixed common variance for all the kernel regressors, each kernel regressor in the generalized kernel model has an individually tuned diagonal covariance matrix that is determined by maximizing the correlation between the training data and the regressor using a repeated guided random search based on boosting optimization. An efficient construction algorithm based on orthogonal forward regression with leave-one-out (LOO) test statistic and local regularization (LR) is then used to select a parsimonious generalized kernel regression model from the resulting full regression matrix. The proposed modeling algorithm is fully automatic and the user is not required to specify any criterion to terminate the construction procedure. Experimental results involving two real data sets demonstrate the effectiveness of the proposed nonlinear system identification approach.

Processes governing the predictability of the Atlantic meridional overturning circulation in a coupled GCM

The processes that govern the predictability of decadal variations in the North Atlantic meridional overturning circulation (MOC) are investigated in a long control simulation of the ECHO-G coupled atmosphere–ocean model. We elucidate the roles of local stochastic forcing by the atmosphere, and other potential ocean processes, and use our results to build a predictive regression model. The primary influence on MOC variability is found to come from air–sea heat fluxes over the Eastern Labrador Sea. The maximum correlation between such anomalies and the variations in the MOC occurs at a lead time of 2 years, but we demonstrate that the MOC integrates the heat flux variations over a period of 10 years. The corresponding univariate regression model accounts for 74.5% of the interannual variability in the MOC (after the Ekman component has been removed). Dense anomalies to the south of the Greenland-Scotland ridge are also shown to precede the overturning variations by 4–6 years, and provide a second predictor. With the inclusion of this second predictor the resulting regression model explains 82.8% of the total variance of the MOC. This final bivariate model is also tested during large rapid decadal overturning events. The sign of the rapid change is always well represented by the bivariate model, but the magnitude is usually underestimated, suggesting that other processes are also important for these large rapid decadal changes in the MOC.

Designer buildings: an evaluation of the price impacts of signature architects

This study investigates whether commercial offices designed by signature architects in the United States achieve rental premiums compared to commercial offices designed by nonsignature architects. Focusing on buildings designed by winners of the Prizker Prize and the Gold Medal awarded by the American Institute of Architects, we create a sample of commercial office buildings designed by signature architects drawing on CoStar's national database. We use a combination of hedonic regression model and a logit model to estimate the various rent determinants. While the first stage measures the typical rental price differential above the typical building in a particular sub-market over a specific timeframe, the second stage identifies a potential price differential over a set of buildings closely matched on important characteristics (such as age, size, location etc.). We find that in both stages offices design by signature architects exhibit a premium. However these results are preliminary. The premium could be indeed an effect of the name of the architect, but others factors such as micro-market conditions might be the cause. Further tests are needed to confirm the validity of our results.

The dynamics of asset prices and transaction activity in illiquid markets: the case of private commercial real estate

This paper investigates the relationship between capital flows, turnover and returns for the UK private real estate market. We examine a number of possible implication of capital flows and turnover on capital returns testing for evidence of a price pressure effect, ‘return chasing’ behaviour and information revelation. The main tool of analysis is a panel vector autoregressive (VAR) regression model in which institutional capital flows, turnover and returns are specified as endogenous variables in a two equation system in which we also control for macro-economic variables. Data on flows, turnover and returns are obtained for the 10 market segments covering the main UK commercial real estate sectors. Our results do not support the widely-held belief among practitioners that capital flows have a ‘price pressure’ effect. Although there is some evidence of return chasing behaviour, the short timescales involved suggest this finding may be due to delayed recording of flows relative to returns given the difficulties of market entry. We find a significant positive relationship between lagged turnover and contemporaneous capital returns, suggesting that asset turnover provides pricing information.

Dietary, lifestyle and clinico-pathological factors associated with APC mutations and promoter methylation in colorectal cancers from the EPIC-Norfolk Study

The tumour suppressor APC is the most commonly altered gene in colorectal cancer (CRC). Genetic and epigenetic alterations of APC may therefore be associated with dietary and lifestyle risk factors for CRC. Analysis of APC mutations in the extended mutation cluster region (codons 1276-1556) and APC promoter 1A methylation was performed on 185 archival CRC samples collected from participants of the European Prospective Investigation into Cancer (EPIC)-Norfolk Study, with the aim of relating these to high quality seven-day dietary and lifestyle data collected prospectively. Truncating APC mutations (APC+) and promoter 1A methylation (PM+) were identified in 43% and 23% of CRCs analysed, respectively. Distal CRCs were more likely than proximal CRCs to be APC+ or PM+ (P = 0.04). APC+ CRCs were more likely to be moderately/well differentiated and microsatellite stable than APC- CRCs (P = 0.05 and 0.03). APC+ CRC cases consumed more alcohol than their counterparts (P = 0.01) and PM+ CRC cases consumed lower levels of folate and fibre (P = 0.01 and 0.004). APC+ or PM+ CRC cases consumedhigher levels of processed meat and iron from red meat and red meat products (P=0.007 and 0.006). Specifically, CRC cases harbouring GC to AT transition mutations consumed higher levels of processed meat (35 versus 24 g/day, P = 0.04) and iron from red meat and red meat products (0.8 versus 0.6 mg/day, P = 0.05). In a logistic regression model adjusted for age, sex and cigarette smoking status, each 19g/day (1SD) increment increase in processed meat consumption was associated with cases with GC to AT mutations (OR 1.68, 95% CI 1.03-2.75). In conclusion, APC+ and PM+ CRCs may be influenced by diet and GC to AT mutations in APC are associated with processed meat consumption, suggesting a mechanistic link with dietary alkylating agents, such as N-nitroso compounds.

A neurofuzzy classifier for two class problems

A neurofuzzy classifier identification algorithm is introduced for two class problems. The initial fuzzy base construction is based on fuzzy clustering utilizing a Gaussian mixture model (GMM) and the analysis of covariance (ANOVA) decomposition. The expectation maximization (EM) algorithm is applied to determine the parameters of the fuzzy membership functions. Then neurofuzzy model is identified via the supervised subspace orthogonal least square (OLS) algorithm. Finally a logistic regression model is applied to produce the class probability. The effectiveness of the proposed neurofuzzy classifier has been demonstrated using a real data set.

Crossbred cow adoption and milk market participation in a multivariate count data framework

Cross-bred cow adoption is an important and potent policy variable precipitating subsistence household entry into emerging milk markets. This paper focuses on the problem of designing policies that encourage and sustain milkmarket expansion among a sample of subsistence households in the Ethiopian highlands. In this context it is desirable to measure households’ ‘proximity’ to market in terms of the level of deficiency of essential inputs. This problem is compounded by four factors. One is the existence of cross-bred cow numbers (count data) as an important, endogenous decision by the household; second is the lack of a multivariate generalization of the Poisson regression model; third is the censored nature of the milk sales data (sales from non-participating households are, essentially, censored at zero); and fourth is an important simultaneity that exists between the decision to adopt a cross-bred cow, the decision about how much milk to produce, the decision about how much milk to consume and the decision to market that milk which is produced but not consumed internally by the household. Routine application of Gibbs sampling and data augmentation overcome these problems in a relatively straightforward manner. We model the count data from two sites close to Addis Ababa in a latent, categorical-variable setting with known bin boundaries. The single-equation model is then extended to a multivariate system that accommodates the covariance between crossbred-cow adoption, milk-output, and milk-sales equations. The latent-variable procedure proves tractable in extension to the multivariate setting and provides important information for policy formation in emerging-market settings

Centennial-scale climate change in Ireland during the Holocene

We examine mid- to late Holocene centennial-scale climate variability in Ireland using proxy data from peatlands, lakes and a speleothem. A high degree of between-record variability is apparent in the proxy data and significant chronological uncertainties are present. However, tephra layers provide a robust tool for correlation and improve the chronological precision of the records. Although we can find no statistically significant coherence in the dataset as a whole, a selection of high-quality peatland water table reconstructions co-vary more than would be expected by chance alone. A locally weighted regression model with bootstrapping can be used to construct a ‘best-estimate’ palaeoclimatic reconstruction from these datasets. Visual comparison and cross-wavelet analysis of peatland water table compilations from Ireland and Northern Britain show that there are some periods of coherence between these records. Some terrestrial palaeoclimatic changes in Ireland appear to coincide with changes in the North Atlantic thermohaline circulation and solar activity. However, these relationships are inconsistent and may be obscured by chronological uncertainties. We conclude by suggesting an agenda for future Holocene climate research in Ireland.

Equator-to-pole temperature differences and the extra-tropical storm track responses of the CMIP5 climate models

This paper aims to understand the physical processes causing the large spread in the storm track projections of the CMIP5 climate models. In particular, the relationship between the climate change responses of the storm tracks, as measured by the 2–6 day mean sea level pressure variance, and the equator-to-pole temperature differences at upper- and lower-tropospheric levels is investigated. In the southern hemisphere the responses of the upper- and lower-tropospheric temperature differences are correlated across the models and as a result they share similar associations with the storm track responses. There are large regions in which the storm track responses are correlated with the temperature difference responses, and a simple linear regression model based on the temperature differences at either level captures the spatial pattern of the mean storm track response as well explaining between 30 and 60 % of the inter-model variance of the storm track responses. In the northern hemisphere the responses of the two temperature differences are not significantly correlated and their associations with the storm track responses are more complicated. In summer, the responses of the lower-tropospheric temperature differences dominate the inter-model spread of the storm track responses. In winter, the responses of the upper- and lower-temperature differences both play a role. The results suggest that there is potential to reduce the spread in storm track responses by constraining the relative magnitudes of the warming in the tropical and polar regions.