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While classification is the problem of predicting a discrete class label for an example, regression predictive modeling (or just regression) is the problem of learning the strength of association between independent variables (or features) and continuous dependent variables (or outcomes). A continuous output variable is a real value such as an integer or floating point value often quantified as amounts and sizes.

Regression predictive modeling (or just regression) is the problem of learning the strength of association between independent variables (or features) and continuous dependent variables (or outcomes). Tuning regression algorithms is similar to tuning classification algorithms. That is, we adjust a model’s hyperparameters until we arrive at an optimal solution.

Yellow fever is a vector-borne disease endemic in tropical regions of Africa, where 90% of the global burden occurs, and Latin America. It is notoriously under-reported with uncertainty arising from a complex transmission cycle including a sylvatic reservoir and non-specific symptom set. Resulting estimates of burden, particularly in Africa, are highly uncertain. We examine two established models of yellow fever transmission within a Bayesian model averaging framework in order to assess the relative evidence for each model’s assumptions and to highlight possible data gaps. Our models assume contrasting scenarios of the yellow fever transmission cycle in Africa. The first takes the force of infection in each province to be static across the observation period; this is synonymous with a constant infection pressure from the sylvatic reservoir. The second model assumes the majority of transmission results from the urban cycle; in this case, the force of infection is dynamic and defined through a fixed value of R0 in each province. Both models are coupled to a generalised linear model of yellow fever occurrence which uses environmental covariates to allow us to estimate transmission intensity in areas where data is sparse. We compare these contrasting descriptions of transmission through a Bayesian framework and trans-dimensional Markov chain Monte Carlo sampling in order to assess each model’s evidence given the range of uncertainty in parameter values. The resulting estimates allow us to produce Bayesian model averaged predictions of yellow fever burden across the African endemic region. We find strong support for the static force of infection model which suggests a higher proportion of yellow fever transmission occurs as a result of infection from an external source such as the sylvatic reservoir. However, the model comparison highlights key data gaps in serological surveys across the African endemic region. As such, conclusions concerning the most prevalent transmission routes for yellow fever will be limited by the sparsity of data which is particularly evident in the areas with highest predicted transmission intensity. Our model and estimation approach provides a robust framework for model comparison and predicting yellow fever burden in Africa. However, key data gaps increase uncertainty surrounding estimates of model parameters and evidence. As more mathematical models are developed to address new research questions, it is increasingly important to compare them with established modelling approaches to highlight uncertainty in structures and data., Author summary Yellow fever (YF) is notoriously under reported due to non-specific symptom spectrum and the true burden is highly uncertain as a result of a complex transmission cycle. As such, estimates surrounding YF burden are highly uncertain and the mechanisms behind transmission are often unclear. We assess these mechanisms and the resulting uncertainty by estimating two existing models of YF transmission within a product space framework. This allows us to produce updated estimates of transmission intensity and to compare the relative support for each model given the data. We find strong support for a model assuming a static force of infection, approximating the constant infection pressure from the sylvatic reservoir of YF. We also highlight areas where data is sparse, often the same areas estimated to have especially high transmission intensity. This is the first robust multi-model approach to applied YF modelling and provides a framework that could be extended to other disease models.

Background Performing well-powered randomised controlled trials (RCTs) of new treatments for rare diseases is often infeasible. However, with the increasing availability of historical data, incorporating existing information into trials with small sample sizes is appealing in order to increase the power. Bayesian approaches enable one to incorporate historical data into a trial’s analysis through a prior distribution. Methods Motivated by a RCT intended to evaluate the impact on event-free survival of mifamurtide in patients with osteosarcoma, we performed a simulation study to evaluate the impact on trial operating characteristics of incorporating historical individual control data and aggregate treatment effect estimates. We used power priors derived from historical individual control data for baseline parameters of Weibull and piecewise exponential models, while we used a mixture prior to summarise aggregate information obtained on the relative treatment effect. The impact of prior-data conflicts, both with respect to the parameters and survival models, was evaluated for a set of pre-specified weights assigned to the historical information in the prior distributions. Results The operating characteristics varied according to the weights assigned to each source of historical information, the variance of the informative and vague component of the mixture prior and the level of commensurability between the historical and new data. When historical and new controls follow different survival distributions, we did not observe any advantage of choosing a piecewise exponential model compared to a Weibull model for the new trial analysis. However, we think that it remains appealing given the uncertainty that will often surround the shape of the survival distribution of the new data. Conclusion In the setting of Sarcome-13 trial, and other similar studies in rare diseases, the gains in power and accuracy made possible by incorporating different types of historical information commensurate with the new trial data have to be balanced against the risk of biased estimates and a possible loss in power if data are not commensurate. The weights allocated to the historical data have to be carefully chosen based on this trade-off. Further simulation studies investigating methods for incorporating historical data are required to generalise the findings. Electronic supplementary material The online version of this article (10.1186/s12874-019-0714-z) contains supplementary material, which is available to authorized users.

International audience; The identification of gene-environment interactions in relation to risk of human diseases has been challenging. One difficulty has been that measurement error in the exposure can lead to massive reductions in the power of the test, as well as in bias toward the null in the interaction effect estimates. Leveraging previous work on linear discriminant analysis, we develop a new test of interaction between genetic variants and a continuous exposure that mitigates these detrimental impacts of exposure measurement error in ExG testing by reversing the role of exposure and the diseases status in the fitted model, thus transforming the analysis to standard linear regression. Through simulation studies, we show that the proposed approach is valid in the presence of classical exposure measurement error as well as when there is correlation between the exposure and the genetic variant. Simulations also demonstrated that the reverse test has greater power compared to logistic regression. Finally, we confirmed that our approach eliminates bias from exposure measurement error in estimation. Computing times are reduced by as much as fivefold in this new approach. For illustrative purposes, we applied the new approach to an ExGWAS study of interactions with alcohol and body mass index among 1,145 cases with invasive breast cancer and 1,142 controls from the Cancer Genetic Markers of Susceptibility study.

In a meta-analysis published in BMC Medicine, we explored whether evidence-based medicine can actually be sure that ‘sucrose = sucrose’ in the treatment of depression. This paper, based upon a reductio ad absurdum, addressed an epistemological question using a ‘scientific’ approach, and could be disconcerting as suggested by Cipriani and Geddes’ commentary. However, most papers are based upon a mixture of observations and discussions about sense and meaning. Ultimately, there is nothing more than a story, told with words or numbers. Randomised controlled trials provide information about average patients that do not exist. These results ignores an entire segment of therapeutics that plays a crucial role, namely care. This information is usually set out using a ‘grammar’ that is ambiguous, since statistical tests of hypothesis have raised epistemological questions that are not as yet solved. Moreover, many of these stories remain untold, and unpublished. For these reasons evidence-based medicine is a vehicle for many paradoxes and controversies. Reductio ad absurdum can be useful in precisely this case, to underline how and why the medical literature can sometimes give an impression of absurdity of this sort. Even if the data analysis in our paper was rather rhetorical, we agree that it should comply with the classic standards of reporting and we provide the important extra data that Cipriani and Geddes have requested. Please see related articles: http://www.biomedcentral.com/1741-7015/11/230 and http://www.biomedcentral.com/1741-7015/12/105.

Journal Article; In epidemiologic studies, measurement error in dietary variables often attenuates association between dietary intake and disease occurrence. To adjust for the attenuation caused by error in dietary intake, regression calibration is commonly used. To apply regression calibration, unbiased reference measurements are required. Short-term reference measurements for foods that are not consumed daily contain excess zeroes that pose challenges in the calibration model. We adapted two-part regression calibration model, initially developed for multiple replicates of reference measurements per individual to a single-replicate setting. We showed how to handle excess zero reference measurements by two-step modeling approach, how to explore heteroscedasticity in the consumed amount with variance-mean graph, how to explore nonlinearity with the generalized additive modeling (GAM) and the empirical logit approaches, and how to select covariates in the calibration model. The performance of two-part calibration model was compared with the one-part counterpart. We used vegetable intake and mortality data from European Prospective Investigation on Cancer and Nutrition (EPIC) study. In the EPIC, reference measurements were taken with 24-hour recalls. For each of the three vegetable subgroups assessed separately, correcting for error with an appropriately specified two-part calibration model resulted in about three fold increase in the strength of association with all-cause mortality, as measured by the log hazard ratio. Further found is that the standard way of including covariates in the calibration model can lead to over fitting the two-part calibration model. Moreover, the extent of adjusting for error is influenced by the number and forms of covariates in the calibration model. For episodically consumed foods, we advise researchers to pay special attention to response distribution, nonlinearity, and covariate inclusion in specifying the calibration model. Yes

Quantitative risk assessments of debris flows and other hydrogeological hazards require the analyst to predict damage potentials. A common way to do so is by use of proportional loss functions. In this paper, we analyze a uniquely rich dataset of 132 buildings that were damaged in one of five large debris flow events in Switzerland. Using the double generalized linear model, we estimate proportional loss functions that may be used for various prediction purposes including hazard mapping, landscape planning, and insurance pricing. Unlike earlier analyses, we control for confounding effects of building characteristics, site specifics, and process intensities as well as for overdispersion in the data. Our results suggest that process intensity parameters are the most meaningful predictors of proportional loss sizes. Cross-validation tests suggest that the mean absolute prediction errors of our models are in the range of 11%, underpinning the accurateness of the approach.

International audience; [1] ELF/VLF waves play a crucial role in the dynamics of the radiation belts and are partly responsible for the main losses and the acceleration of energetic electrons. Modeling wave-particle interactions requires detailed information of wave amplitudes and wave normal distribution over L-shells and over magnetic latitudes for different geomagnetic activity conditions. We performed a statistical study of ELF/VLF emissions using wave measurements in the whistler frequency range for 10 years (2001–2010) aboard Cluster spacecraft. We utilized data from the STAFF-SA experiment, which spans the frequency range from 8 Hz to 4 kHz. We present distributions of wave magnetic and electric field amplitudes and wave normal directions as functions of magnetic latitude, magnetic local time, L-shell, and geomagnetic activity. We show that wave normals are directed approximately along the background magnetic field (with the mean value of  — the angle between the wave normal and the background magnetic field, about 10 ı –15 ı) in the vicinity of the geomagnetic equator. The distribution changes with magnetic latitude: Plasmaspheric hiss normal angles increase with latitude to quasi-perpendicular direction at 35 ı –40 ı where hiss can be reflected; lower band chorus are observed as two wave populations: One population of wave normals tends toward the resonance cone and at latitudes of around 35 ı –45 ı wave normals become nearly perpendicular to the magnetic field; the other part remains quasi-parallel at latitudes up to 30 ı. The observed angular distribution is significantly different from Gaussian, and the width of the distribution increases with latitude. Due to the rapid increase of  , the wave mode becomes quasi-electrostatic, and the corresponding electric field increases with latitude and has a maximum near 30 ı. The magnetic field amplitude of the chorus in the day sector has a minimum at the magnetic equator but increases rapidly with latitude with a local maximum near 12 ı –15 ı. The wave magnetic field maximum is observed in the night sector at L > 7 during low geomagnetic activity (at L 5 for K p > 3). Our results confirm the strong dependence of wave amplitude on geomagnetic activity found in earlier studies. (2013), Statistics of whistler-mode waves in the outer radiation belt: Cluster STAFF-SA measurements

We propose a task for eliciting attitudes towards risk that is close to real world risky decisions which typically involve gains and losses. The task consists of accepting or rejecting gambles that provide a gain with probability p and a loss with probability 1 − p. We employ finite mixture models to uncover heterogeneity in risk preferences and find that (i) behavior is heterogeneous, with slightly less than one half of the subjects behaving as expected utility maximizers, (ii) for the others, reference-dependent models perform better than those where subjects derive utility from final outcomes, (iii) models with sign dependent decision weights perform better than those without, and (iv) there is no evidence for loss aversion. The procedure is sufficiently simple so that it can be easily used in field or lab experiments where risk elicitation is not the main experiment.