Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying confidence intervals to multivariate data. In this paper we define confidence intervals for multivariate data that extend the one-dimensional definition in a natural way. In our definition every variable is associated with its own confidence interval as usual, but a data vector can be outside of a few of these, and still be considered to be within the confidence area. We analyze the problem and show that the resulting confidence areas retain the good qualities of their one-dimensional counterparts: they are informative and easy to interpret. Furthermore, we show that the problem of finding multivariate confidence intervals is hard, but provide efficient approximate algorithms to solve the problem.

Even for a medical discipline steeped in a tradition of randomized trials, the evidence basis for only a few guidelines is based on randomized trials (Tricoci et al., 2009). In part this is due to continued development of treatments, in part to enormous expense of clinical trials, and in large part to the hundreds of treatments and their nuances involved in real-world, heterogeneous clinical practice. Thus, many therapeutic decisions are based on observational studies. However, comparative treatment effectiveness studies of observational data suffer from two major problems: only partial overlap of treatments and selection bias. Each treatment is to a degree bounded within constraints of indication and appropriateness. Thus, transplantation is constrained by variables such as age, a mitral valve procedure is constrained by presence of mitral valve regurgitation. However, these boundaries overlap widely, and the same patient may be treated differently by different physicians or different hospitals, often without explicit or evident reasons. Thus, a fundamental hurdle in observational studies evaluating comparative effectiveness of treatment options is to address the resulting selection bias or confounding. Naively evaluating differences in outcomes without doing so leads to biased results and flawed scientific conclusions.

Contingency Tables are good visualization method, with counts, percentiles in your case a 5 x 5 mosaic plot and table of counts, etc. Chi Sq tests use likelihood ratio and Pearson tests for example, but there are numerous options in stat software for analysis of those mosaic plots and their contingency table data. And of course the Nominal Logistic Regression Modeling tools have effects tests (Wald, Likelihood Ratio) for the main effects and interactions of your model. JMP.com or most other stat software tools support this type of data. Pasted below are list of OPTIONS for the Mosaic Plot and its Contingency Table from JMP help file (no detail, just names or tests and analysis options for your consideration). This list is property of JMP.com

All the regression theory developed by statisticians over the last 200 years (related to the general linear model) is useless. Regression can be performed as accurately without statistical models, including the computation of confidence intervals (for estimates, predicted values or regression parameters). The non-statistical approach is also more robust than theory described in all statistics textbooks and taught in all statistical courses. It does not require Map-Reduce when data is really big, nor any matrix inversion, maximum likelihood estimation, or mathematical optimization (Newton algorithm). It is indeed incredibly simple, robust, easy to interpret, and easy to code (no statistical libraries required).

This review examines the applications of electronic noses and tongues in food analysis. A brief history of the development of sensors is included and this is illustrated by descriptions of the different types of sensors utilized in these devices. As pattern recognition techniques are widely used to analyse the data obtained from these multisensor arrays, a discussion of principal components analysis and artificial neural networks is essential. An introduction to the integration of electronic tongues and noses is also incorporated and the strengths and weaknesses of both are described. Applications described include identification and classification of flavour and aroma and other measurements of quality using the electronic nose.

Some colleagues of mine are working with survey responses, and are attempting to predict behaviors with demographic data. So, the plan is to define a dependent variable from some combination of responses to the survey questions, and then use a regression technique to model this dependent variable using other characteristics of the respondents. We all agree on the 5 or so questions that will define the dependent variable, but we disagree on how to specify the definition. I want to look at the actual questions being answered, and create a "score" as a weighted count of the'yeses' to the questions (weights based on how "on point" each question is to the behavior we are trying to define). My colleagues thought that this was too imprecise, and particularly criticised the'intuitive' weight assignment.

Stability is an important aspect of a classification procedure because unstable predictions can potentially reduce users' trust in a classification system and also harm the reproducibility of scientific conclusions. The major goal of our work is to introduce a novel concept of classification instability, i.e., decision boundary instability (DBI), and incorporate it with the generalization error (GE) as a standard for selecting the most accurate and stable classifier. Specifically, we implement a two-stage algorithm: (i) initially select a subset of classifiers whose estimated GEs are not significantly different from the minimal estimated GE among all the candidate classifiers; (ii) the optimal classifier is chosen as the one achieving the minimal DBI among the subset selected in stage (i). This general selection principle applies to both linear and nonlinear classifiers. Large-margin classifiers are used as a prototypical example to illustrate the above idea. Our selection method is shown to be consistent in the sense that the optimal classifier simultaneously achieves the minimal GE and the minimal DBI. Various simulations and real examples further demonstrate the advantage of our method over several alternative approaches.

In rare disease physician targeting, a major challenge is how to identify physicians who are treating diagnosed or underdiagnosed rare diseases patients. Rare diseases have extremely low incidence rate. For a specified rare disease, only a small number of patients are affected and a fractional of physicians are involved. The existing targeting methodologies, such as segmentation and profiling, are developed under mass market assumption. They are not suitable for rare disease market where the target classes are extremely imbalanced. The authors propose a graphical model approach to predict targets by jointly modeling physician and patient features from different data spaces and utilizing the extra relational information. Through an empirical example with medical claim and prescription data, the proposed approach demonstrates better accuracy in finding target physicians. The graph representation also provides visual interpretability of relationship among physicians and patients. The model can be extended to incorporate more complex dependency structures. This article contributes to the literature of exploring the benefit of utilizing relational dependencies among entities in healthcare industry.

We introduce a new dynamical system for sequentially observed multivariate count data. This model is based on the gamma--Poisson construction---a natural choice for count data---and relies on a novel Bayesian nonparametric prior that ties and shrinks the model parameters, thus avoiding overfitting. We present an efficient MCMC inference algorithm that advances recent work on augmentation schemes for inference in negative binomial models. Finally, we demonstrate the model's inductive bias using a variety of real-world data sets, showing that it exhibits superior predictive performance over other models and infers highly interpretable latent structure.

Random forest (RF) missing data algorithms are an attractive approach for dealing with missing data. They have the desirable properties of being able to handle mixed types of missing data, they are adaptive to interactions and nonlinearity, and they have the potential to scale to big data settings. Currently there are many different RF imputation algorithms but relatively little guidance about their efficacy, which motivated us to study their performance. Using a large, diverse collection of data sets, performance of various RF algorithms was assessed under different missing data mechanisms. Algorithms included proximity imputation, on the fly imputation, and imputation utilizing multivariate unsupervised and supervised splitting---the latter class representing a generalization of a new promising imputation algorithm called missForest. Performance of algorithms was assessed by ability to impute data accurately. Our findings reveal RF imputation to be generally robust with performance improving with increasing correlation. Performance was good under moderate to high missingness, and even (in certain cases) when data was missing not at random.