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The association between N-terminal pro B-type natriuretic peptide (NT-proBNP) concentrations and in-hospital and 1-year mortality in acute exacerbations of chronic obstructive pulmonary disease (AECOPD) patients is largely unknown. Our objective was to explore the usefulness of NT-proBNP concentrations in AECOPD patients as a prognostic marker for in-hospital and 1-year mortality. NT-proBNP levels were measured in patients upon admission and laboratory and clinical data were also recorded. The cut-point for the NT-proBNP concentration level for in-hospital death was obtained using the receiver operating characteristic (ROC) curve. Univariate and multivariate logistic regression and Cox regression were used in the analyses of factors of in-hospital and 1-year mortality. A total of 429 patients were enrolled. Twenty-nine patients died during hospitalization and 59 patients died during the 1-year follow-up. Patients who died in-hospital compared with those in-hospital survivors were older (80.14±6.56 vs 75.93±9.45 years, p=0.003), had a higher percentage of congestive heart failure (65.52% vs 33.75%, p<0.001), had higher NT-proBNP levels (5767.00 (1372.50-12,887.00) vs 236.25 (80.03-1074.75) ng/L, p<0.001), higher neutrophil counts (10.52±5.82 vs 7.70±4.31, p=0.016), higher D-dimer levels (1231.62±1921.29 vs 490.11±830.19, p=0.048), higher blood urea nitrogen levels (9.91±6.33 vs 6.51±4.01 mmol/L, p=0.001), a lower body mass index (19.49±3.57 vs 22.19±4.76, p=0.003), and higher hemoglobin levels (122.34±25.36 vs 130.57±19.63, p=0.034). The area under the ROC curve (AUC) for NT-proBNP concentration was 0.88 (95% confidence interval [CI], 0.84-0.93). NT-proBNP concentrations ≥551.35 ng/L were an independent prognostic factor for both in-hospital and 1-year mortality after adjustment for relative risk (RR) (RR=29.54, 95% CI 3.04-286.63, p=0.004 for the multivariate logistic regression analysis) and hazard ratio (HR) (HR=4.47, 95% CI, 2.38-8.41, p <0.001 for the multivariate cox regression analysis). NT-proBNP was a strong and independent predictor of in-hospital and 1-year mortality in AECOPD patients.

An investigation into the pollution of stormwater runoff from automobile workshops in Nigeria was performed. Also, multivariate regression was used to predict the pH, oil, and grease (O&G) as well as the electrical conductivity (EC) in relation to the characteristics of the solids and metals pollutants of the untreated automobile workshop stormwater. The results indicated that automobile workshops contributed notable amounts of pollutants to stormwater runoff. Results were compared with Nigerian and USEPA standards. It was found that most of the parameters had mean value ranges far greater than standard limits. The multivariate regression showed variations in the results obtained from different automobile workshops. These variations could be due to the influence of factors such as the volume of automobile servicing activities and the waste generated from these activities that flow in the stormwater runoff. However, the bulk of the EC and pH of the stormwater were associated with the concentrations of the total dissolved solids and copper while the bulk of the O&G concentration was associated with the concentrations of lead and cadmium. It is recommended to treat automobile workshop stormwater to prevent detrimental effects in aquatic systems. Future research is aimed at modeling such treatment using multivariate regression techniques is warranted.

Research summary: In multivariate regression analyses of correlated variables, we sometimes observe pairs of estimated beta coefficients large in absolute magnitude and opposite in sign. T-statistics are also large, suggesting meaningful findings. I found 64 recently published Strategic Management Journal articles with results exhibiting these characteristics. In this article, I demonstrate that such results may be Type 1 errors (false positives): If regressors are correlated via an unobservable common factor, estimated beta coefficients will misleadingly tend toward infinite magnitudes in opposite directions, even if the variables' real effects are small and of the same sign. Diagnostics such as Variance Inflation Factors (VIF) will misleadingly validate Type 1 errors as legitimate results. After establishing general results via mathematical analysis and simulation, I provide guidelines for detection and mitigation. Managerial summary: This article demonstrates mathematically how regression analyses with correlated independent variables may generate beta coefficients of opposite sign to the variables' true effects. To assess the likelihood of this possibility, I propose that: if (a) absolute correlation of two independent variables is about ±0.3 or more (smaller correlations may be problematic for large data sets), (b) the two variables have beta coefficients of opposite sign, if correlated positively, and of the same sign, if correlated negatively, and (c) the bivariate correlation of one independent variable with the dependent variable is of the opposite sign from the beta coefficient, then the beta might be a false positive. To facilitate such analysis, authors should provide complete correlation tables, including dependent variables, interaction terms, and quadratic terms.

Background Targeting the modifiable risk factors may help halt the progression of CKD, thus risk factor analysis is better performed using the parameters in the follow-up. This study aimed to examine the time-dependent risk factors for CKD progression using time-averaged values and to investigate the characteristics of rapid progression group. Methods This is a retrospective cohort study enrolling 770 patients of CKD stage 3–4. Time-dependent parameters were calculated as time-averaged values by a trapezoidal rule. % decline of estimated GFR (eGFR) per year from entry was divided to three groups: <10 % (stable), 10–25 % (moderate progression), and ≥25 % (rapid progression). Multivariate regression analyses were employed for the baseline and the time-averaged datasets. Results eGFR decline was 2.83 ± 4.04 mL/min/1.73 m 2 /year (8.8 ± 12.9 %) in male and 1.66 ± 3.23 mL/min/1.73 m 2 /year (5.4 ± 11.0 %) in female ( p  < 0.001). % decline of eGFR was associated with male, proteinuria, phosphorus, and systolic blood pressure as risk factors and with age, albumin, and hemoglobin as protective factors using either dataset. Baseline eGFR and diabetic nephropathy appeared in the baseline dataset, while uric acid appeared in the time-averaged dataset. The rapid progression group was associated with proteinuria, phosphorus, albumin, and hemoglobin in the follow-up. Conclusion These results suggest that time-averaged values provide insightful clinical guide in targeting the risk factors. Rapid decline of eGFR is strongly associated with hyperphosphatemia, proteinuria, and anemia indicating that these risk factors should be intervened in the follow-up of CKD.

We propose a Bayesian procedure for simultaneous variable and covariance selection using continuous spike-and-slab priors in multivariate linear regression models where q possibly correlated responses are regressed onto p predictors. Rather than relying on a stochastic search through the high-dimensional model space, we develop an ECM algorithm similar to the EMVS procedure of Ročková and George targeting modal estimates of the matrix of regression coefficients and residual precision matrix. Varying the scale of the continuous spike densities facilitates dynamic posterior exploration and allows us to filter out negligible regression coefficients and partial covariances gradually. Our method is seen to substantially outperform regularization competitors on simulated data. We demonstrate our method with a re-examination of data from a recent observational study of the effect of playing high school football on several later-life cognition, psychological, and socio-economic outcomes. An R package, scripts for replicating examples in this article, and results from further simulation studies are provided in the supplementary materials available online.

Allometry refers to the size-related changes of morphological traits and remains an essential concept for the study of evolution and development. This review is the first systematic comparison of allometric methods in the context of geometric morphometrics that considers the structure of morphological spaces and their implications for characterizing allometry and performing size correction. The distinction of two main schools of thought is useful for understanding the differences and relationships between alternative methods for studying allometry. The Gould–Mosimann school defines allometry as the covariation of shape with size. This concept of allometry is implemented in geometric morphometrics through the multivariate regression of shape variables on a measure of size. In the Huxley–Jolicoeur school, allometry is the covariation among morphological features that all contain size information. In this framework, allometric trajectories are characterized by the first principal component, which is a line of best fit to the data points. In geometric morphometrics, this concept is implemented in analyses using either Procrustes form space or conformation space (the latter also known as size-and-shape space). Whereas these spaces differ substantially in their global structure, there are also close connections in their localized geometry. For the model of small isotropic variation of landmark positions, they are equivalent up to scaling. The methods differ in their emphasis and thus provide investigators with flexible tools to address specific questions concerning evolution and development, but all frameworks are logically compatible with each other and therefore unlikely to yield contradictory results.

This paper aims to monitor the ambient level of particulate matter less than 2.5 μm (PM2.5) by learning from multi-weather sensors. Over the past decade, China has established a high-density network of automatic weather stations. In contrast, the number of PM monitors is much smaller than the number of weather stations. Since the haze process is closely related to the variation of meteorological parameters, it is possible and promising to calculate the concentration of PM2.5 by studying the data from weather sensors. Here, we use three machine learning methods, namely multivariate linear regression, multivariate nonlinear regression, and neural network, in order to monitor PM2.5 by exploring the data of multi-weather sensors. The results show that the multivariate linear regression method has the root mean square error (RMSE) of 24.6756 μg/m3 with a correlation coefficient of 0.6281, by referring to the ground truth of PM2.5 time series data; and the multivariate nonlinear regression method has the RMSE of 24.9191 μg/m3 with a correlation coefficient of 0.6184, while the neural network based method has the best performance, of which the RMSE of PM2.5 estimates is 15.6391 μg/m3 with the correlation coefficient of 0.8701.

Multiple imputation is a straightforward method for handling missing data in a principled fashion. This paper presents an overview of multiple imputation, including important theoretical results and their practical implications for generating and using multiple imputations. A review of strategies for generating imputations follows, including recent developments in flexible joint modeling and sequential regression/chained equations/fully conditional specification approaches. Finally, we compare and contrast different methods for generating imputations on a range of criteria before identifying promising avenues for future research.

The reduced-rank regression is an effective method in predicting multiple response variables from the same set of predictor variables. It reduces the number of model parameters and takes advantage of interrelations between the response variables and hence improves predictive accuracy. We propose to select relevant variables for reduced-rank regression by using a sparsity-inducing penalty. We apply a group-lasso type penalty that treats each row of the matrix of the regression coefficients as a group and show that this penalty satisfies certain desirable invariance properties. We develop two numerical algorithms to solve the penalized regression problem and establish the asymptotic consistency of the proposed method. In particular, the manifold structure of the reduced-rank regression coefficient matrix is considered and studied in our theoretical analysis. In our simulation study and real data analysis, the new method is compared with several existing variable selection methods for multivariate regression and exhibits competitive performance in prediction and variable selection.

Background Preoperative anxiety comprising anesthesia and surgery related anxiety is common and perceived by many patients as the worst aspect of the surgical episode. The aim of this study was to identify independent predictors of these three anxieties dimensions and to quantify the relevance of specific fears particularly associated with anesthesia. Methods This study was part of a cross-sectional survey in patients scheduled to undergo elective surgery. Anxiety levels were measured with the Amsterdam Preoperative Anxiety and Information Scale (APAIS). Modified numeric rating scales (mNRS, range 0–10) were used to assess the severity of eight selected specific fears which were predominantly analyzed descriptively. Multivariate stepwise linear regression was applied to determine independent predictors of all three anxiety dimensions (APAIS anxiety subscales). Results 3087 of the 3200 enrolled patients were analyzed. Mean (SD) total preoperative anxiety (APAIS-A-T, range 4–20) was 9.9 (3.6). High anxiety (APAIS-A-T > 10) was reported by 40.5% of subjects. Mean (SD) levels of concern regarding the eight studied specific fears ranged from 3.9 (3.08) concerning “Anesthesiologist error” to 2.4 (2.29) concerning “Fatigue and drowsiness” with an average of 3.2 (2.84) concerning all specific fears. Ranking of all specific fears according to mean mNRS scores was almost identical in patients with high versus those with low anxiety. Among nine independent predictors of anxiety, only 3 variables (female gender, negative and positive anesthetic experience) independently predicted all three APAIS anxiety subscales. Other variables had a selective impact on one or two APAIS anxiety subscales only. Female gender had the strongest impact on all three APAIS anxiety subscales. Adjusted r 2 values of the three models were all below 13%. Conclusions The high variability of importance assigned to all specific fears suggests an individualized approach is advisable when support of anxious patients is intended. Considering independent predictors of anxiety to estimate each patient’s anxiety level is of limited use given the very low predictive capacity of all three models. The clinical benefit of dividing patients into those with high and low anxiety is questionable. Trial registration German Registry of Clinical Trials ( DRKS00016725 ), retrospectively registered.