Murine genetic models of obesity: type I error rates and the power of commonly used analyses as assessed by plasmode-based simulation.

BACKGROUND/OBJECTIVES: Genetic contributors to obesity are frequently studied in murine models. However, the sample sizes of these studies are often small, and the data may violate assumptions of common statistical tests, such as normality of distributions. We examined whether, in these cases, type I error rates and power are affected by the choice of statistical test. SUBJECTS/METHODS: We conducted "plasmode"-based simulation using empirical data on body mass (weight) from murine genetic models of obesity. For the type I error simulation, the weight distributions were adjusted to ensure no difference in means between control and mutant groups. For the power simulation, the distributions of the mutant groups were shifted to ensure specific effect sizes. Three to twenty mice were resampled from the empirical distributions to create a plasmode. We then computed type I error rates and power for five common tests on the plasmodes: Student's t test, Welch's t test, Wilcoxon rank sum test (aka, Mann-Whitney U test), permutation test, and bootstrap test. RESULTS: We observed type I error inflation for all tests, except the bootstrap test, with small samples (≤5). Type I error inflation decreased as sample size increased (≥8) but remained. The Wilcoxon test should be avoided because of heterogeneity of distributions. For power, a departure from the reference was observed with small samples for all tests. Compared with the other tests, the bootstrap test had less power with small samples. CONCLUSIONS: Overall, the bootstrap test is recommended for small samples to avoid type I error inflation, but this benefit comes at the cost of lower power. When sample size is large enough, Welch's t test is recommended because of high power with minimal type I error inflation.

Assessment of individual bioequivalence using sufficient bootstrap procedure.

This paper proposes a sufficient bootstrap method, which uses only the unique observations in the resamples, to assess the individual bioequivalence under 2 × 4 randomized crossover design. The finite sample performance of the proposed method is illustrated by extensive Monte Carlo simulations as well as a real-experimental data set, and the results are compared with those obtained by the traditional bootstrap technique. Our records reveal that the proposed method is a good competitor or even better than the classical percentile bootstrap confidence limits.

Robust scalar-on-function partial quantile regression.

Compared with the conditional mean regression-based scalar-on-function regression model, the scalar-on-function quantile regression is robust to outliers in the response variable. However, it is susceptible to outliers in the functional predictor (called leverage points). This is because the influence function of the regression quantiles is bounded in the response variable but unbounded in the predictor space. The leverage points may alter the eigenstructure of the predictor matrix, leading to poor estimation and prediction results. This study proposes a robust procedure to estimate the model parameters in the scalar-on-function quantile regression method and produce reliable predictions in the presence of both outliers and leverage points. The proposed method is based on a functional partial quantile regression procedure. We propose a weighted partial quantile covariance to obtain functional partial quantile components of the scalar-on-function quantile regression model. After the decomposition, the model parameters are estimated via a weighted loss function, where the robustness is obtained by iteratively reweighting the partial quantile components. The estimation and prediction performance of the proposed method is evaluated by a series of Monte-Carlo experiments and an empirical data example. The results are compared favorably with several existing methods. The method is implemented in an R package robfpqr.

Robust bootstrap prediction intervals for univariate and multivariate autoregressive time series models.

The bootstrap procedure has emerged as a general framework to construct prediction intervals for future observations in autoregressive time series models. Such models with outlying data points are standard in real data applications, especially in the field of econometrics. These outlying data points tend to produce high forecast errors, which reduce the forecasting performances of the existing bootstrap prediction intervals calculated based on non-robust estimators. In the univariate and multivariate autoregressive time series, we propose a robust bootstrap algorithm for constructing prediction intervals and forecast regions. The proposed procedure is based on the weighted likelihood estimates and weighted residuals. Its finite sample properties are examined via a series of Monte Carlo studies and two empirical data examples.

Prediction of copper ions adsorption by attapulgite adsorbent using tuned-artificial intelligence model.

Copper (Cu) ion in wastewater is considered as one of the crucial hazardous elements to be quantified. This research is established to predict copper ions adsorption (Ad) by Attapulgite clay from aqueous solutions using computer-aided models. Three artificial intelligent (AI) models are developed for this purpose including Grid optimization-based random forest (Grid-RF), artificial neural network (ANN) and support vector machine (SVM). Principal component analysis (PCA) is used to select model inputs from different variables including the initial concentration of Cu (IC), the dosage of Attapulgite clay (Dose), contact time (CT), pH, and addition of NaNO3 (SN). The ANN model is found to predict Ad with minimum root mean square error (RMSE = 0.9283) and maximum coefficient of determination (R2 = 0.9974) when all the variables (i.e., IC, Dose, CT, pH, SN) were considered as input. The prediction accuracy of Grid-RF model is found similar to ANN model when a few numbers of predictors are used. According to prediction accuracy, the models can be arranged as ANN-M5> Grid-RF-M5> Grid-RF-M4> ANN-M4> SVM-M4> SVM-M5. Overall, the applied statistical analysis of the results indicates that ANN and Grid-RF models can be employed as a computer-aided model for monitoring and simulating the adsorption from aqueous solutions by Attapulgite clay.