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Background The nonparametric bootstrap is widely used to measure the branch support of phylogenetic trees. However, bootstrapping is computationally expensive and remains a bottleneck in phylogenetic analyses. Recently, an ultrafast bootstrap approximation (UFBoot) approach was proposed for maximum likelihood analyses. However, such an approach is still missing for maximum parsimony. Results To close this gap we present MPBoot, an adaptation and extension of UFBoot to compute branch supports under the maximum parsimony principle. MPBoot works for both uniform and non-uniform cost matrices. Our analyses on biological DNA and protein showed that under uniform cost matrices, MPBoot runs on average 4.7 (DNA) to 7 times (protein data) (range: 1.2–20.7) faster than the standard parsimony bootstrap implemented in PAUP*; but 1.6 (DNA) to 4.1 times (protein data) slower than the standard bootstrap with a fast search routine in TNT (fast-TNT). However, for non-uniform cost matrices MPBoot is 5 (DNA) to 13 times (protein data) (range:0.3–63.9) faster than fast-TNT. We note that MPBoot achieves better scores more frequently than PAUP* and fast-TNT. However, this effect is less pronounced if an intensive but slower search in TNT is invoked. Moreover, experiments on large-scale simulated data show that while both PAUP* and TNT bootstrap estimates are too conservative, MPBoot bootstrap estimates appear more unbiased. Conclusions MPBoot provides an efficient alternative to the standard maximum parsimony bootstrap procedure. It shows favorable performance in terms of run time, the capability of finding a maximum parsimony tree, and high bootstrap accuracy on simulated as well as empirical data sets. MPBoot is easy-to-use, open-source and available at http://www.cibiv.at/software/mpboot .

Missing data is a common occurrence in mediation analysis. As a result, the methods used to construct confidence intervals around the indirect effect should consider missing data. Previous research has demonstrated that, for the indirect effect in data with complete cases, the Monte Carlo method performs as well as nonparametric bootstrap confidence intervals (see MacKinnon et al., Multivariate Behavioral Research, 39 (1), 99–128, 2004 ; Preacher & Selig, Communication Methods and Measures, 6 (2), 77–98, 2012 ; Tofighi & MacKinnon, Structural Equation Modeling: A Multidisciplinary Journal, 23 (2), 194–205, 2015 ). In this manuscript, we propose a simple, fast, and accurate two-step approach for generating confidence intervals for the indirect effect, in the presence of missing data, based on the Monte Carlo method. In the first step, an appropriate method, for example, full-information maximum likelihood or multiple imputation, is used to estimate the parameters and their corresponding sampling variance-covariance matrix in a mediation model. In the second step, the sampling distribution of the indirect effect is simulated using estimates from the first step. A confidence interval is constructed from the resulting sampling distribution. A simulation study with various conditions is presented. Implications of the results for applied research are discussed.

This study aimed to gain an in-depth understanding of the pulmonary fate of three experimental fluticasone propionate (FP) dry powder inhaler formulations which differed in mass median aerodynamic diameters (MMAD; A-4.5 µm, B-3.8 µm and C-3.7 µm; total single dose: 500 µg). Systemic disposition parameter estimates were obtained from published pharmacokinetic data after intravenous dosing to improve robustness. A biphasic pulmonary absorption model, with mucociliary clearance from the slower absorption compartment, and three systemic disposition compartments was most suitable. Rapid absorption, presumably from peripheral lung, had half-lives of 6.9 to 14.6 min. The peripherally deposited dose (12.6 µg) was significantly smaller for formulation A-4.5 µm than for the other formulations (38.7 and 39.3 µg for B-3.8 µm and C-3.7 µm). The slow absorption half-lives ranged from 6.86 to 9.13 h and were presumably associated with more central lung regions, where mucociliary clearance removed approximately half of the centrally deposited dose. Simulation-estimation studies showed that a biphasic absorption model could be reliably identified and that parameter estimates were unbiased and reasonably precise. Bioequivalence assessment of population pharmacokinetics derived central and peripheral lung doses suggested that formulation A-4.5 µm lacked bioequivalence compared to the other formulations both for central and peripheral doses. In contrast, the other fomulations were bioequivalent. Overall, population pharmacokinetics holds promise to provide important insights into the pulmonary fate of inhalation drugs, which are not available from non-compartmental analysis. This supports the assessment of the pulmonary bioequivalence of fluticasone propionate inhaled formulations through pharmacokinetic approaches, and may be helpful for discussions on evaluating alternatives to clinical endpoint studies.

Gridded data products, for example interpolated daily measurements of precipitation from weather stations, are commonly used as a convenient substitute for direct observations because these products provide a spatially and temporally continuous and complete source of data. However, when the goal is to characterize climatological features of extreme precipitation over a spatial domain (e.g., a map of return values) at the native spatial scales of these phenomena, then gridded products may lead to incorrect conclusions because daily precipitation is a fractal field and hence any smoothing technique will dampen local extremes. To address this issue, we create a new “probabilistic” gridded product specifically designed to characterize the climatological properties of extreme precipitation by applying spatial statistical analysis to daily measurements of precipitation from the Global Historical Climatology Network over the contiguous United States. The essence of our method is to first estimate the climatology of extreme precipitation based on station data and then use a data-driven statistical approach to interpolate these estimates to a fine grid. We argue that our method yields an improved characterization of the climatology within a grid cell because the probabilistic behavior of extreme precipitation is much better behaved (i.e., smoother) than daily weather. Furthermore, the spatial smoothing innate to our approach significantly increases the signal-to-noise ratio in the estimated extreme statistics relative to an analysis without smoothing. Finally, by deriving a data-driven approach for translating extreme statistics to a spatially complete grid, the methodology outlined in this paper resolves the issue of how to properly compare station data with output from earth system models. We conclude the paper by comparing our probabilistic gridded product with a standard extreme value analysis of the Livneh gridded daily precipitation product. Our new data product is freely available on the Harvard Dataverse (https://bit.ly/2CXdnuj).

The availability index is commonly used to measure the availability of a plant or equipment in maintenance management. To control this index, guaranteeing suitable levels of availability, a control chart can be employed. In this paper, it is proposed a bootstrap chart to control the availability index. The proposed chart is based on a nonparametric bootstrap, being distribution-free. The chart is applied in normal data and also in lognormal data with distinct subgroup sizes. Simulations are performed to test the chart in under control and out-of-control second phase situations. The proposed bootstrap chart outperformed the individuals’ chart, detecting shifts more quickly when dealing with out-of-control data from the lognormal distribution. Therefore, the proposed bootstrap chart for the availability index is suitable when dealing with non-normal availability data.

Abstract Prospective economic evaluations conducted alongside clinical trials have become an increasingly popular approach in evaluating the cost-effectiveness of a public health initiative or treatment intervention. These types of economic studies provide improved internal validity and accuracy of cost and effectiveness estimates of health interventions and, compared with simulation or decision-analytic models, have the advantage of jointly observing health and economics outcomes of trial participants. However, missing data due to incomplete response or patient attrition, and sampling uncertainty are common concerns in econometric analysis of clinical trials. Missing data are a particular problem for comparative effectiveness trials of substance use disorder interventions. Multiple imputation and inverse probability weighting are 2 widely recommended methods to address missing data bias, and the nonparametric bootstrap is recommended to address uncertainty in predicted mean cost and effectiveness between trial interventions. Although these methods have been studied extensively by themselves, little is known about how to appropriately combine them and about the potential pitfalls and advantages of different approaches. We provide a review of statistical methods used in 29 economic evaluations of substance use disorder intervention identified from 4 published systematic reviews and a targeted search of the literature. We evaluate how each study addressed missing data bias, whether the recommended nonparametric bootstrap was used, how these 2 methods were combined, and conclude with recommendations for future research.

Fisher–von Mises–Langevin distributions are widely used for modeling directional data. In this paper, the problem of testing homogeneity of mean directions of several Fisher–von Mises–Langevin populations is considered when the concentration parameters are unknown and heterogeneous. First, an adaptive test based on the likelihood ratio statistic is proposed. Critical points are evaluated using a parametric bootstrap. Second, a heuristic test statistic is considered based on pairwise group differences. A nonparametric bootstrap procedure is adapted for evaluating critical points. Finally, a permutation test is also proposed. An extensive simulation study is performed to compare the size and power values of these tests with those proposed earlier. It is observed that both parametric and nonparametric bootstrap based tests achieve size values quite close to the nominal size. Asymptotic tests and permutation tests have size values higher than the nominal size. Bootstrap tests are seen to have very good power performance. The robustness of tests is also studied by considering contamination in Fisher–von Mises–Langevin distributions. R packages are developed for the actual implementation of all tests. A real data set has been considered for illustrations.

Uncertainty of greenhouse gas (GHG) emissions was analyzed using the parametric Monte Carlo simulation (MCS) method and the non-parametric bootstrap method. There was a certain number of observations required of a dataset before GHG emissions reached an asymptotic value. Treating a coefficient (i.e., GHG emission factor) as a random variable did not alter the mean; however, it yielded higher uncertainty of GHG emissions compared to the case when treating a coefficient constant. The non-parametric bootstrap method reduces the variance of GHG. A mathematical model for estimating GHG emissions should treat the GHG emission factor as a random variable. When the estimated probability density function (PDF) of the original dataset is incorrect, the nonparametric bootstrap method, not the parametric MCS method, should be the method of choice for the uncertainty analysis of GHG emissions.

In order to have confidence in model-based phylogenetic analysis, the model of nucleotide substitution adopted must be selected in a statistically rigorous manner. Several model-selection methods are applicable to maximum likelihood (ML) analysis, including the hierarchical likelihood-ratio test (hLRT), Akaike information criterion (AIC), Bayesian information criterion (BIC), and decision theory (DT), but their performance relative to empirical data has not been investigated thoroughly. In this study, we use 250 phylogenetic data sets obtained from TreeBASE to examine the effects that choice in model selection has on ML estimation of phylogeny, with an emphasis on optimal topology, bootstrap support, and hypothesis testing. We show that the use of different methods leads to the selection of two or more models for ∼ 80% of the data sets and that the AIC typically selects more complex models than alternative approaches. Although ML estimation with different best-fit models results in incongruent tree topologies ∼50% of the time, these differences are primarily attributable to alternative resolutions of poorly supported nodes. Furthermore, topologies and bootstrap values estimated with ML using alternative statistically supported models are more similar to each other than to topologies and bootstrap values estimated with ML under the Kimura two-parameter (K2P) model or maximum parsimony (MP). In addition, Swofford-Olsen-Waddell-Hillis (SOWH) tests indicate that ML trees estimated with alternative best-fit models are usually not significantly different from each other when evaluated with the same model. However, ML trees estimated with statistically supported models are often significantly suboptimal to ML trees made with the K2P model when both are evaluated with K2P, indicating that not all models perform in an equivalent manner. Nevertheless, the use of alternative statistically supported models generally does not affect tests of monophyletic relationships under either the Shimodaira-Hasegawa (S-H) or SOWH methods. Our results suggest that although choice in model selection has a strong impact on optimal tree topology, it rarely affects evolutionary inferences drawn from the data because differences are mainly confined to poorly supported nodes. Moreover, since ML with alternative best-fit models tends to produce more similar estimates of phylogeny than ML under the K2P model or MP, the use of any statistically based model-selection method is vastly preferable to forgoing the model-selection process altogether.

Random effects models for hierarchically dependent data, for example, clustered data, are widely used. A popular bootstrap method for such data is the parametric bootstrap based on the same random effects model as that used in inference. However, it is hard to justify this type of bootstrap when this model is known to be an approximation. In this article, we describe a random effect block bootstrap approach for clustered data that is simple to implement, free of both the distribution and the dependence assumptions of the parametric bootstrap, and is consistent when the mixed model assumptions are valid. Results based on Monte Carlo simulation show that the proposed method seems robust to failure of the dependence assumptions of the assumed mixed model. An application to a realistic environmental dataset indicates that the method produces sensible results. Supplementary materials for the article, including the data used for the application, are available online.