Deriving confidence intervals for mutation rates across a wide range of evolutionary distances using FracMinHash.

Sketching methods offer computational biologists scalable techniques to analyze data sets that continue to grow in size. MinHash is one such technique to estimate set similarity that has enjoyed recent broad application. However, traditional MinHash has previously been shown to perform poorly when applied to sets of very dissimilar sizes. FracMinHash was recently introduced as a modification of MinHash to compensate for this lack of performance when set sizes differ. This approach has been successfully applied to metagenomic taxonomic profiling in the widely used tool sourmash gather. Although experimental evidence has been encouraging, FracMinHash has not yet been analyzed from a theoretical perspective. In this paper, we perform such an analysis to derive various statistics of FracMinHash, and prove that although FracMinHash is not unbiased (in the sense that its expected value is not equal to the quantity it attempts to estimate), this bias is easily corrected for both the containment and Jaccard index versions. Next, we show how FracMinHash can be used to compute point estimates as well as confidence intervals for evolutionary mutation distance between a pair of sequences by assuming a simple mutation model. We also investigate edge cases in which these analyses may fail to effectively warn the users of FracMinHash indicating the likelihood of such cases. Our analyses show that FracMinHash estimates the containment of a genome in a large metagenome more accurately and more precisely compared with traditional MinHash, and the point estimates and confidence intervals perform significantly better in estimating mutation distances.

Four-Month Rifapentine Regimens with or without Moxifloxacin for Tuberculosis.

BACKGROUND: Rifapentine-based regimens have potent antimycobacterial activity that may allow for a shorter course in patients with drug-susceptible pulmonary tuberculosis. METHODS: In an open-label, phase 3, randomized, controlled trial involving persons with newly diagnosed pulmonary tuberculosis from 13 countries, we compared two 4-month rifapentine-based regimens with a standard 6-month regimen consisting of rifampin, isoniazid, pyrazinamide, and ethambutol (control) using a noninferiority margin of 6.6 percentage points. In one 4-month regimen, rifampin was replaced with rifapentine; in the other, rifampin was replaced with rifapentine and ethambutol with moxifloxacin. The primary efficacy outcome was survival free of tuberculosis at 12 months. RESULTS: Among 2516 participants who had undergone randomization, 2343 had a culture positive for Mycobacterium tuberculosis that was not resistant to isoniazid, rifampin, or fluoroquinolones (microbiologically eligible population; 768 in the control group, 791 in the rifapentine-moxifloxacin group, and 784 in the rifapentine group), of whom 194 were coinfected with human immunodeficiency virus and 1703 had cavitation on chest radiography. A total of 2234 participants could be assessed for the primary outcome (assessable population; 726 in the control group, 756 in the rifapentine-moxifloxacin group, and 752 in the rifapentine group). Rifapentine with moxifloxacin was noninferior to the control in the microbiologically eligible population (15.5% vs. 14.6% had an unfavorable outcome; difference, 1.0 percentage point; 95% confidence interval [CI], -2.6 to 4.5) and in the assessable population (11.6% vs. 9.6%; difference, 2.0 percentage points; 95% CI, -1.1 to 5.1). Noninferiority was shown in the secondary and sensitivity analyses. Rifapentine without moxifloxacin was not shown to be noninferior to the control in either population (17.7% vs. 14.6% with an unfavorable outcome in the microbiologically eligible population; difference, 3.0 percentage points [95% CI, -0.6 to 6.6]; and 14.2% vs. 9.6% in the assessable population; difference, 4.4 percentage points [95% CI, 1.2 to 7.7]). Adverse events of grade 3 or higher occurred during the on-treatment period in 19.3% of participants in the control group, 18.8% in the rifapentine-moxifloxacin group, and 14.3% in the rifapentine group. CONCLUSIONS: The efficacy of a 4-month rifapentine-based regimen containing moxifloxacin was noninferior to the standard 6-month regimen in the treatment of tuberculosis. (Funded by the Centers for Disease Control and Prevention and others; Study 31/A5349 ClinicalTrials.gov number, NCT02410772.).

Multivessel PCI Guided by FFR or Angiography for Myocardial Infarction.

BACKGROUND: In patients with ST-elevation myocardial infarction (STEMI) who have multivessel disease, percutaneous coronary intervention (PCI) for nonculprit lesions (complete revascularization) is superior to treatment of the culprit lesion alone. However, whether complete revascularization that is guided by fractional flow reserve (FFR) is superior to an angiography-guided procedure is unclear. METHODS: In this multicenter trial, we randomly assigned patients with STEMI and multivessel disease who had undergone successful PCI of the infarct-related artery to receive complete revascularization guided by either FFR or angiography. The primary outcome was a composite of death from any cause, nonfatal myocardial infarction, or unplanned hospitalization leading to urgent revascularization at 1 year. RESULTS: The mean (±SD) number of stents that were placed per patient for nonculprit lesions was 1.01±0.99 in the FFR-guided group and 1.50±0.86 in the angiography-guided group. During follow-up, a primary outcome event occurred in 32 of 586 patients (5.5%) in the FFR-guided group and in 24 of 577 patients (4.2%) in the angiography-guided group (hazard ratio, 1.32; 95% confidence interval, 0.78 to 2.23; P = 0.31). Death occurred in 9 patients (1.5%) in the FFR-guided group and in 10 (1.7%) in the angiography-guided group; nonfatal myocardial infarction in 18 (3.1%) and 10 (1.7%), respectively; and unplanned hospitalization leading to urgent revascularization in 15 (2.6%) and 11 (1.9%), respectively. CONCLUSIONS: In patients with STEMI undergoing complete revascularization, an FFR-guided strategy did not have a significant benefit over an angiography-guided strategy with respect to the risk of death, myocardial infarction, or urgent revascularization at 1 year. However, given the wide confidence intervals for the estimate of effect, the findings do not allow for a conclusive interpretation. (Funded by the French Ministry of Health and Abbott; FLOWER-MI ClinicalTrials.gov number, NCT02943954.).

Endovascular Therapy for Stroke Due to Basilar-Artery Occlusion.

BACKGROUND: The effectiveness of endovascular therapy in patients with stroke caused by basilar-artery occlusion has not been well studied. METHODS: We randomly assigned patients within 6 hours after the estimated time of onset of a stroke due to basilar-artery occlusion, in a 1:1 ratio, to receive endovascular therapy or standard medical care. The primary outcome was a favorable functional outcome, defined as a score of 0 to 3 on the modified Rankin scale (range, 0 to 6, with 0 indicating no disability, 3 indicating moderate disability, and 6 indicating death) at 90 days. The primary safety outcomes were symptomatic intracranial hemorrhage within 3 days after the initiation of treatment and mortality at 90 days. RESULTS: A total of 300 patients were enrolled (154 in the endovascular therapy group and 146 in the medical care group). Intravenous thrombolysis was used in 78.6% of the patients in the endovascular group and in 79.5% of those in the medical group. Endovascular treatment was initiated at a median of 4.4 hours after stroke onset. A favorable functional outcome occurred in 68 of 154 patients (44.2%) in the endovascular group and 55 of 146 patients (37.7%) in the medical care group (risk ratio, 1.18; 95% confidence interval [CI], 0.92 to 1.50). Symptomatic intracranial hemorrhage occurred in 4.5% of the patients after endovascular therapy and in 0.7% of those after medical therapy (risk ratio, 6.9; 95% CI, 0.9 to 53.0); mortality at 90 days was 38.3% and 43.2%, respectively (risk ratio, 0.87; 95% CI, 0.68 to 1.12). CONCLUSIONS: Among patients with stroke from basilar-artery occlusion, endovascular therapy and medical therapy did not differ significantly with respect to a favorable functional outcome, but, as reflected by the wide confidence interval for the primary outcome, the results of this trial may not exclude a substantial benefit of endovascular therapy. Larger trials are needed to determine the efficacy and safety of endovascular therapy for basilar-artery occlusion. (Funded by the Dutch Heart Foundation and others; BASICS ClinicalTrials.gov number, NCT01717755; Netherlands Trial Register number, NL2500.).

Treatment of Multisystem Inflammatory Syndrome in Children.

BACKGROUND: Evidence is urgently needed to support treatment decisions for children with multisystem inflammatory syndrome (MIS-C) associated with severe acute respiratory syndrome coronavirus 2. METHODS: We performed an international observational cohort study of clinical and outcome data regarding suspected MIS-C that had been uploaded by physicians onto a Web-based database. We used inverse-probability weighting and generalized linear models to evaluate intravenous immune globulin (IVIG) as a reference, as compared with IVIG plus glucocorticoids and glucocorticoids alone. There were two primary outcomes: the first was a composite of inotropic support or mechanical ventilation by day 2 or later or death; the second was a reduction in disease severity on an ordinal scale by day 2. Secondary outcomes included treatment escalation and the time until a reduction in organ failure and inflammation. RESULTS: Data were available regarding the course of treatment for 614 children from 32 countries from June 2020 through February 2021; 490 met the World Health Organization criteria for MIS-C. Of the 614 children with suspected MIS-C, 246 received primary treatment with IVIG alone, 208 with IVIG plus glucocorticoids, and 99 with glucocorticoids alone; 22 children received other treatment combinations, including biologic agents, and 39 received no immunomodulatory therapy. Receipt of inotropic or ventilatory support or death occurred in 56 patients who received IVIG plus glucocorticoids (adjusted odds ratio for the comparison with IVIG alone, 0.77; 95% confidence interval [CI], 0.33 to 1.82) and in 17 patients who received glucocorticoids alone (adjusted odds ratio, 0.54; 95% CI, 0.22 to 1.33). The adjusted odds ratios for a reduction in disease severity were similar in the two groups, as compared with IVIG alone (0.90 for IVIG plus glucocorticoids and 0.93 for glucocorticoids alone). The time until a reduction in disease severity was similar in the three groups. CONCLUSIONS: We found no evidence that recovery from MIS-C differed after primary treatment with IVIG alone, IVIG plus glucocorticoids, or glucocorticoids alone, although significant differences may emerge as more data accrue. (Funded by the European Union's Horizon 2020 Program and others; BATS ISRCTN number, ISRCTN69546370.).

Exact confidence intervals for population growth rate, longevity and generation time.

By quantifying key life history parameters in populations, such as growth rate, longevity, and generation time, researchers and administrators can obtain valuable insights into its dynamics. Although point estimates of demographic parameters have been available since the inception of demography as a scientific discipline, the construction of confidence intervals has typically relied on approximations through series expansions or computationally intensive techniques. This study introduces the first mathematical expression for calculating confidence intervals for the aforementioned life history traits when individuals are unidentifiable and data are presented as a life table. The key finding is the accurate estimation of the confidence interval for r, the instantaneous growth rate, which is tested using Monte Carlo simulations with four arbitrary discrete distributions. In comparison to the bootstrap method, the proposed interval construction method proves more efficient, particularly for experiments with a total offspring size below 400. We discuss handling cases where data are organized in extended life tables or as a matrix of vital rates. We have developed and provided accompanying code to facilitate these computations.

On exact randomization-based covariate-adjusted confidence intervals.

Randomization-based inference using the Fisher randomization test allows for the computation of Fisher-exact P-values, making it an attractive option for the analysis of small, randomized experiments with non-normal outcomes. Two common test statistics used to perform Fisher randomization tests are the difference-in-means between the treatment and control groups and the covariate-adjusted version of the difference-in-means using analysis of covariance. Modern computing allows for fast computation of the Fisher-exact P-value, but confidence intervals have typically been obtained by inverting the Fisher randomization test over a range of possible effect sizes. The test inversion procedure is computationally expensive, limiting the usage of randomization-based inference in applied work. A recent paper by Zhu and Liu developed a closed form expression for the randomization-based confidence interval using the difference-in-means statistic. We develop an important extension of Zhu and Liu to obtain a closed form expression for the randomization-based covariate-adjusted confidence interval and give practitioners a sufficiency condition that can be checked using observed data and that guarantees that these confidence intervals have correct coverage. Simulations show that our procedure generates randomization-based covariate-adjusted confidence intervals that are robust to non-normality and that can be calculated in nearly the same time as it takes to calculate the Fisher-exact P-value, thus removing the computational barrier to performing randomization-based inference when adjusting for covariates. We also demonstrate our method on a re-analysis of phase I clinical trial data.

Cutoff estimation and construction of their confidence intervals for continuous biomarkers under ternary umbrella and tree stochastic ordering settings.

Tuberculosis (TB) studies often involve four different states under consideration, namely, "healthy," "latent infection," "pulmonary active disease," and "extra-pulmonary active disease." While highly accurate clinical diagnosis tests do exist, they are expensive and generally not accessible in regions where they are most needed; thus, there is an interest in assessing the accuracy of new and easily obtainable biomarkers. For some such biomarkers, the typical stochastic ordering assumption might not be justified for all disease classes under study, and usual ROC methodologies that involve ROC surfaces and hypersurfaces are inadequate. Different types of orderings may be appropriate depending on the setting, and these may involve a number of ambiguously ordered groups that stochastically exhibit larger (or lower) marker scores than the remaining groups. Recently, there has been scientific interest on ROC methods that can accommodate these so-called "tree" or "umbrella" orderings. However, there is limited work discussing the estimation of cutoffs in such settings. In this article, we discuss the estimation and inference around optimized cutoffs when accounting for such configurations. We explore different cutoff alternatives and provide parametric, flexible parametric, and non-parametric kernel-based approaches for estimation and inference. We evaluate our approaches using simulations and illustrate them through a real data set that involves TB patients.

Point estimation, confidence intervals, and P-values for optimal adaptive two-stage designs with normal endpoints.

Due to the dependency structure in the sampling process, adaptive trial designs create challenges in point and interval estimation and in the calculation of P-values. Optimal adaptive designs, which are designs where the parameters governing the adaptivity are chosen to maximize some performance criterion, suffer from the same problem. Various analysis methods which are able to handle this dependency structure have already been developed. In this work, we aim to give a comprehensive summary of these methods and show how they can be applied to the class of designs with planned adaptivity, of which optimal adaptive designs are an important member. The defining feature of these kinds of designs is that the adaptive elements are completely prespecified. This allows for explicit descriptions of the calculations involved, which makes it possible to evaluate different methods in a fast and accurate manner. We will explain how to do so, and present an extensive comparison of the performance characteristics of various estimators between an optimal adaptive design and its group-sequential counterpart.

A nonparametric relative treatment effect for direct comparisons of censored paired survival outcomes.

A frequently addressed issue in clinical trials is the comparison of censored paired survival outcomes, for example, when individuals were matched based on their characteristics prior to the analysis. In this regard, a proper incorporation of the dependence structure of the paired censored outcomes is required and, up to now, appropriate methods are only rarely available in the literature. Moreover, existing methods are not motivated by the strive for insights by means of an easy-to-interpret parameter. Hence, we seek to develop a new estimand-driven method to compare the effectiveness of two treatments in the context of right-censored survival data with matched pairs. With the help of competing risks techniques, the so-called relative treatment effect is estimated. This estimand describes the probability that individuals under Treatment 1 have a longer lifetime than comparable individuals under Treatment 2. We derive hypothesis tests and confidence intervals based on a studentized version of the estimator, where resampling-based inference is established by means of a randomization method. In a simulation study, we demonstrate for numerous sample sizes and different amounts of censoring that the developed test exhibits a good power. Finally, we apply the methodology to a well-known benchmark data set from a trial with patients suffering from diabetic retinopathy.

Confidence intervals for odds ratio from multistage randomized phase II trials.

A multi-stage randomized trial design can significantly improve efficiency by allowing early termination of the trial when the experimental arm exhibits either low or high efficacy compared to the control arm during the study. However, proper inference methods are necessary because the underlying distribution of the target statistic changes due to the multi-stage structure. This article focuses on multi-stage randomized phase II trials with a dichotomous outcome, such as treatment response, and proposes exact conditional confidence intervals for the odds ratio. The usual single-stage confidence intervals are invalid when used in multi-stage trials. To address this issue, we propose a linear ordering of all possible outcomes. This ordering is conditioned on the total number of responders in each stage and utilizes the exact conditional distribution function of the outcomes. This approach enables the estimation of an exact confidence interval accounting for the multi-stage designs.

A fast bootstrap algorithm for causal inference with large data.

Estimating causal effects from large experimental and observational data has become increasingly prevalent in both industry and research. The bootstrap is an intuitive and powerful technique used to construct standard errors and confidence intervals of estimators. Its application however can be prohibitively demanding in settings involving large data. In addition, modern causal inference estimators based on machine learning and optimization techniques exacerbate the computational burden of the bootstrap. The bag of little bootstraps has been proposed in non-causal settings for large data but has not yet been applied to evaluate the properties of estimators of causal effects. In this article, we introduce a new bootstrap algorithm called causal bag of little bootstraps for causal inference with large data. The new algorithm significantly improves the computational efficiency of the traditional bootstrap while providing consistent estimates and desirable confidence interval coverage. We describe its properties, provide practical considerations, and evaluate the performance of the proposed algorithm in terms of bias, coverage of the true 95% confidence intervals, and computational time in a simulation study. We apply it in the evaluation of the effect of hormone therapy on the average time to coronary heart disease using a large observational data set from the Women's Health Initiative.

Confidence intervals for validation statistics with data truncation in genomic prediction.

BACKGROUND: Validation by data truncation is a common practice in genetic evaluations because of the interest in predicting the genetic merit of a set of young selection candidates. Two of the most used validation methods in genetic evaluations use a single data partition: predictivity or predictive ability (correlation between pre-adjusted phenotypes and estimated breeding values (EBV) divided by the square root of the heritability) and the linear regression (LR) method (comparison of "early" and "late" EBV). Both methods compare predictions with the whole dataset and a partial dataset that is obtained by removing the information related to a set of validation individuals. EBV obtained with the partial dataset are compared against adjusted phenotypes for the predictivity or EBV obtained with the whole dataset in the LR method. Confidence intervals for predictivity and the LR method can be obtained by replicating the validation for different samples (or folds), or bootstrapping. Analytical confidence intervals would be beneficial to avoid running several validations and to test the quality of the bootstrap intervals. However, analytical confidence intervals are unavailable for predictivity and the LR method. RESULTS: We derived standard errors and Wald confidence intervals for the predictivity and statistics included in the LR method (bias, dispersion, ratio of accuracies, and reliability). The confidence intervals for the bias, dispersion, and reliability depend on the relationships and prediction error variances and covariances across the individuals in the validation set. We developed approximations for large datasets that only need the reliabilities of the individuals in the validation set. The confidence intervals for the ratio of accuracies and predictivity were obtained through the Fisher transformation. We show the adequacy of both the analytical and approximated analytical confidence intervals and compare them versus bootstrap confidence intervals using two simulated examples. The analytical confidence intervals were closer to the simulated ones for both examples. Bootstrap confidence intervals tend to be narrower than the simulated ones. The approximated analytical confidence intervals were similar to those obtained by bootstrapping. CONCLUSIONS: Estimating the sampling variation of predictivity and the statistics in the LR method without replication or bootstrap is possible for any dataset with the formulas presented in this study.

Probabilistic precision calculations for the planning of studies assessing negative binomial rates.

PURPOSE: Outcome variables that are assumed to follow a negative binomial distribution are frequently used in both clinical and epidemiological studies. Epidemiological studies, particularly those performed by pharmaceutical companies often aim to describe a population rather than compare treatments. Such descriptive studies are often analysed using confidence intervals. While precision calculations and sample size calculations are not always performed in these settings, they have the important role of setting expectations of what results the study may generate. Current methods for precision calculations for the negative binomial rate are based on plugging in parameter values into the confidence interval formulae. This method has the downside of ignoring the randomness of the confidence interval limits. To enable better practice for precision calculations, methods are needed that address the randomness. METHODS: Using the well-known delta-method we develop a method for calculating the precision probability, that is, the probability of achieving a certain width. We assess the performance of the method in smaller samples through simulations. RESULTS: The method for the precision probability performs well in small to medium sample sizes, and the usefulness of the method is demonstrated through an example. CONCLUSIONS: We have developed a simple method for calculating the precision probability for negative binomial rates. This method can be used when planning epidemiological studies in for example, asthma, while correctly taking the randomness of confidence intervals into account.

P-values and confidence intervals of linear rank tests for left-truncated data under truncated binomial design.

The paper provides computations comparing the accuracy of the saddlepoint approximation approach and the normal approximation method in approximating the mid-p-value of Wilcoxon and log-rank tests for the left-truncated data using a truncated binomial design. The paper uses real data examples to apply the comparison, along with some simulated studies. Confidence intervals are provided by the inversion of the tests under consideration.

Estimation of median survival time and its 95% confidence interval using SAS PROC LIFETEST.

Estimation of median survival and its 95% confidence interval depends on the choice of the survival function, standard error, and a method for constructing the confidence interval. This paper outlines several available possibilities in SAS® (version 9.4) PROC LIFETEST and compares them on theoretical grounds and using simulated data, with criteria: ability to estimate the 95% CI, coverage probability, interval width, and appropriateness for practical use. Data are generated with varying hazard patterns, N, % censoring, and censoring patterns (early, uniform, late, last visit). LIFETEST was run using the Kaplan-Meier and Nelson-Aalen estimators and the transformations available (linear, log, logit, complementary log-log, and arcsine square root). Using the Kaplan-Meier estimator with the logarithmic transformation as well as with the logit leads to a high frequency of LIFETEST not being able to estimate the 95% CI. The combination of Kaplan-Meier with the linear transformation is associated with poor coverage achieved. For small samples, late/last visit censoring has a negative effect on being able to estimate the 95% CI. Heavy early censoring can lead to low coverage of the 95% CI of median survival for sample sizes up to and including N = 40. The two combinations that are optimal for being able to estimate the 95% CI and having adequate coverage are the Kaplan-Meier estimator with complementary log-log transformation, and the Nelson-Aalen estimator with linear transformation. The former fares best on the third criterion (smaller width) and is also the SAS® default and validates the choice of default.

Editorial Commentary: The Statistical Fragility Index of Medical Trials Is Low By Design: Critical Evaluation of Confidence Intervals Is Required.

The Fragility Index (FI) provides the number of patients whose outcome would need to have changed for the results of a clinical trial to no longer be statistically significant. Although it's a well-intended and easily interpreted metric, its calculation is based on reversing a significant finding and therefore its interpretation is only relevant in the domain of statistical significance. Its interpretation is only relevant in the domain of statistical significance. A well-designed clinical trial includes an a priori sample size calculation that aims to find the bare minimum of patients needed to obtain statistical significance. Such trials are fragile by design! Examining the robustness of clinical trials requires an estimation of uncertainty, rather than a misconstrued, dichotomous focus on statistical significance. Confidence intervals (CIs) provide a range of values that are compatible with a study's data and help determine the precision of results and the compatibility of the data with different hypotheses. The width of the CI speaks to the precision of the results, and the extent to which the values contained within have potential to be clinically important. Finally, one should not assume that a large FI indicates robust findings. Poorly executed trials are prone to bias, leading to large effects, and therefore, small P values, and a large FI. Let's move our future focus from the FI toward the CI.

A Generalized Bootstrap Procedure of the Standard Error and Confidence Interval Estimation for Inverse Probability of Treatment Weighting.

The inverse probability of treatment weighting (IPTW) approach is commonly used in propensity score analysis to infer causal effects in regression models. Due to oversized IPTW weights and errors associated with propensity score estimation, the IPTW approach can underestimate the standard error of causal effect. To remediate this, bootstrap standard errors have been recommended to replace the IPTW standard error, but the ordinary bootstrap (OB) procedure might still result in underestimation of the standard error because of its inefficient resampling scheme and untreated oversized weights. In this paper, we develop a generalized bootstrap (GB) procedure for estimating the standard error and confidence intervals of the IPTW approach. Compared with the OB procedure and other three procedures in comparison, the GB procedure has the highest precision and yields conservative standard error estimates. As a result, the GB procedure produces short confidence intervals with highest coverage rates. We demonstrate the effectiveness of the GB procedure via two simulation studies and a dataset from the National Educational Longitudinal Study-1988 (NELS-88).

Analysis of two binomial proportions in noninferiority confirmatory trials.

In this article, we propose considering an approximate exact score (AES) test for noninferiority comparisons and we derive its test-based confidence interval for the difference between two independent binomial proportions. This test was published in the literature, but not its associated confidence interval. The p-value for this test is obtained by using exact binomial probabilities with the nuisance parameter being replaced by its restricted maximum likelihood estimate. Calculated type I errors revealed that the AES method has important advantages for noninferiority comparisons over popular asymptotic methods for adequately powered confirmatory clinical trials, at 80% or 90% statistical power. For unbalanced sample sizes of the compared groups, type I errors for the asymptotic score method were shown to be higher than the nominal level in a systematic pattern over a range of true proportions, but the AES method did not suffer from such a problem. On average, the true type I error of the AES method was closer to the nominal level than all considered methods in the empirical comparisons. In rare cases, type I errors of the AES test exceeded the nominal level, but only by a small amount. Presented examples showed that the AES method can be more attractive in practice than practical exact methods. In addition, p-value and confidence interval of the AES method can be obtained in <30 s of computer time for most confirmatory trials. Theoretical arguments, combined with empirical evidence and fast computation time should make the AES method attractive in statistical practice.

Principal Component Analysis Enhanced with Bootstrapped Confidence Interval for the Classification of Parkinsonian Patients Using Gaussian Mixture Model and Gait Initiation Parameters.

Parkinson's disease is one of the major neurodegenerative diseases that affects the postural stability of patients, especially during gait initiation. There is actually an increasing demand for the development of new non-pharmacological tools that can easily classify healthy/affected patients as well as the degree of evolution of the disease. The experimental characterization of gait initiation (GI) is usually done through the simultaneous acquisition of about 20 variables, resulting in very large datasets. Dimension reduction tools are therefore suitable, considering the complexity of the physiological processes involved. The principal Component Analysis (PCA) is very powerful at reducing the dimensionality of large datasets and emphasizing correlations between variables. In this paper, the Principal Component Analysis (PCA) was enhanced with bootstrapping and applied to the study of the GI to identify the 3 majors sets of variables influencing the postural control disability of Parkinsonian patients during GI. We show that the combination of these methods can lead to a significant improvement in the unsupervised classification of healthy/affected patients using a Gaussian mixture model, since it leads to a reduced confidence interval on the estimated parameters. The benefits of this method for the identification and study of the efficiency of potential treatments is not addressed in this paper but could be addressed in future works.