OBJECTIVE: In meta-analyses with few studies, between-study heterogeneity is poorly estimated. The Hartung and Knapp (HK) correction and the prediction intervals can account for the uncertainty in estimating heterogeneity and the range of effect sizes we may encounter in future trials, respectively. The aim of this study was to assess the reported use of the HK correction in oral health meta-analyses and to compare the published reported results and interpretation i) to those calculated using eight heterogeneity estimators and the HK adjustment ii) and to the prediction intervals (PIs).
METHODS: We sourced systematic reviews (SRs) published between 2021 and 2023 in eighteen leading specialty and general dental journals. We extracted study characteristics at the SR and meta-analysis level and re-analyzed the selected meta-analyses via the random-effects model and eight heterogeneity estimators, with and without the HK correction. For each meta-analysis, we re-calculated the overall estimate, the P-value, the 95% confidence interval (CI) and the PI.
RESULTS: We analysed 292 meta-analyses. The median number of primary studies included in meta-analysis was 8 (interquartile range [IQR]= [5.75-15] range: 3-121). Only 3/292 meta-analyses used the HK adjustment and 12/292 reported PIs. The percentage of statistically significant results that became non-significant varied across the heterogeneity estimators (7.45%- 16.59%). Based on the PIs, more than 60% of meta-analyses with statistically significant results are likely to change in the future and more than 40% of the PIs included the opposite pooled effect.
CONCLUSIONS: The precision and statistical significance of the pooled estimates from meta-analyses with at least three studies is sensitive to the HK correction, the heterogeneity variance estimator, and the PIs.
CONCLUSIONS: Uncertainty in meta-analyses estimates should be considered especially when a small number of trials is available or vary notably in their precision. Misinterpretation of the summary results can lead to ineffective interventions being applied in clinical practice.

We often estimate a parameter of interest ψ $$ \\psi $$ when the identifying conditions involve a finite-dimensional nuisance parameter θ ∈ ℝ d $$ \\theta \\in {\\mathbb{R}}^d $$ . Examples from causal inference are inverse probability weighting, marginal structural models and structural nested models, which all lead to unbiased estimating equations. This article presents a consistent sandwich estimator for the variance of estimators ψ ^ $$ \\hat{\\psi} $$ that solve unbiased estimating equations including θ $$ \\theta $$ which is also estimated by solving unbiased estimating equations. This article presents four additional results for settings where θ ^ $$ \\hat{\\theta} $$ solves (partial) score equations and ψ $$ \\psi $$ does not depend on θ $$ \\theta $$ . This includes many causal inference settings where θ $$ \\theta $$ describes the treatment probabilities, missing data settings where θ $$ \\theta $$ describes the missingness probabilities, and measurement error settings where θ $$ \\theta $$ describes the error distribution. These four additional results are: (1) Counter-intuitively, the asymptotic variance of ψ ^ $$ \\hat{\\psi} $$ is typically smaller when θ $$ \\theta $$ is estimated. (2) If estimating θ $$ \\theta $$ is ignored, the sandwich estimator for the variance of ψ ^ $$ \\hat{\\psi} $$ is conservative. (3) A consistent sandwich estimator for the variance of ψ ^ $$ \\hat{\\psi} $$ . (4) If ψ ^ $$ \\hat{\\psi} $$ with the true θ $$ \\theta $$ plugged in is efficient, the asymptotic variance of ψ ^ $$ \\hat{\\psi} $$ does not depend on whether θ $$ \\theta $$ is estimated. To illustrate we use observational data to calculate confidence intervals for (1) the effect of cazavi versus colistin on bacterial infections and (2) how the effect of antiretroviral treatment depends on its initiation time in HIV-infected patients.

Background: The factors associated with unplanned higher-level re-amputation (UHRA) and one-year mortality among patients with chronic limb-threatening ischemia (CLTI) after lower extremity amputation are poorly understood. Methods: This was a single-center retrospective study of patients who underwent amputations for CLTI between 2014 and 2017. Unadjusted bivariate analyses and adjusted odds ratios (AOR) from logistic regression models were used to assess associations between pre-amputation risk factors and outcomes (UHRA and one-year mortality). Results: We obtained data on 203 amputations from 182 patients (median age 65 years [interquartile range (IQR) 57, 75]; 70.7% males), including 118 (58.1%) toe, 20 (9.9%) transmetatarsal (TMA), 37 (18.2%) below-knee (BKA), and 28 (13.8%) amputations at or above the knee. Median follow-up was 285 days (IQR 62, 1348). Thirty-six limbs (17.7%) had a UHRA, and the majority of these (72.2%) were following index forefoot amputations. Risk factors for UHRA included non-ambulatory status (AOR 6.74, 95% confidence interval (CI) 1.74-26.18; p < 0.10) and toe pressure < 30 mm Hg (AOR 4.89, 95% CI 1.52-15.78; p < 0.01). One-year mortality was 17.2% (n = 32), and risk factors included coronary artery disease (AOR 3.93, 95% CI 1.56-9.87; p < 0.05), congestive heart failure (AOR 4.90, 95% CI 1.96-12.29; p = 0.001), end-stage renal disease (AOR 7.54, 95% CI 3.10-18.34; p < 0.001), and non-independent ambulation (AOR 4.31, 95% CI 1.20-15.49; p = 0.03). Male sex was associated with a reduced odds of death at 1 year (AOR 0.37, 95% CI 0.15-0.89; p < 0.05). UHRA was not associated with one-year mortality. Conclusions: Rates of UHRA after toe amputations and TMA are high despite revascularization and one-year mortality is high among patients with CLTI requiring amputation.

As widely noted in the literature and by international bodies such as the American Statistical Association, severe misinterpretations of P-values, confidence intervals, and statistical significance are sadly common in public health. This scenario poses serious risks concerning terminal decisions such as the approval or rejection of therapies. Cognitive distortions about statistics likely stem from poor teaching in schools and universities, overly simplified interpretations, and - as we suggest - the reckless use of calculation software with predefined standardized procedures. In light of this, we present a framework to recalibrate the role of frequentist-inferential statistics within clinical and epidemiological research. In particular, we stress that statistics is only a set of rules and numbers that make sense only when properly placed within a well-defined scientific context beforehand. Practical examples are discussed for educational purposes. Alongside this, we propose some tools to better evaluate statistical outcomes, such as multiple compatibility or surprisal intervals or tuples of various point hypotheses. Lastly, we emphasize that every conclusion must be informed by different kinds of scientific evidence (e.g., biochemical, clinical, statistical, etc.) and must be based on a careful examination of costs, risks, and benefits.

BACKGROUND: The physical therapy profession has made efforts to increase the use of confidence intervals due to the valuable information they provide for clinical decision-making. Confidence intervals indicate the precision of the results and describe the strength and direction of a treatment effect measure.
OBJECTIVE: To determine the prevalence of reporting of confidence intervals, achievement of intended sample size, and adjustment for multiple primary outcomes in randomised trials of physical therapy interventions.
METHODS: We randomly selected 100 trials published in 2021 and indexed on the Physiotherapy Evidence Database. Two independent reviewers extracted the number of participants, any sample size calculation, and any adjustments for multiple primary outcomes. We extracted whether at least one between-group comparison was reported with a 95 % confidence interval and whether any confidence intervals were interpreted.
RESULTS: The prevalence of use of confidence intervals was 47 % (95 % CI 38, 57). Only 6 % of trials (95 % CI: 3, 12) both reported and interpreted a confidence interval. Among the 100 trials, 59 (95 % CI: 49, 68) calculated and achieved the required sample size. Among the 100 trials, 19 % (95 % CI: 13, 28) had a problem with unadjusted multiplicity on the primary outcomes.
CONCLUSIONS: Around half of trials of physical therapy interventions published in 2021 reported confidence intervals around between-group differences. This represents an increase of 5 % from five years earlier. Very few trials interpreted the confidence intervals. Most trials reported a sample size calculation, and among these most achieved that sample size. There is still a need to increase the use of adjustment for multiple comparisons.

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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.

The statistical significance of a clinical trial analysis result is determined by a mathematical calculation and probability based on null hypothesis significance testing. However, statistical significance does not always align with meaningful clinical effects; thus, assigning clinical relevance to statistical significance is unreasonable. A statistical result incorporating a clinically meaningful difference is a better approach to present statistical significance. Thus, the minimal clinically important difference (MCID), which requires integrating minimum clinically relevant changes from the early stages of research design, has been introduced. As a follow-up to the previous statistical round article on P values, confidence intervals, and effect sizes, in this article, we present hands-on examples of MCID and various effect sizes and discuss the terms statistical significance and clinical relevance, including cautions regarding their use.

Modern anesthetic drugs ensure the efficacy of general anesthesia. Goals include reducing variability in surgical, tracheal extubation, post-anesthesia care unit, or intraoperative response recovery times. Generalized confidence intervals based on the log-normal distribution compare variability between groups, specifically ratios of standard deviations. The alternative statistical approaches, performing robust variance comparison tests, give P-values, not point estimates nor confidence intervals for the ratios of the standard deviations. We performed Monte-Carlo simulations to learn what happens to confidence intervals for ratios of standard deviations of anesthesia-associated times when analyses are based on the log-normal, but the true distributions are Weibull. We used simulation conditions comparable to meta-analyses of most randomized trials in anesthesia, n ≈ 25 and coefficients of variation ≈ 0.30 . The estimates of the ratios of standard deviations were positively biased, but slightly, the ratios being 0.11% to 0.33% greater than nominal. In contrast, the 95% confidence intervals were very wide (i.e., > 95% of P ≥ 0.05). Although substantive inferentially, the differences in the confidence limits were small from a clinical or managerial perspective, with a maximum absolute difference in ratios of 0.016. Thus, P < 0.05 is reliable, but investigators should plan for Type II errors at greater than nominal rates.

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.