Meta-análisis: Intervalos de confianza e Intervalos de predicción / Meta-analysis: Confidence intervals and Prediction intervals

En los informes meta-analíticos se suelen reportar varios tipos de intervalos, hecho que ha generado cierta confusión a la hora de interpretarlos. Los intervalos de confianza reflejan la incertidumbre relacionada con un número, el tamaño del efecto medio paramétrico. Los intervalos de predicción reflejan el tamaño paramétrico probable en cualquier estudio de la misma clase que los incluidos en un meta-análisis. Su interpretación y aplicaciones son diferentes. En este artículo explicamos su diferente naturaleza y cómo se pueden utilizar para responder preguntas específicas. Se incluyen ejemplos numéricos, así como su cálculo con el paquete metafor en R.(AU)

Several types of intervals are usually employed in meta-analysis, a fact that has generated some confusion when interpreting them. Confidence intervals reflect the uncertainty related to a single number, the parametric mean effect size. Prediction intervals reflect the probable parametric effect size in any study of the same class as those included in a meta-analysis. Its interpretation and applications are different. In this article we explain in de-tail their different nature and how they can be used to answer specific ques-tions. Numerical examples are included, as well as their computation with the metafor Rpackage.(AU)

Replication of null results: Absence of evidence or evidence of absence?

In several large-scale replication projects, statistically non-significant results in both the original and the replication study have been interpreted as a 'replication success.' Here, we discuss the logical problems with this approach: Non-significance in both studies does not ensure that the studies provide evidence for the absence of an effect and 'replication success' can virtually always be achieved if the sample sizes are small enough. In addition, the relevant error rates are not controlled. We show how methods, such as equivalence testing and Bayes factors, can be used to adequately quantify the evidence for the absence of an effect and how they can be applied in the replication setting. Using data from the Reproducibility Project: Cancer Biology, the Experimental Philosophy Replicability Project, and the Reproducibility Project: Psychology we illustrate that many original and replication studies with 'null results' are in fact inconclusive. We conclude that it is important to also replicate studies with statistically non-significant results, but that they should be designed, analyzed, and interpreted appropriately.

Sequential covariate-adjusted randomization via hierarchically minimizing Mahalanobis distance and marginal imbalance.

In comparative studies, covariate balance and sequential allocation schemes have attracted growing academic interest. Although many theoretically justified adaptive randomization methods achieve the covariate balance, they often allocate patients in pairs or groups. To better meet the practical requirements where the clinicians cannot wait for other participants to assign the current patient for some economic or ethical reasons, we propose a method that randomizes patients individually and sequentially. The proposed method conceptually separates the covariate imbalance, measured by the newly proposed modified Mahalanobis distance, and the marginal imbalance, that is the sample size difference between the 2 groups, and it minimizes them with an explicit priority order. Compared with the existing sequential randomization methods, the proposed method achieves the best possible covariate balance while maintaining the marginal balance directly, offering us more control of the randomization process. We demonstrate the superior performance of the proposed method through a wide range of simulation studies and real data analysis, and also establish theoretical guarantees for the proposed method in terms of both the convergence of the imbalance measure and the subsequent treatment effect estimation.

A method for determining groups in cumulative incidence curves in competing risk data.

The cumulative incidence function is the standard method for estimating the marginal probability of a given event in the presence of competing risks. One basic but important goal in the analysis of competing risk data is the comparison of these curves, for which limited literature exists. We proposed a new procedure that lets us not only test the equality of these curves but also group them if they are not equal. The proposed method allows determining the composition of the groups as well as an automatic selection of their number. Simulation studies show the good numerical behavior of the proposed methods for finite sample size. The applicability of the proposed method is illustrated using real data.

Doubly robust proximal synthetic controls.

To infer the treatment effect for a single treated unit using panel data, synthetic control (SC) methods construct a linear combination of control units' outcomes that mimics the treated unit's pre-treatment outcome trajectory. This linear combination is subsequently used to impute the counterfactual outcomes of the treated unit had it not been treated in the post-treatment period, and used to estimate the treatment effect. Existing SC methods rely on correctly modeling certain aspects of the counterfactual outcome generating mechanism and may require near-perfect matching of the pre-treatment trajectory. Inspired by proximal causal inference, we obtain two novel nonparametric identifying formulas for the average treatment effect for the treated unit: one is based on weighting, and the other combines models for the counterfactual outcome and the weighting function. We introduce the concept of covariate shift to SCs to obtain these identification results conditional on the treatment assignment. We also develop two treatment effect estimators based on these two formulas and generalized method of moments. One new estimator is doubly robust: it is consistent and asymptotically normal if at least one of the outcome and weighting models is correctly specified. We demonstrate the performance of the methods via simulations and apply them to evaluate the effectiveness of a pneumococcal conjugate vaccine on the risk of all-cause pneumonia in Brazil.

Robustness of response-adaptive randomization.

Doubly adaptive biased coin design (DBCD), a response-adaptive randomization scheme, aims to skew subject assignment probabilities based on accrued responses for ethical considerations. Recent years have seen substantial advances in understanding DBCD's theoretical properties, assuming correct model specification for the responses. However, concerns have been raised about the impact of model misspecification on its design and analysis. In this paper, we assess the robustness to both design model misspecification and analysis model misspecification under DBCD. On one hand, we confirm that the consistency and asymptotic normality of the allocation proportions can be preserved, even when the responses follow a distribution other than the one imposed by the design model during the implementation of DBCD. On the other hand, we extensively investigate three commonly used linear regression models for estimating and inferring the treatment effect, namely difference-in-means, analysis of covariance (ANCOVA) I, and ANCOVA II. By allowing these regression models to be arbitrarily misspecified, thereby not reflecting the true data generating process, we derive the consistency and asymptotic normality of the treatment effect estimators evaluated from the three models. The asymptotic properties show that the ANCOVA II model, which takes covariate-by-treatment interaction terms into account, yields the most efficient estimator. These results can provide theoretical support for using DBCD in scenarios involving model misspecification, thereby promoting the widespread application of this randomization procedure.

Using Bayesian statistics in confirmatory clinical trials in the regulatory setting: a tutorial review.

Bayesian statistics plays a pivotal role in advancing medical science by enabling healthcare companies, regulators, and stakeholders to assess the safety and efficacy of new treatments, interventions, and medical procedures. The Bayesian framework offers a unique advantage over the classical framework, especially when incorporating prior information into a new trial with quality external data, such as historical data or another source of co-data. In recent years, there has been a significant increase in regulatory submissions using Bayesian statistics due to its flexibility and ability to provide valuable insights for decision-making, addressing the modern complexity of clinical trials where frequentist trials are inadequate. For regulatory submissions, companies often need to consider the frequentist operating characteristics of the Bayesian analysis strategy, regardless of the design complexity. In particular, the focus is on the frequentist type I error rate and power for all realistic alternatives. This tutorial review aims to provide a comprehensive overview of the use of Bayesian statistics in sample size determination, control of type I error rate, multiplicity adjustments, external data borrowing, etc., in the regulatory environment of clinical trials. Fundamental concepts of Bayesian sample size determination and illustrative examples are provided to serve as a valuable resource for researchers, clinicians, and statisticians seeking to develop more complex and innovative designs.

Improved clinical data imputation via classical and quantum determinantal point processes.

Imputing data is a critical issue for machine learning practitioners, including in the life sciences domain, where missing clinical data is a typical situation and the reliability of the imputation is of great importance. Currently, there is no canonical approach for imputation of clinical data and widely used algorithms introduce variance in the downstream classification. Here we propose novel imputation methods based on determinantal point processes (DPP) that enhance popular techniques such as the multivariate imputation by chained equations and MissForest. Their advantages are twofold: improving the quality of the imputed data demonstrated by increased accuracy of the downstream classification and providing deterministic and reliable imputations that remove the variance from the classification results. We experimentally demonstrate the advantages of our methods by performing extensive imputations on synthetic and real clinical data. We also perform quantum hardware experiments by applying the quantum circuits for DPP sampling since such quantum algorithms provide a computational advantage with respect to classical ones. We demonstrate competitive results with up to 10 qubits for small-scale imputation tasks on a state-of-the-art IBM quantum processor. Our classical and quantum methods improve the effectiveness and robustness of clinical data prediction modeling by providing better and more reliable data imputations. These improvements can add significant value in settings demanding high precision, such as in pharmaceutical drug trials where our approach can provide higher confidence in the predictions made.

Statistical analysis plan for the replacing protein via enteral nutrition in a stepwise approach in critically ill patients (REPLENISH) randomized clinical trial.

BACKGROUND: The optimal amount and timing of protein intake in critically ill patients are unknown. REPLENISH (Replacing Protein via Enteral Nutrition in a Stepwise Approach in Critically Ill Patients) trial evaluates whether supplemental enteral protein added to standard enteral nutrition to achieve a high amount of enteral protein given from ICU day five until ICU discharge or ICU day 90 as compared to no supplemental enteral protein to achieve a moderate amount of enteral protein would reduce all-cause 90-day mortality in adult critically ill mechanically ventilated patients. METHODS: In this multicenter randomized trial, critically ill patients will be randomized to receive supplemental enteral protein (1.2 g/kg/day) added to standard enteral nutrition to achieve a high amount of enteral protein (range of 2-2.4 g/kg/day) or no supplemental enteral protein to achieve a moderate amount of enteral protein (0.8-1.2 g/kg/day). The primary outcome is 90-day all-cause mortality; other outcomes include functional and health-related quality-of-life assessments at 90 days. The study sample size of 2502 patients will have 80% power to detect a 5% absolute risk reduction in 90-day mortality from 30 to 25%. Consistent with international guidelines, this statistical analysis plan specifies the methods for evaluating primary and secondary outcomes and subgroups. Applying this statistical analysis plan to the REPLENISH trial will facilitate unbiased analyses of clinical data. CONCLUSION: Ethics approval was obtained from the institutional review board, Ministry of National Guard Health Affairs, Riyadh, Saudi Arabia (RC19/414/R). Approvals were also obtained from the institutional review boards of each participating institution. Our findings will be disseminated in an international peer-reviewed journal and presented at relevant conferences and meetings. TRIAL REGISTRATION: ClinicalTrials.gov, NCT04475666 . Registered on July 17, 2020.

The psychological reality of the learned "p < .05" boundary.

The .05 boundary within Null Hypothesis Statistical Testing (NHST) "has made a lot of people very angry and been widely regarded as a bad move" (to quote Douglas Adams). Here, we move past meta-scientific arguments and ask an empirical question: What is the psychological standing of the .05 boundary for statistical significance? We find that graduate students in the psychological sciences show a boundary effect when relating p-values across .05. We propose this psychological boundary is learned through statistical training in NHST and reading a scientific literature replete with "statistical significance". Consistent with this proposal, undergraduates do not show the same sensitivity to the .05 boundary. Additionally, the size of a graduate student's boundary effect is not associated with their explicit endorsement of questionable research practices. These findings suggest that training creates distortions in initial processing of p-values, but these might be dampened through scientific processes operating over longer timescales.

Upstrapping to determine futility: predicting future outcomes nonparametrically from past data.

BACKGROUND: Clinical trials often involve some form of interim monitoring to determine futility before planned trial completion. While many options for interim monitoring exist (e.g., alpha-spending, conditional power), nonparametric based interim monitoring methods are also needed to account for more complex trial designs and analyses. The upstrap is one recently proposed nonparametric method that may be applied for interim monitoring. METHODS: Upstrapping is motivated by the case resampling bootstrap and involves repeatedly sampling with replacement from the interim data to simulate thousands of fully enrolled trials. The p-value is calculated for each upstrapped trial and the proportion of upstrapped trials for which the p-value criteria are met is compared with a pre-specified decision threshold. To evaluate the potential utility for upstrapping as a form of interim futility monitoring, we conducted a simulation study considering different sample sizes with several different proposed calibration strategies for the upstrap. We first compared trial rejection rates across a selection of threshold combinations to validate the upstrapping method. Then, we applied upstrapping methods to simulated clinical trial data, directly comparing their performance with more traditional alpha-spending and conditional power interim monitoring methods for futility. RESULTS: The method validation demonstrated that upstrapping is much more likely to find evidence of futility in the null scenario than the alternative across a variety of simulations settings. Our three proposed approaches for calibration of the upstrap had different strengths depending on the stopping rules used. Compared to O'Brien-Fleming group sequential methods, upstrapped approaches had type I error rates that differed by at most 1.7% and expected sample size was 2-22% lower in the null scenario, while in the alternative scenario power fluctuated between 15.7% lower and 0.2% higher and expected sample size was 0-15% lower. CONCLUSIONS: In this proof-of-concept simulation study, we evaluated the potential for upstrapping as a resampling-based method for futility monitoring in clinical trials. The trade-offs in expected sample size, power, and type I error rate control indicate that the upstrap can be calibrated to implement futility monitoring with varying degrees of aggressiveness and that performance similarities can be identified relative to considered alpha-spending and conditional power futility monitoring methods.

The left atrial appendage closure by surgery 2 trial: statistical analysis plan for a randomized multicenter trial exploring if the closure of the left atrial appendage during open-heart surgery reduces stroke irrespective of patients' stroke risk and preoperative atrial fibrillation status.

BACKGROUND: Surgical left atrial appendage (LAA) closure concomitant to open-heart surgery prevents thromboembolism in high-risk patients. Nevertheless, high-level evidence does not exist for LAA closure performed in patients with any CHA2DS2-VASc score and preoperative atrial fibrillation or flutter (AF) status-the current trial attempts to provide such evidence. METHODS: The study is designed as a randomized, open-label, blinded outcome assessor, multicenter trial of adult patients undergoing first-time elective open-heart surgery. Patients with and without AF and any CHA2DS2-VASc score will be enrolled. The primary exclusion criteria are planned LAA closure, planned AF ablation, or ongoing endocarditis. Before randomization, a three-step stratification process will sort patients by site, surgery type, and preoperative or expected oral anticoagulation treatment. Patients will undergo balanced randomization (1:1) to LAA closure on top of the planned cardiac surgery or standard care. Block sizes vary from 8 to 16. Neurologists blinded to randomization will adjudicate the primary outcome of stroke, including transient ischemic attack (TIA). The secondary outcomes include a composite outcome of stroke, including TIA, and silent cerebral infarcts, an outcome of ischemic stroke, including TIA, and a composite outcome of stroke and all-cause mortality. LAA closure is expected to provide a 60% relative risk reduction. In total, 1500 patients will be randomized and followed for 2 years. DISCUSSION: The trial is expected to help form future guidelines within surgical LAA closure. This statistical analysis plan ensures transparency of analyses and limits potential reporting biases. TRIAL REGISTRATION: Clinicaltrials.gov, NCT03724318. Registered 26 October 2018, https://clinicaltrials.gov/study/NCT03724318 . PROTOCOL VERSION: https://doi.org/10.1016/j.ahj.2023.06.003 .

Efficient data integration under prior probability shift.

Conventional supervised learning usually operates under the premise that data are collected from the same underlying population. However, challenges may arise when integrating new data from different populations, resulting in a phenomenon known as dataset shift. This paper focuses on prior probability shift, where the distribution of the outcome varies across datasets but the conditional distribution of features given the outcome remains the same. To tackle the challenges posed by such shift, we propose an estimation algorithm that can efficiently combine information from multiple sources. Unlike existing methods that are restricted to discrete outcomes, the proposed approach accommodates both discrete and continuous outcomes. It also handles high-dimensional covariate vectors through variable selection using an adaptive least absolute shrinkage and selection operator penalty, producing efficient estimates that possess the oracle property. Moreover, a novel semiparametric likelihood ratio test is proposed to check the validity of prior probability shift assumptions by embedding the null conditional density function into Neyman's smooth alternatives (Neyman, 1937) and testing study-specific parameters. We demonstrate the effectiveness of our proposed method through extensive simulations and a real data example. The proposed methods serve as a useful addition to the repertoire of tools for dealing dataset shifts.

A new and unified method for regression analysis of interval-censored failure time data under semiparametric transformation models with missing covariates.

This paper discusses regression analysis of interval-censored failure time data arising from semiparametric transformation models in the presence of missing covariates. Although some methods have been developed for the problem, they either apply only to limited situations or may have some computational issues. Corresponding to these, we propose a new and unified two-step inference procedure that can be easily implemented using the existing or standard software. The proposed method makes use of a set of working models to extract partial information from incomplete observations and yields a consistent estimator of regression parameters assuming missing at random. An extensive simulation study is conducted and indicates that it performs well in practical situations. Finally, we apply the proposed approach to an Alzheimer's Disease study that motivated this study.

Testing conditional quantile independence with functional covariate.

We propose a new non-parametric conditional independence test for a scalar response and a functional covariate over a continuum of quantile levels. We build a Cramer-von Mises type test statistic based on an empirical process indexed by random projections of the functional covariate, effectively avoiding the "curse of dimensionality" under the projected hypothesis, which is almost surely equivalent to the null hypothesis. The asymptotic null distribution of the proposed test statistic is obtained under some mild assumptions. The asymptotic global and local power properties of our test statistic are then investigated. We specifically demonstrate that the statistic is able to detect a broad class of local alternatives converging to the null at the parametric rate. Additionally, we recommend a simple multiplier bootstrap approach for estimating the critical values. The finite-sample performance of our statistic is examined through several Monte Carlo simulation experiments. Finally, an analysis of an EEG data set is used to show the utility and versatility of our proposed test statistic.

Impact of redefining statistical significance on P-hacking and false positive rates: An agent-based model.

In recent years, concern has grown about the inappropriate application and interpretation of P values, especially the use of P<0.05 to denote "statistical significance" and the practice of P-hacking to produce results below this threshold and selectively reporting these in publications. Such behavior is said to be a major contributor to the large number of false and non-reproducible discoveries found in academic journals. In response, it has been proposed that the threshold for statistical significance be changed from 0.05 to 0.005. The aim of the current study was to use an evolutionary agent-based model comprised of researchers who test hypotheses and strive to increase their publication rates in order to explore the impact of a 0.005 P value threshold on P-hacking and published false positive rates. Three scenarios were examined, one in which researchers tested a single hypothesis, one in which they tested multiple hypotheses using a P<0.05 threshold, and one in which they tested multiple hypotheses using a P<0.005 threshold. Effects sizes were varied across models and output assessed in terms of researcher effort, number of hypotheses tested and number of publications, and the published false positive rate. The results supported the view that a more stringent P value threshold can serve to reduce the rate of published false positive results. Researchers still engaged in P-hacking with the new threshold, but the effort they expended increased substantially and their overall productivity was reduced, resulting in a decline in the published false positive rate. Compared to other proposed interventions to improve the academic publishing system, changing the P value threshold has the advantage of being relatively easy to implement and could be monitored and enforced with minimal effort by journal editors and peer reviewers.

Perspective on statistical power and equivalence tests.

The use of both sexes or genders should be considered in experimental design, analysis, and reporting. Since there is no requirement to double the sample size or to have sufficient power to study sex differences, challenges for the statistical analysis can arise. In this article, we focus on the topics of statistical power and ways to increase this power. We also discuss the choice of an appropriate design and statistical method and include a separate section on equivalence tests needed to show the absence of a relevant difference.