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)

Improving prediction of linear regression models by integrating external information from heterogeneous populations: James-Stein estimators.

We consider the setting where (1) an internal study builds a linear regression model for prediction based on individual-level data, (2) some external studies have fitted similar linear regression models that use only subsets of the covariates and provide coefficient estimates for the reduced models without individual-level data, and (3) there is heterogeneity across these study populations. The goal is to integrate the external model summary information into fitting the internal model to improve prediction accuracy. We adapt the James-Stein shrinkage method to propose estimators that are no worse and are oftentimes better in the prediction mean squared error after information integration, regardless of the degree of study population heterogeneity. We conduct comprehensive simulation studies to investigate the numerical performance of the proposed estimators. We also apply the method to enhance a prediction model for patella bone lead level in terms of blood lead level and other covariates by integrating summary information from published literature.

Regression without regrets -initial data analysis is a prerequisite for multivariable regression.

Statistical regression models are used for predicting outcomes based on the values of some predictor variables or for describing the association of an outcome with predictors. With a data set at hand, a regression model can be easily fit with standard software packages. This bears the risk that data analysts may rush to perform sophisticated analyses without sufficient knowledge of basic properties, associations in and errors of their data, leading to wrong interpretation and presentation of the modeling results that lacks clarity. Ignorance about special features of the data such as redundancies or particular distributions may even invalidate the chosen analysis strategy. Initial data analysis (IDA) is prerequisite to regression analyses as it provides knowledge about the data needed to confirm the appropriateness of or to refine a chosen model building strategy, to interpret the modeling results correctly, and to guide the presentation of modeling results. In order to facilitate reproducibility, IDA needs to be preplanned, an IDA plan should be included in the general statistical analysis plan of a research project, and results should be well documented. Biased statistical inference of the final regression model can be minimized if IDA abstains from evaluating associations of outcome and predictors, a key principle of IDA. We give advice on which aspects to consider in an IDA plan for data screening in the context of regression modeling to supplement the statistical analysis plan. We illustrate this IDA plan for data screening in an example of a typical diagnostic modeling project and give recommendations for data visualizations.

A simple and effective method for simulating nested exchangeable correlated binary data for longitudinal cluster randomised trials.

BACKGROUND: Simulation is an important tool for assessing the performance of statistical methods for the analysis of data and for the planning of studies. While methods are available for the simulation of correlated binary random variables, all have significant practical limitations for simulating outcomes from longitudinal cluster randomised trial designs, such as the cluster randomised crossover and the stepped wedge trial designs. For these trial designs as the number of observations in each cluster increases these methods either become computationally infeasible or their range of allowable correlations rapidly shrinks to zero. METHODS: In this paper we present a simple method for simulating binary random variables with a specified vector of prevalences and correlation matrix. This method allows for the outcome prevalence to change due to treatment or over time, and for a 'nested exchangeable' correlation structure, in which observations in the same cluster are more highly correlated if they are measured in the same time period than in different time periods, and where different individuals are measured in each time period. This means that our method is also applicable to more general hierarchical clustered data contexts, such as students within classrooms within schools. The method is demonstrated by simulating 1000 datasets with parameters matching those derived from data from a cluster randomised crossover trial assessing two variants of stress ulcer prophylaxis. RESULTS: Our method is orders of magnitude faster than the most well known general simulation method while also allowing a much wider range of correlations than alternative methods. An implementation of our method is available in an R package NestBin. CONCLUSIONS: This simulation method is the first to allow for practical and efficient simulation of large datasets of binary outcomes with the commonly used nested exchangeable correlation structure. This will allow for much more effective testing of designs and inference methods for longitudinal cluster randomised trials with binary outcomes.

Introducing prediction intervals for sample means.

Researchers and practitioners are typically familiar with descriptive statistics and statistical inference. However, outside of regression techniques, little attention may be given to questions around prediction. In the current paper, we introduce prediction intervals using fundamental concepts that are learned in descriptive and inferential statistical training (i.e., sampling error, standard deviation). We walk through an example using simple hand calculations and reference a simple R package that can be used to calculate prediction intervals.

Nonparametric second-order estimation for spatiotemporal point patterns.

Many existing methodologies for analyzing spatiotemporal point patterns are developed based on the assumption of stationarity in both space and time for the second-order intensity or pair correlation. In practice, however, such an assumption often lacks validity or proves to be unrealistic. In this paper, we propose a novel and flexible nonparametric approach for estimating the second-order characteristics of spatiotemporal point processes, accommodating non-stationary temporal correlations. Our proposed method employs kernel smoothing and effectively accounts for spatial and temporal correlations differently. Under a spatially increasing-domain asymptotic framework, we establish consistency of the proposed estimators, which can be constructed using different first-order intensity estimators to enhance practicality. Simulation results reveal that our method, in comparison with existing approaches, significantly improves statistical efficiency. An application to a COVID-19 dataset further illustrates the flexibility and interpretability of our procedure.

Clinical trials with mechanism evaluation of intervention(s): mind the power and sample size calculation.

BACKGROUND: Mediation analysis, often completed as secondary analysis to estimating the main treatment effect, investigates situations where an exposure may affect an outcome both directly and indirectly through intervening mediator variables. Although there has been much research on power in mediation analyses, most of this has focused on the power to detect indirect effects. Little consideration has been given to the extent to which the strength of the mediation pathways, i.e., the intervention-mediator path and the mediator-outcome path respectively, may affect the power to detect the total effect, which would correspond to the intention-to-treat effect in a randomized trial. METHODS: We conduct a simulation study to evaluate the relation between the mediation pathways and the power of testing the total treatment effect, i.e., the intention-to-treat effect. Consider a sample size that is computed based on the usual formula for testing the total effect in a two-arm trial. We generate data for a continuous mediator and a normal outcome using the conventional mediation models. We estimate the total effect using simple linear regression and evaluate the power of a two-sided test. We explore multiple data generating scenarios by varying the magnitude of the mediation paths whilst keeping the total effect constant. RESULTS: Simulations show the estimated total effect is unbiased across the considered scenarios as expected, but the mean of its standard error increases with the magnitude of the mediator-outcome path and the variability in the residual error of the mediator, respectively. Consequently, this affects the power of testing the total effect, which is always lower than planned when the mediator-outcome path is non-trivial and a naive sample size was employed. Analytical explanation confirms that the intervention-mediator path does not affect the power of testing the total effect but the mediator-outcome path. The usual effect size consideration can be adjusted to account for the magnitude of the mediator-outcome path and its residual error. CONCLUSIONS: The sample size calculation for studies with efficacy and mechanism evaluation should account for the mediator-outcome association or risk the power to detect the total effect/intention-to-treat effect being lower than planned.

Comparison of Imputation Methods for Categorical Real-World Prostate Cancer Data with Natural Order.

Missing values (NA) often occur in cancer research, which may be due to reasons such as data protection, data loss, or missing follow-up data. Such incomplete patient information can have an impact on prediction models and other data analyses. Imputation methods are a tool for dealing with NA. Cancer data is often presented in an ordered categorical form, such as tumour grading and staging, which requires special methods. This work compares mode imputation, k nearest neighbour (knn) imputation, and, in the context of Multiple Imputation by Chained Equations (MICE), logistic regression model with proportional odds (mice_polr) and random forest (mice_rf) on a real-world prostate cancer dataset provided by the Cancer Registry of Rhineland-Palatinate in Germany. Our dataset contains relevant information for the risk classification of patients and the time between date of diagnosis and date of death. For the imputation comparison, we use Rubin's (1974) Missing Completely At Random (MCAR) mechanism to remove 10%, 20%, 30%, and 50% observations. The results are evaluated and ranked based on the accuracy per patient. Mice_rf performs significantly best for each percentage of NA, followed by knn, and mice_polr performs significantly worst. Furthermore, our findings indicate that the accuracy of imputation methods increases with a lower number of categories, a relatively even proportion of patients in the categories, or a majority of patients in a particular category.

Factor-augmented transformation models for interval-censored failure time data.

Interval-censored failure time data frequently arise in various scientific studies where each subject experiences periodical examinations for the occurrence of the failure event of interest, and the failure time is only known to lie in a specific time interval. In addition, collected data may include multiple observed variables with a certain degree of correlation, leading to severe multicollinearity issues. This work proposes a factor-augmented transformation model to analyze interval-censored failure time data while reducing model dimensionality and avoiding multicollinearity elicited by multiple correlated covariates. We provide a joint modeling framework by comprising a factor analysis model to group multiple observed variables into a few latent factors and a class of semiparametric transformation models with the augmented factors to examine their and other covariate effects on the failure event. Furthermore, we propose a nonparametric maximum likelihood estimation approach and develop a computationally stable and reliable expectation-maximization algorithm for its implementation. We establish the asymptotic properties of the proposed estimators and conduct simulation studies to assess the empirical performance of the proposed method. An application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study is provided. An R package ICTransCFA is also available for practitioners. Data used in preparation of this article were obtained from the ADNI database.

A note on the Wilcoxon-Mann-Whitney test and tied observations.

Recently, it was recommended to omit tied observations before applying the two-sample Wilcoxon-Mann-Whitney test McGee M. et al. (2018). Using a simulation study, we argue for exact tests using all the data (including tied values) as a preferable approach. Exact tests, with tied observations included guarantee the type I error rate with a better exploitation of the significance level and a larger power than the corresponding tests after the omission of tied observations. The omission of ties can produce a considerable change in the shape of the sample, and so can violate underlying test assumptions. Thus, on both theoretical and practical grounds, the recommendation to omit tied values cannot be supported, relative to analysing the whole data set in the same way whether or not ties occur, preferably with an exact permutation test.

Handling Missing Data in COVID-19 Incidence Estimation: Secondary Data Analysis.

Background: The COVID-19 pandemic has revealed significant challenges in disease forecasting and in developing a public health response, emphasizing the need to manage missing data from various sources in making accurate forecasts. Objective: We aimed to show how handling missing data can affect estimates of the COVID-19 incidence rate (CIR) in different pandemic situations. Methods: This study used data from the COVID-19/SARS-CoV-2 surveillance system at the National Institute of Hygiene and Epidemiology, Vietnam. We separated the available data set into 3 distinct periods: zero COVID-19, transition, and new normal. We randomly removed 5% to 30% of data that were missing completely at random, with a break of 5% at each time point in the variable daily caseload of COVID-19. We selected 7 analytical methods to assess the effects of handling missing data and calculated statistical and epidemiological indices to measure the effectiveness of each method. Results: Our study examined missing data imputation performance across 3 study time periods: zero COVID-19 (n=3149), transition (n=1290), and new normal (n=9288). Imputation analyses showed that K-nearest neighbor (KNN) had the lowest mean absolute percentage change (APC) in CIR across the range (5% to 30%) of missing data. For instance, with 15% missing data, KNN resulted in 10.6%, 10.6%, and 9.7% average bias across the zero COVID-19, transition, and new normal periods, compared to 39.9%, 51.9%, and 289.7% with the maximum likelihood method. The autoregressive integrated moving average model showed the greatest mean APC in the mean number of confirmed cases of COVID-19 during each COVID-19 containment cycle (CCC) when we imputed the missing data in the zero COVID-19 period, rising from 226.3% at the 5% missing level to 6955.7% at the 30% missing level. Imputing missing data with median imputation methods had the lowest bias in the average number of confirmed cases in each CCC at all levels of missing data. In detail, in the 20% missing scenario, while median imputation had an average bias of 16.3% for confirmed cases in each CCC, which was lower than the KNN figure, maximum likelihood imputation showed a bias on average of 92.4% for confirmed cases in each CCC, which was the highest figure. During the new normal period in the 25% and 30% missing data scenarios, KNN imputation had average biases for CIR and confirmed cases in each CCC ranging from 21% to 32% for both, while maximum likelihood and moving average imputation showed biases on average above 250% for both CIR and confirmed cases in each CCC. Conclusions: Our study emphasizes the importance of understanding that the specific imputation method used by investigators should be tailored to the specific epidemiological context and data collection environment to ensure reliable estimates of the CIR.

Testing for similarity of multivariate mixed outcomes using generalized joint regression models with application to efficacy-toxicity responses.

A common problem in clinical trials is to test whether the effect of an explanatory variable on a response of interest is similar between two groups, for example, patient or treatment groups. In this regard, similarity is defined as equivalence up to a pre-specified threshold that denotes an acceptable deviation between the two groups. This issue is typically tackled by assessing if the explanatory variable's effect on the response is similar. This assessment is based on, for example, confidence intervals of differences or a suitable distance between two parametric regression models. Typically, these approaches build on the assumption of a univariate continuous or binary outcome variable. However, multivariate outcomes, especially beyond the case of bivariate binary responses, remain underexplored. This paper introduces an approach based on a generalized joint regression framework exploiting the Gaussian copula. Compared to existing methods, our approach accommodates various outcome variable scales, such as continuous, binary, categorical, and ordinal, including mixed outcomes in multi-dimensional spaces. We demonstrate the validity of this approach through a simulation study and an efficacy-toxicity case study, hence highlighting its practical relevance.

Ultrasound-guided supraclavicular block versus Bier block for emergency reduction of upper limb injuries: statistical analysis plan.

BACKGROUND: Ultrasound-guided supraclavicular block (UGSCB) is an emerging technique gaining interest amongst emergency physicians that provides regional anaesthesia to the upper limb to tolerate painful procedures. It offers an alternative to the more traditional technique of a Bier block (BB). However, the effectiveness or safety of UGSCB when performed in the emergency department (ED) is unclear. METHODS: SUPERB (SUPraclavicular block for Emergency Reduction versus Bier block) is a prospective open-label non-inferiority randomised controlled trial comparing the effectiveness of UGSCB versus BB for closed reduction of upper limb fractures and/or dislocations. Adult patients presenting with upper limb fracture and/or dislocation requiring closed reduction in ED were randomised to either UGSCB or BB. Once regional anaesthesia is obtained, closed reduction of the injured part was performed and immobilised. The primary outcome is maximal pain experienced during closed reduction measured via a visual analogue scale (VAS). Secondary outcomes include post-reduction pain, patient satisfaction, total opioid requirement in ED, ED length of stay, adverse events and regional anaesthesia failure. RESULTS: Primary outcome analysis will be performed using both the intention-to-treat and per-protocol populations. The between-group difference in maximum pain intensity will be assessed using linear regression modelling with trial group allocation (UGSCB vs BB) included as a main affect. A pre-specified non-inferiority margin of 20 mm on the VAS scale will be used to establish non-inferiority of UGSCB compared to BB. CONCLUSION: SUPERB is the first randomised controlled trial to investigate the effectiveness and safety of UGSCB in the ED. The trial has the potential to demonstrate that UGSCB is an alternative safe and effective option for the management of upper extremity emergencies in the ED.

Reduced-rank clustered coefficient regression for addressing multicollinearity in heterogeneous coefficient estimation.

Clustered coefficient regression (CCR) extends the classical regression model by allowing regression coefficients varying across observations and forming clusters of observations. It has become an increasingly useful tool for modeling the heterogeneous relationship between the predictor and response variables. A typical issue of existing CCR methods is that the estimation and clustering results can be unstable in the presence of multicollinearity. To address the instability issue, this paper introduces a low-rank structure of the CCR coefficient matrix and proposes a penalized non-convex optimization problem with an adaptive group fusion-type penalty tailor-made for this structure. An iterative algorithm is developed to solve this non-convex optimization problem with guaranteed convergence. An upper bound for the coefficient estimation error is also obtained to show the statistical property of the estimator. Empirical studies on both simulated datasets and a COVID-19 mortality rate dataset demonstrate the superiority of the proposed method to existing methods.

Controlling false discovery rate for mediator selection in high-dimensional data.

The need to select mediators from a high dimensional data source, such as neuroimaging data and genetic data, arises in much scientific research. In this work, we formulate a multiple-hypothesis testing framework for mediator selection from a high-dimensional candidate set, and propose a method, which extends the recent development in false discovery rate (FDR)-controlled variable selection with knockoff to select mediators with FDR control. We show that the proposed method and algorithm achieved finite sample FDR control. We present extensive simulation results to demonstrate the power and finite sample performance compared with the existing method. Lastly, we demonstrate the method for analyzing the Adolescent Brain Cognitive Development (ABCD) study, in which the proposed method selects several resting-state functional magnetic resonance imaging connectivity markers as mediators for the relationship between adverse childhood events and the crystallized composite score in the NIH toolbox.

An interpretable Bayesian clustering approach with feature selection for analyzing spatially resolved transcriptomics data.

Recent breakthroughs in spatially resolved transcriptomics (SRT) technologies have enabled comprehensive molecular characterization at the spot or cellular level while preserving spatial information. Cells are the fundamental building blocks of tissues, organized into distinct yet connected components. Although many non-spatial and spatial clustering approaches have been used to partition the entire region into mutually exclusive spatial domains based on the SRT high-dimensional molecular profile, most require an ad hoc selection of less interpretable dimensional-reduction techniques. To overcome this challenge, we propose a zero-inflated negative binomial mixture model to cluster spots or cells based on their molecular profiles. To increase interpretability, we employ a feature selection mechanism to provide a low-dimensional summary of the SRT molecular profile in terms of discriminating genes that shed light on the clustering result. We further incorporate the SRT geospatial profile via a Markov random field prior. We demonstrate how this joint modeling strategy improves clustering accuracy, compared with alternative state-of-the-art approaches, through simulation studies and 3 real data applications.

Sample size calculation for comparing two ROC curves.

Biomarkers are key components of personalized medicine. In this paper, we consider biomarkers taking continuous values that are associated with disease status, called case and control. The performance of such a biomarker is evaluated by the area under the curve (AUC) of its receiver operating characteristic curve. Oftentimes, two biomarkers are collected from each subject to test if one has a larger AUC than the other. We propose a simple non-parametric statistical test for comparing the performance of two biomarkers. We also present a simple sample size calculation method for this test statistic. Our sample size formula requires specification of AUC values (or the standardized effect size of each biomarker between cases and controls together with the correlation coefficient between two biomarkers), prevalence of cases in the study population, type I error rate, and power. Through simulations, we show that the testing on two biomarkers controls type I error rate accurately and the proposed sample size closely maintains specified statistical power.

Absolute risk from double nested case-control designs: cause-specific proportional hazards models with and without augmented estimating equations.

We estimate relative hazards and absolute risks (or cumulative incidence or crude risk) under cause-specific proportional hazards models for competing risks from double nested case-control (DNCC) data. In the DNCC design, controls are time-matched not only to cases from the cause of primary interest, but also to cases from competing risks (the phase-two sample). Complete covariate data are available in the phase-two sample, but other cohort members only have information on survival outcomes and some covariates. Design-weighted estimators use inverse sampling probabilities computed from Samuelsen-type calculations for DNCC. To take advantage of additional information available on all cohort members, we augment the estimating equations with a term that is unbiased for zero but improves the efficiency of estimates from the cause-specific proportional hazards model. We establish the asymptotic properties of the proposed estimators, including the estimator of absolute risk, and derive consistent variance estimators. We show that augmented design-weighted estimators are more efficient than design-weighted estimators. Through simulations, we show that the proposed asymptotic methods yield nominal operating characteristics in practical sample sizes. We illustrate the methods using prostate cancer mortality data from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial Study of the National Cancer Institute.

Prompt closure versus gradual weaning of external ventricular drain for hydrocephalus following aneurysmal subarachnoid haemorrhage: a statistical analysis plan for the DRAIN randomised clinical trial.

BACKGROUND: Insertion of an external ventricular drain (EVD) is a first-line treatment of acute hydrocephalus caused by aneurysmal subarachnoid haemorrhage (aSAH). Once the patient is clinically stable, the EVD is either removed or replaced by a permanent internal shunt. The optimal strategy for cessation of the EVD is unknown. Prompt closure carries a risk of acute hydrocephalus or redundant shunt implantations, whereas gradual weaning may increase the risk of EVD-related infections. METHODS: DRAIN (Danish RAndomised Trial of External Ventricular Drainage Cessation IN Aneurysmal Subarachnoid Haemorrhage) is an international multicentre randomised clinical trial comparing prompt closure versus gradual weaning of the EVD after aSAH. The primary outcome is a composite of VP-shunt implantation, all-cause mortality, or EVD-related infection. Secondary outcomes are serious adverse events excluding mortality and health-related quality of life (EQ-5D-5L). Exploratory outcomes are modified Rankin Scale, Fatigue Severity Scale, Glasgow Outcome Scale Extended, and length of stay in the neurointensive care unit and hospital. Outcome assessment will be performed 6 months after ictus. Based on the sample size calculation (event proportion 80% in the gradual weaning group, relative risk reduction 20%, alpha 5%, power 80%), 122 participants are required in each intervention group. Outcome assessment for the primary outcome, statistical analyses, and conclusion drawing will be blinded. Two independent statistical analyses and reports will be tracked using a version control system, and both will be published. Based on the final statistical report, the blinded steering group will formulate two abstracts. CONCLUSION: We present a pre-defined statistical analysis plan for the randomised DRAIN trial, which limits bias, p-hacking, and data-driven interpretations. This statistical analysis plan is accompanied by tables with simulated data, which increases transparency and reproducibility. TRIAL REGISTRATION: ClinicalTrials.gov identifier: NCT03948256. Registered on May 13, 2019.