Confidence Intervals

Misinterpretation and abuse of statistical tests, confidence intervals, and statistical power have been decried for decades, yet remain rampant. A key problem is that there are no interpretations of these concepts that are at once simple, intuitive, correct, and foolproof. Instead, correct use and interpretation of these statistics requires an attention to detail which seems to tax the patience of working scientists. This high cognitive demand has led to an epidemic of shortcut definitions and interpretations that are simply wrong, sometimes disastrously so-and yet these misinterpretations dominate much of the scientific literature. In light of this problem, we provide definitions and a discussion of basic statistics that are more general and critical than typically found in traditional introductory expositions. Our goal is to provide a resource for instructors, researchers, and consumers of statistics whose knowledge of statistical theory and technique may be limited but who wish to avoid and spot misinterpretations. We emphasize how violation of often unstated analysis protocols (such as selecting analyses for presentation based on the P values they produce) can lead to small P values even if the declared test hypothesis is correct, and can lead to large P values even if that hypothesis is incorrect. We then provide an explanatory list of 25 misinterpretations of P values, confidence intervals, and power. We conclude with guidelines for improving statistical interpretation and reporting.

BackgroundThe GRADE-CERQual (Confidence in Evidence from Reviews of Qualitative research) approach has been developed by the GRADE (Grading of Recommendations Assessment, Development and Evaluation) Working Group. The approach has been developed to support the use of findings from qualitative evidence syntheses in decision making, including guideline development and policy formulation. CERQual includes four components for assessing how much confidence to place in findings from reviews of qualitative research (also referred to as qualitative evidence syntheses): (1) methodological limitations, (2) coherence, (3) adequacy of data and (4) relevance. This paper is part of a series providing guidance on how to apply CERQual and focuses on making an overall assessment of confidence in a review finding and creating a CERQual Evidence Profile and a CERQual Summary of Qualitative Findings table.MethodsWe developed this guidance by examining the methods used by other GRADE approaches, gathering feedback from relevant research communities and developing consensus through project group meetings. We then piloted the guidance on several qualitative evidence syntheses before agreeing on the approach.ResultsConfidence in the evidence is an assessment of the extent to which a review finding is a reasonable representation of the phenomenon of interest. Creating a summary of each review finding and deciding whether or not CERQual should be used are important steps prior to assessing confidence. Confidence should be assessed for each review finding individually, based on the judgements made for each of the four CERQual components. Four levels are used to describe the overall assessment of confidence: high, moderate, low or very low. The overall CERQual assessment for each review finding should be explained in a CERQual Evidence Profile and Summary of Qualitative Findings table.ConclusionsStructuring and summarising review findings, assessing confidence in those findings using CERQual and creating a CERQual Evidence Profile and Summary of Qualitative Findings table should be essential components of undertaking qualitative evidence syntheses. This paper describes the end point of a CERQual assessment and should be read in conjunction with the other papers in the series that provide information on assessing individual CERQual components.

Interval estimates - estimates of parameters that include an allowance for sampling uncertainty - have long been touted as a key component of statistical analyses. There are several kinds of interval estimates, but the most popular are confidence intervals (CIs): intervals that contain the true parameter value in some known proportion of repeated samples, on average. The width of confidence intervals is thought to index the precision of an estimate; CIs are thought to be a guide to which parameter values are plausible or reasonable; and the confidence coefficient of the interval (e.g., 95 %) is thought to index the plausibility that the true parameter is included in the interval. We show in a number of examples that CIs do not necessarily have any of these properties, and can lead to unjustified or arbitrary inferences. For this reason, we caution against relying upon confidence interval theory to justify interval estimates, and suggest that other theories of interval estimation should be used instead.

Sequential trial emulation (STE) is an approach to estimating causal treatment effects by emulating a sequence of target trials from observational data. In STE, inverse probability weighting is commonly utilised to address time-varying confounding and/or dependent censoring. Then structural models for potential outcomes are applied to the weighted data to estimate treatment effects. For inference, the simple sandwich variance estimator is popular but conservative, while nonparametric bootstrap is computationally expensive, and a more efficient alternative, linearised estimating function (LEF) bootstrap, has not been adapted to STE. We evaluated the performance of various methods for constructing confidence intervals (CIs) of marginal risk differences in STE with survival outcomes by comparing the coverage of CIs based on nonparametric/LEF bootstrap, jackknife, and the sandwich variance estimator through simulations. LEF bootstrap CIs demonstrated better coverage than nonparametric bootstrap CIs and sandwich-variance-estimator-based CIs with small/moderate sample sizes, low event rates and low treatment prevalence, which were the motivating scenarios for STE. They were less affected by treatment group imbalance and faster to compute than nonparametric bootstrap CIs. With large sample sizes and medium/high event rates, the sandwich-variance-estimator-based CIs had the best coverage and were the fastest to compute. These findings offer guidance in constructing CIs in causal survival analysis using STE.