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Trial Sequential Analysis: Novel Approach for Meta-Analysis Anesth Pain Med 2021;16:138-150 https://doi.org/10.17085/apm.21038 Review pISSN 1975-5171 • eISSN 2383-7977 Trial sequential analysis: novel approach for meta-analysis Hyun Kang Received April 19, 2021 Department of Anesthesiology and Pain Medicine, Chung-Ang University College of Accepted April 25, 2021 Medicine, Seoul, Korea Systematic reviews and meta-analyses rank the highest in the evidence hierarchy. However, they still have the risk of spurious results because they include too few studies and partici- pants. The use of trial sequential analysis (TSA) has increased recently, providing more infor- mation on the precision and uncertainty of meta-analysis results. This makes it a powerful tool for clinicians to assess the conclusiveness of meta-analysis. TSA provides monitoring boundaries or futility boundaries, helping clinicians prevent unnecessary trials. The use and Corresponding author Hyun Kang, M.D., Ph.D. interpretation of TSA should be based on an understanding of the principles and assump- Department of Anesthesiology and tions behind TSA, which may provide more accurate, precise, and unbiased information to Pain Medicine, Chung-Ang University clinicians, patients, and policymakers. In this article, the history, background, principles, and College of Medicine, 84 Heukseok-ro, assumptions behind TSA are described, which would lead to its better understanding, imple- Dongjak-gu, Seoul 06974, Korea mentation, and interpretation. Tel: 82-2-6299-2586 Fax: 82-2-6299-2585 E-mail: [email protected] Keywords: Interim analysis; Meta-analysis; Statistics; Trial sequential analysis. INTRODUCTION termined number of patients was reached [2]. A systematic review is a research method that attempts Sequential analysis is a statistical method in which the fi- to collect all empirical evidence according to predefined nal number of patients analyzed is not predetermined, but inclusion and exclusion criteria to answer specific and fo- sampling or enrollment of patients is decided by a prede- cused questions [3]. It uses clear, transparent, and explicit termined stopping rule such as satisfying a statistical sig- methods to minimize bias, providing more reliable infor- nificance. Accordingly, the investigators may draw a con- mation [4]. Meta-analysis is a statistical analytic method clusion earlier than that with the traditional statistical that integrates and summarizes the results from individual methods, reducing time, cost, effort, and resources. studies or examines the sources of heterogeneity among The concept and method of sequential analysis were in- studies [5]. troduced and described as expeditious industrial quality Systematic review and meta-analysis rank highest in evi- control methods during World War II by Abraham Wald [1]. dence hierarchy and provides evidence for clinical prac- This concept was used to prove the desired or undesired tice, healthcare, and policy development. Its use and appli- intervention effects by analyzing data from ongoing trials. cation in clinical practice have increased [6,7]; however, After World War II, Peter Armitage introduced a sequential they are not free from errors and biases [8]. Many system- analysis method to medical research and suggested apply- atic reviews and meta-analyses have included too few ing a strict significance level to stop a trial before a prede- studies and patients to obtain sufficient statistical power, This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Copyright © the Korean Society of Anesthesiologists, 2021 138 Trial sequential analysis leading to spurious positive results [9]. Some positive find- The RIS in meta-analysis is defined as the number of ings from the meta-analysis may be caused by a random events or patients from the included studies necessary to error (by chance) rather than the true effects of the inter- accept or reject the statistical hypothesis [15]. vention. Therefore, results from systematic reviews and The sample size calculation performed in a single RCT is meta-analyses may often increase the likelihood of overes- based on the effect size, significance level, and power [16]. timation (Type I errors) or underestimation (Type II errors) In a single RCT setting, predetermined homogenous pa- [10,11]. Furthermore, because meta-analysis can be updat- tients, intervention, and methodology are used. However, ed when there is a new clinical trial, the inflation of Type I in a meta-analysis setting, a wide range of patients, regi- and II errors from multiple and sequential testing is of ma- mens of intervention, different experimental environ- jor concern [12]. ments, and quality of methodology may be applied in each Trial sequential analysis (TSA) has been developed to re- study. Heterogeneity may arise across the included studies, solve these problems. Conceptually, TSA adopts sequential which increases the sample size needed to accept or reject analysis methods for systematic reviews and meta-analy- the statistical hypothesis. Therefore, the RIS in meta-analy- ses. However, TSA is different from sequential analysis in a sis should be adjusted considering the heterogeneity be- single trial in that the enrolled unit is not a patient but a tween included studies and should be at least as large as study. Sequential analysis is performed at predetermined, the sample size in a homogenous single RCT [15]. regular intervals, although the number of enrolled patients As in a single RCT, assumptions to calculate RIS should did not reach predetermined number of patients. However, be predefined before the systematic review and meta-anal- in TSA, the trials were included in chronological order, and ysis. A single RCT with too few patients is thought to have analysis was performed repetitively and cumulatively after low precision and power. Similarly, results from meta-anal- new trials were conducted. TSA also provided an adjusted yses with too few studies and patients are assumed to have significance level for controlling Type I and II errors. an increased likelihood of overestimation or underestima- Therefore, the adaptation of TSA when performing and tion due to lack of precision and power in the intervention presenting a meta-analysis has been increasing recently effect [10,17]. Therefore, the use of appropriate RIS is im- [13,14]. portant to increase the quality of meta-analysis. This article aims to describe the history, background, The TSA program (Copenhagen Trial Unit, Centre for principles, and assumptions behind the use and interpre- Clinical Intervention Research, Denmark) provides a sim- tation of TSA. ple and useful way to calculate the RIS. The TSA program uses the heterogeneity-adjustment factor (AF) to adjust for BACKGROUND AND PRINCIPLE OF TRIAL heterogeneity among the included trials. AF is calculated SEQUENTIAL ANALYSIS as the total variance in a random-effects model divided by the total variance in a fixed-effect model as follows: Required information size AF = Meta-analysis is a statistical method used to synthesize a pooled estimate by combining the estimates of two or more AF: heterogeneity-adjustment factor individual studies. As the number of events or patients in- VR: total variance in a random-effects model crease, the power and precision of the intervention effect VF: total variance in a fixed-effect model estimate also increases. Thus, a more reliable estimate can Because the total variance in a random-effects model is be obtained from meta-analysis than a single randomized greater than or equal to the total variance in a fixed-effect controlled trial (RCT) [4]. model (VR ≥VF), AF is always greater than or equal to 1. A single RCT performs sample size calculation or power Finally, the RIS adjusted for heterogeneity between trials analysis to ensure that the study provides reliable statistical (random) is calculated by multiplying the non-adjusted inference and targeted power. Similar to sample size calcu- RIS (fixed) with AF. lation or power analysis in a single RCT, the required infor- mation size (RIS) or optimum information size was pro- Adjusted RIS = AF × nonadjusted RIS posed and used in the meta-analysis. www.anesth-pain-med.org 139 Anesth Pain Med In the TSA program, RIS is automatically calculated by Multiple comparisons and multiple testing problems oc- defining the statistical hypotheses, namely information cur when data is sampled repeatedly from the same data size, Type I error, power, relative risk reduction, incidence set, data is analyzed simultaneously or multiple times, or in the intervention and control arms, and heterogeneity data is analyzed sequentially by observing more results. correction in the Alpha-spending boundaries setting win- Multiple comparisons inflate the possibility of a Type I er- dow is activated in TSA tab and displayed in the TSA dia- ror (α). For example, if statistical analysis is performed at a gram (Fig. 1). This will be discussed later in TSA tab sec- significance level of 5% and the null hypothesis for statisti- tion. cal analysis is true, there is a 5% chance for a Type I error. However, if statistical analyses were performed 100 times Alpha spending functions and monitoring boundaries for the same situation, the expected number of Type I er- rors would be 5, and the probability of occurrence of at Type I error, or false positive, is the error of rejecting a least one Type I error would be 99.45% (Fig. 2). Therefore, null hypothesis when it is true, and Type II error, or false it is very important to adjust the α level so that the overall negative, is the error of accepting a null hypothesis when Type I error remains within the desired level. the alternative hypothesis is true. Intuitively, Type I error An interim analysis before the completion of data collec- occurs when a statistical difference is observed, although tion may also cause inflation of Type I error in the absence there is no statistically significant difference in truth, and of appropriate adjustment.
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