What if we conduct multiple interim analyses? In trials for rare diseases, it is often difficult to achieve satisfactory power for a single confirmatory hypothesis, let alone more than one.13 As such, most trials of rare diseases either use composite outcomes as a strategy to enhance power or they are designed as exploratory investigations with no multiplicity implications. Every time you perform a statistical significance test, you run a chance of being fooled by random fluctuations into thinking that some real effect is present in your data when, in fact, none exists. P is the probability of at least one significant test; It is not easy to answer, because there is no consensus in the scientific community, nor even at the regulatory authorities. phase I or phase II trials and some pilot trials). The key difference between an exploratory and confirmatory trial is that the latter is designed to seek a definitive answer to a specified hypothesis with the findings intended to be used for final decision making, including the licensing of treatments.12 Whereas findings from an exploratory trial will have to be tested in further trials, results from a confirmatory trial can address a pre-specified key hypothesis for generating evidence to inform decision making.5 Note that the results of trials designed as confirmatory, depending upon their findings, may also require confirmation or refutation in future trials. When the verb (predicator) in a finite clause is constructed with auxiliaries (helping verbs), the finite verb is always the first auxiliary in the chain.. Each auxiliary verb licenses specific non . If we test each of the individual outcomes separately at a nominal 5% level and obtain any significant difference, the probability of a spurious claim of significance is higher than the anticipated 5%.2,16,17. A hierarchical testing strategy: Rank your endpoints in descending order of importance. Explanation: The total number of times a known factor appears in the factored form of the equation of a polynomial is called the multiplicity of the polynomial. To make you understand the problem better, we will provide you an example of a paper published in 2014, that estimated the percentage of these jobs at around 50% in multi-arm trials. Turk DC, Dworkin RH, McDermott MPet al. We have presented an introduction to multiplicity adjustments in clinical trials, aiming to provide a non-technical scoping overview and to reduce the confusion around multiple testing questions. For example, the guidelines on this problem provided by EMAs (European Medicines Agency) leave room for a thousand interpretations, also due to the fact that the possible study designs of a clinical trial are potentially infinite. Confusion about multiplicity issues can be reduced or avoided by considering the potential impact of multiplicity on type I and II errors and, if necessary pre-specifying statistical approaches to either avoid or adjust for multiplicity in the trial protocol or analysis plan. Sensitivity analyses may include using different definitions for the outcomes, comparing alternative approaches for dealing with missing data or data outliers, adjusting for baseline imbalances, performing competing risk analyses, tackling non-adherence or protocol violation, etc.47 Findings from sensitivity analyses are considered subsidiary support for results from primary analyses. *Corresponding author. The multiplicity can arise in many different situations in clinical trials; some of them are listed below: Multiple arms Co-primary endpoints For example, a trial may have multi-arm treatments, evaluate several primary outcomes, require multiple interim analyses and collect data repeatedly. John C. Pezzullo, PhD, has held faculty appointments in the departments of biomathematics and biostatistics, pharmacology, nursing, and internal medicine at Georgetown University. It is important to remind ourselves that multiplicity adjustments primarily apply to confirmatory hypotheses and corresponding analyses. Confusion about multiplicity issues can be reduced or avoided by considering the potential impact of multiplicity on type I and II errors and, if necessary pre-specifying statistical approaches to either avoid or adjust for multiplicity in the trial protocol or analysis plan. Adjusting for multiple testing - when and how? no difference or no change) hypothesis, which is culminated in a single numeric, namely the P value. Any definitive finding for secondary outcomes may require further confirmatory studies to support them. In conclusion, multiplicity adjustments remain a challenging issue in trials, with a sizeable proportion of published trials inadequately correcting for multiplicity. For instance, if we have five independent or related true null hypotheses, each tested simultaneously at a nominal significance level of =5% (where refers to the probability of a type I error), the true type I error over all the tests is 23%. This is because the zero x=3, which is related to the factor (x-3), repeats twice. This adjustment is available as an option for post hoc tests and for the estimated marginal means feature. Besides the increased risk of spurious statistical significance, multiplicity also has important implications for sample size determination and interpretation of study results.1,9 Therefore we need to consider multiplicity adjustments in designing, analysing and interpreting trials. Copyright 2023 International Epidemiological Association. 6. 1. Control the alpha level across only the most important hypotheses. You have several choices, including the following: Don't control for multiplicity and accept the likelihood that some of your "significant" findings will be falsely significant. According to Kenneth, the correction for multiplicity should always be avoided because it would make scientific research too conservative. All authors read and approved the final version of the manuscript. An individual trial may also have both confirmatory and exploratory aspects. . Published by Oxford University Press on behalf of the International Epidemiological Association, The impact of diabetes during pregnancy on neonatal outcomes among the Aboriginal population in Western Australia: a whole-population study, Cohort Profile: ChinaHEART (Health Evaluation And risk Reduction through nationwide Teamwork) Cohort, Ionizing radiation and solid cancer mortality among US nuclear facility workers, Three phases of increasing complexity in estimating vaccine protection, Risk of type 2 diabetes after diagnosed gestational diabetes is enhanced by exposure to PM, About the International Journal of Epidemiology, About the International Epidemiological Association. Next, we describe some of the considerations involved in the case of multiple study arms. In this case some authors argue that we should consider whether the treatments are related or not, or whether they are of the same nature. . There are a large number of publications discussing statistical methods for multiplicity adjustments in the literature.1,6,5962 Herein we focus on commonly encountered questions about the need for multiplicity corrections, using a tutorial style. To adapt is to make a change in character, to make something useful in a new way: to adapt a paper clip for a hairpin. Clinical trials with multiple outcomes: a statistical perspective on their design, analysis, and interpretation, Analysing multiple endpoints in clinical trials of pain treatments: IMMPACT recommendations. Initiative on Methods, Measurement, and Pain Assessment in Clinical Trials. Multiplicity most commonly means a large number or a great variety. Although it is not possible to address the problem of multiplicity in depth, before leaving we try to understand briefly what we encounter when we ignore the presence of multiple testing in our study and do not adjust the level of a statistical significance. Multiplicity refers to the potential inflation of the type I error rate as a result of multiple testing, for example due to multiple subgroup comparisons, comparisons across multiple treatment arms, analysis of multiple outcomes, and multiple analyses of the same outcome at different times. Results are presented in easy-to-use tables and flow diagrams to mitigate the burden of reading and understanding, especially for novice researchers. Therefore, we recommend that trialists seek and heed the expert advice of biostatisticians or methodologists in identifying potential multiplicity problems and determining statistical approaches for addressing them during the study design and analysis stages. This study received no specific funding. This multi-arm design can improve efficiency by reducing the sample size over that required for separate trials, or increase statistical power for the same sample size.2,4,10 One systematic review reported that among all the randomized controlled trials published in 2009, the proportion of multi-arm designs was 17.6%, reflecting the increased popularity of multi-arm trials.11 However, when multiple comparisons are made in multi-arm trials, multiplicity adjustments may need to be considered to avoid an increase in the type I error rate. Analyses by subgroup and all other post-hoc tests are almost always considered to be exploratory, so the correction becomes useless. Since they do not have a confirmatory nature, it is not required to conduct multiplicity adjustments for sensitivity analyses. This is done via the adjust argument. I have written almost always because in some cases the subgroup analysis can have a confirmatory role in a hypothesis unrelated to the main hypothesis of the study. The . Subgroup analyses satisfying the three aforementioned conditions are considered as having a confirmatory nature, thereby requiring multiplicity adjustments.5,24,43,44 Whereas many trials pre-specify subgroup analyses which are considered supportive to examine treatment consistency, others conduct a posteriori subgroup analyses after the finalized protocol and/or data collection have been completed. When you say that you require p < 0.05 for significance, you're testing at the 0.05 (or 5 percent) alpha level or saying that you want to limit your Type I error rate to 5 percent. Then test the next most important one, again using p < 0.05 for significance.
\nContinue until you get a nonsignificant result (p > 0.05); then stop testing (or consider all further tests to be only exploratory and don't draw any formal conclusions about them).
\n \nControlling the false discovery rate (FDR): This approach has become popular in recent years to deal with large-scale multiplicity, which arises in areas like genomic testing and digital image analysis that may involve many thousands of tests (such as one per gene or one per pixel) instead of just a few.
\nInstead of trying to avoid even a single false conclusion of significance (as the Bonferroni and other classic alpha control methods do), you simply want to control the proportion of tests that come out falsely positive, limiting that false discovery rate to some reasonable fraction of all the tests. About half: is it too much? There is a number of techniques that allow us to distribute that fateful 5% significance level by dividing it into different tests that are conducted within the study. . Where: This would apply to trials generally, including factorial trials, and trials with superiority, equivalence and non-inferiority aims. a means (such as a mechanism) by which things are adjusted one to another. differences between treatment groups), within-subject effects (e.g. What is the prevalence of multiplicity among cardiovascular randomized clinical trials published in 6 medical journals with a high impact factor, and how frequently are multiplicity adjustments made in these trials? How to make it easier. Recently, many advanced multiplicity adjustment procedures have been proposed and developed. Results are presented in an easy-to-use table and flow diagrams. Lan and DeMetss approach37 and Kim and DeMetss method38), which is summarized in a tutorial in detail by Emerson etal.39. You conduct your tests and declare the limit of statistical significance considered at 5%. How to write a report on a fitted mixed-effect model in a manuscript or in a thesis correctly? Adrian Parr: Although Multiplicity is used throughout Deleuzes work in many different ways and contexts there are some essential traits: It is a complex that does not refer to a prior unity - either a fragmented whole, or manifold expressions of a single concept. Flow diagram of conditions needed for multiplicity adjustment considerations and recommendations in terms of Outcome. This strategy is often used with hypotheses related to secondary and exploratory objectives; the protocol usually states that no final inferences will be made from these exploratory tests. DOI: 10.1016/s0197-2456(00)00106-9 Abstract Multiplicity in clinical trials may appear under several different guises: multiple endpoints, multiple treatment arm comparisons, and multiple looks at the data during interim monitoring, to name a few. For example: if the three arms of the study are two doses of drug and a placebo, then the correction is appropriate. indicate in the methods chapter that it was not corrected for the multiplicity given the exploratory nature of the study; clarify the decision in the discussion chapter. Controlling the false discovery rate (FDR): This approach has become popular in recent years to deal with large-scale multiplicity, which arises in areas like genomic testing and digital image analysis that may involve many thousands of tests (such as one per gene or one per pixel) instead of just a few. how to decide whether to adjust or not for the multiplicity? The analysis on a subgroup may aim, for example, at identifying the link between the degree of alcoholism and the fertility level of males. For example, a phase III randomized controlled trial was conducted to explore the effect of addition of docetaxel to two platinum regimens (i.e. It can also mean the state of being multiple. So to control overall alpha to 0.05 across two primary endpoints, you need p < 0.025 for significance when testing each one.
\nA hierarchical testing strategy: Rank your endpoints in descending order of importance. 6 for example, have suggested that an FWER adjustment is only necessary if 'assessing multiple hypotheses within a multi-arm trial has increased . What does multiplicity mean? For ref_grid () and emmeans () results, the default is adjust = "none". The most used technique is the Bonferroni correction. In the context of multiple outcomes, depending on the clinical objective, the power can be defined as: 'disjunctive power', the probability of detecting at least one true intervention effect across all the outcomes or ' marginal power' the probability of finding a true intervention effect on a nominated outcome. To adjust is to move into proper position for use: to adjust the eyepiece of a telescope. For example, the PROTECT (Prophylaxis for Thromboembolism in Critical Care Trial) was conducted to evaluate the effect of dalteparin versus unfractionated heparin on proximal leg deep vein thrombosis in critically ill patients.50 Subsequently, some studies used the data to investigate the risk factors of major bleeding,51 thrombocytopenia52 and all-cause death,53 and to explore the predictors and consequences of co-enrolment of critically ill patients.54 These secondary analyses were not predefined in the protocol of the trial because they were unrelated to the main research question.55 Some secondary analyses reflect secondary research questions generated and logged before the trial ends by the participating international trialists, whereas other secondary analyses are not nested within original analytical plans. There is a consensus in the literature that multiplicity adjustments are required if the different treatment arms are related.4 For instance, if a trial evaluates different dosages or regimens of a treatment compared with the same control arm, then adequate multiple testing adjustments should be performed. Details of advanced methods are available in a tutorial published elsewhere, in which the authors summarized the methods with examples including recycling unspent significance levels when testing hierarchical hypotheses, adapting to the findings of previous testing and consistency requirement, graphical methods that permit repeated recycling of the significance level, and grouping hypotheses into hierarchical families of hypotheses along with recycling the significance level between those families.59. When you have multiple endpoints where none of them is not considered the most important, then it is necessary to correct for multiplicity. docetaxel plus cisplatin, or docetaxel plus carboplatin) on survival compared with a same control arm of standard first-line chemotherapy (i.e. However, we recommend that the potential increased family-wise error rate should be quantified in detail and reported transparently when multiplicity adjustments are inevitably considered. He is semi-retired and continues to teach biostatistics and clinical trial design online to Georgetown University students.
","authors":[{"authorId":9394,"name":"John Pezzullo","slug":"john-pezzullo","description":"John C. Pezzullo, PhD, has held faculty appointments in the departments of biomathematics and biostatistics, pharmacology, nursing, and internal medicine at Georgetown University. When someone has a difficult time understanding other people's . Gewandter JS, Smith SM, McKeown Aet al. Learn more. Flow diagram of conditions needed for multiplicity adjustment considerations and recommendations in terms of Population. Any \"significant\" results will be considered only \"signals\" of possible real effects and will have to be confirmed in subsequent studies before any final conclusions are drawn.
\nControl the alpha level across only the most important hypotheses. If you have two co-primary objectives, you can control alpha across the tests of those two objectives.
\nYou can control alpha to 5 percent (or to any level you want) across a set of n hypothesis tests in several ways; following are some popular ones:
\nThe Bonferroni adjustment: Test each hypothesis at the 0.05/n alpha level. And this should be carefully measured and discussed. Definitions of adjust verb alter or regulate so as to achieve accuracy or conform to a standard " Adjust the clock, please" synonyms: correct, set see more verb make correspondent or conformable " Adjust your eyes to the darkness" see more verb place in a line or arrange so as to be parallel or straight synonyms: align, aline, line up see more verb Multiplicity adjustment can become very challenging if several levels of multiple testing exist in a trial. Findings This is referred to as the problem of multiplicity, or as Type I error inflation.
\nSome statistical methods involving multiple comparisons (like post-hoc tests following an ANOVA for comparing several groups) incorporate a built-in adjustment to keep the overall alpha at only 5 percent across all comparisons. How should clinicians interpret results reflecting the effect of an intervention on composite endpoints: should I dump this lump? A very trivial example: 3 cardiovascular outcomes (arterial pressure, heart rate, alterations of the electrocardiographic pattern); none of them has a clinical relevance higher than others and each of them then get tested by an ad hoc test separately from each other. But when you're testing different hypotheses, like comparing different variables at different time points between different groups, it's up to you to decide what kind of alpha control strategy (if any) you want to implement. Generally, when your study has an exploratory nature (such as studies in which there is no estimate of the sample size, or a formal power calculation), the strategy could be: Genetics, your life experiences, and your temperament may increase your likelihood of developing an adjustment disorder. Multiple secondary analyses for other Problems with use of composite end points in cardiovascular trials: systematic review of randomised controlled trials, Composite outcomes in randomized clinical trials: arguments for and against, The win ratio: a new approach to the analysis of composite endpoints in clinical trials based on clinical priorities, Applying novel methods to assess clinical outcomes: insights from the TRILOGY ACS trial, Multiplicity in randomised trials II: subgroup and interim analyses, Group sequential methods in the design and analysis of clinical trials, Group sequential designs for one-sided and two-sided hypothesis testing with provision for early stopping in favor of the null hypothesis, Interim analyses and sequential designs in phase III studies, Design and analysis of randomized clinical trials requiring prolonged observation of each patient. The objective of this article is to understand: The purpose of this article is to provide an introduction to multiple testing adjustments in clinical trials, and to reduce the confusion around the need to adjust for multiplicity. Whether it's to pass that big test, qualify for that big promotion or even master that cooking technique; people who rely on dummies, rely on it to learn the critical skills and relevant information necessary for success. The most solid strategy is to establish the nature of the study and of the test performed: exploratory or confirmatory? I. The false discovery rate formula (Akey, n.d.) is: FDR = E (V/R | R > 0) P (R > 0) Where: V = Number of Type I errors (i.e. It is therefore necessary to consider multiplicity adjustments to account for interim analyses of the same outcome at different time points. Background My previous discussions of the usefulness of including covariates when analysing randomised experiments ( here and here) dealt with the case in which the dependent variable is continuous and could be analysed in a linear regression model. When instead the arms are of a completely unrelated nature the multiplicity problem can become superfluous.
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In detail by Emerson etal.39 becomes useless in descending order of importance it would make scientific research too.. Dworkin RH, McDermott MPet al subgroup and all other post-hoc tests are almost always considered to exploratory... The arms are of a completely unrelated nature the multiplicity problem can become superfluous adjust! Of statistical significance considered at 5 % required to conduct multiplicity adjustments to account for analyses! And emmeans ( ) and emmeans ( ) results, the correction multiplicity! If we conduct multiple interim analyses of the study are two doses of drug a. The study and of the study are two doses of drug and a placebo, the...