The inability to reproduce key scientific results in certain areas of research is a growing concern among scientists, funding agencies, journals and the public (Nature, 2013; Fosang and Colbran, 2015; National Institutes of Health, 2015a; National Institutes of Health, 2015b; Nature, 2017). Problems with the statistical analyses used in published studies, along with inadequate reporting of the experimental and statistical techniques employed in the studies, are likely to have contributed to these concerns. Older studies suggest that statistical errors, such as failing to specify what test was used or using incorrect or suboptimal statistical tests, are common (Müllner et al., 2002; Ruxton, 2006; Strasak et al., 2007), and more recent studies suggest that these problems persist. A study published in 2011 found that half of the neuroscience articles published in five top journals used inappropriate statistical techniques to compare the magnitude of two experimental effects (Nieuwenhuis et al., 2011). A more recent study of papers reporting the results of experiments that examined the effects of prenatal interventions on offspring found that the statistical analyses in 46% of the papers were invalid because authors failed to account for non-independent observations (i.e., animals from the same litter; Lazic et al., 2018). Many studies omit essential details when describing experimental design or statistical methods (Real et al., 2016; Lazic et al., 2018). Errors in reported p-values are also common and can sometimes alter the conclusions of a study (Nuijten et al., 2016).

A main principle of the SAMPL guidelines for reporting statistical analyses and methods in the published literature is that authors should "describe statistical methods with enough detail to enable a knowledgeable reader with access to the original data to verify the reported results" (Lang and Altman, 2013). However, these guidelines have not been widely adopted.

Clear statistical reporting also allows errors to be identified and corrected prior to publication. The journal Science has attempted to improve statistical reporting by adding a Statistical Board of Reviewing Editors (McNutt, 2014). Other journals, including Nature and affiliated journals (Nature, 2013; Nature, 2017), eLife (Teare, 2016) and The EMBO Journal (EMBO Press, 2017) have recently implemented policies to encourage transparent statistical reporting. These policies may include specifying which test was used for each analysis, reporting test statistics and exact p-values, and using dot plots, box plots or other figures that show the distribution of continuous data.

T-tests and analysis of variance (ANOVA) are the statistical bread-and-butter of basic biomedical science research (Strasak et al., 2007). However, statistical methods in these papers are often limited to vague statements such as: "Data were analyzed by t-tests or ANOVA, as appropriate, and statistical significance was defined as p<0.05." There are several problems with such descriptions. First, there are many different types of t-tests and ANOVAs. Vague statistical methods deprive reviewers, editors and readers of the opportunity to confirm that an appropriate type of t-test or ANOVA was used and that the results support the conclusions in the paper. For example, if authors use an unpaired t-test when a paired t-test is needed, the failure to account for repeated measurements on the same subject will lead to an incorrect p-value. Analyses that use inappropriate tests give potentially misleading results because the tests make incorrect assumptions about the study design or data and often test the wrong hypothesis. Without the original data, it is difficult to determine how the test results would have been different had an appropriate test been used. Clear reporting allows readers to confirm that an appropriate test was used and makes it easier to identify and fix potential errors prior to publication.

The second problem is that stating that tests were used "as appropriate" relies on the assumption that others received similar statistical training and would make the same decisions. This is problematic because it is possible to complete a PhD without being trained in statistics: only 67.5% of the top NIH-funded physiology departments in the United States required statistics training for some or all PhD programs that the department participated in (Weissgerber et al., 2016a). When training is offered, course content can vary widely among fields, institutions and departments as there are no accepted standards for the topics that should be covered or the level of proficiency required. Moreover, courses are rarely designed to meet the needs of basic scientists who work with small sample size datasets (Vaux, 2012; Weissgerber et al., 2016a). Finally, these vague statements fail to explain why t-tests and ANOVA were selected, as opposed to other techniques that can be useful for small sample size datasets.

This systematic review focuses on the quality of reporting for ANOVA and t-tests, which are two of the most common statistical tests performed in basic biomedical science papers. Our objectives were to determine whether articles provided sufficient information to determine which type of ANOVA or t-test was performed and to verify the test result. We also assessed the prevalence of two common problems: i) using a one-way ANOVA when the study groups could be divided into two or more factors, and ii) not specifying that the analysis included repeated measures or within-subjects factors when ANOVA was performed on non-independent or longitudinal data.

To obtain our sample two reviewers independently examined all original research articles published in June 2017 (n = 328, Figure 1) in the top 25% of physiology journals, as determined by 2016 journal impact factor (see Methods for full details). Disagreements were resolved by consensus. 84.5% of the articles (277/328) included either a t-test or an ANOVA, and 38.7% of articles (127/328) included both. ANOVA (n = 225, 68.6%) was more common than t-tests (n = 179, 54.5%). Among papers that reported the number of factors for at least one ANOVA, most were using a maximum of one (n = 112, 49.8%) or two (n = 69, 30.7%) factors. ANOVAs with three or more factors were uncommon (n = 6, 2.7%). This approach involved a number of limitations. All the journals in our sample were indexed in PubMed and only published English language articles, so our results may not be generalizable to brief reports, journals with lower impact factors, journals that publish articles in other languages, or journals that are not indexed in PubMed. Further research is also needed to determine if statistical reporting practices in other fields are similar to what we found in physiology.

Figure 1

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Figure 1—source data 1

Data from systematic review.

https://doi.org/10.7554/eLife.36163.003

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While ANOVA encompasses a wide variety of techniques, basic biomedical science papers generally use one and two-way ANOVAs, with or without repeated measures. We focused on reporting requirements for these basic tests, as more complex types of ANOVA were rare in our dataset (<3%; Figure 1—source data 1). Authors need to report three key pieces of information to allow readers to confirm that the type of ANOVA that was used is appropriate for the study design (see Box 1 for terminology and Box 2 for a detailed description of what should be reported). Many papers were missing some or all of this information (Figure 2). 213 papers (95% of the papers that used ANOVA) did not contain all information needed to determine what type of ANOVA was performed, including the names and number of factors and whether each factor was entered as a between-subjects or within-subjects factor.

Figure 2

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The number of factors included in the ANOVA and the names and levels of each factor

16.9% of papers (38/225) failed to specify how many factors were included for any ANOVA performed in the paper. 54% of papers did not specify which factors were included in any ANOVA, whereas fewer than half of papers specified which factors were included for some (n = 13, 5.8%) or all (n = 90, 40%) ANOVAs reported in the manuscript.

Our data suggest that reporting the number, names and levels of factors may be particularly important to determine whether the statistical test is appropriate for the study design. Among papers that used one-way ANOVAs, 60.9% (67/110) used a one-way ANOVA for an analysis where the study design included two or more factors. (Note: Two papers that reported using a maximum of one factor in the ANOVA were excluded, as these papers also included a repeated measures ANOVA with an unknown number of factors.) For example, investigators might have used a one-way ANOVA to compare four independent groups: wild-type mice that received vehicle (placebo), wild-type mice that received a treatment, knockout mice that received vehicle (placebo), and knockout mice that received a treatment. This approach may be appropriate for extremely small sample sizes, as these datasets may not have enough power for an ANOVA with two or more factors. In most cases, however, a two-way ANOVA with mouse strain (wild-type vs. knockout) and treatment (placebo vs. treatment) as factors may provide more information. Figure 3 and Figure 4 show the difference between these two approaches and illustrate how the two-way ANOVA may offer additional insight. The two-way ANOVA allows investigators to examine the effects of both factors simultaneously and may help investigators to avoid unnecessary post-hoc tests. If the sample size is large enough, the two-way ANOVA can test for an interaction between the two factors (i.e., whether the effect of mouse strain depends on treatment).

Figure 3

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Figure 4

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Whether each factor was entered as a between (independent) or within (non-independent) subjects factor

Among the 18.2% of papers (41/225) that reported using repeated measures ANOVA, 63.4% (n = 26) did not specify whether each factor was entered as a between or within-subjects factor. Many of the 15 papers that provided adequate information reported using one-way repeated measures ANOVA. When the ANOVA only includes one factor, stating that repeated measures were used demonstrates that this factor was treated as a within-subjects or non-independent factor. When a repeated measures ANOVA includes two or more factors, however, authors need to clearly report which factors were treated as between vs. within-subjects factors. A two-way repeated measures ANOVA could refer to two different tests – an ANOVA with two within-subjects factors, or an ANOVA with one within-subjects factor and one between-subjects factor (Box 1).

The remaining 81.8% of papers that included ANOVA did not indicate whether repeated measures were used. Only one of these papers stated that all factors were entered as between-subjects factors (1/184, 0.5%). If repeated measures or within-subjects factors are not mentioned, one would typically assume that all factors were independent or between-subjects. Our data suggest that scientists should be cautious about this assumption, as 28.3% of papers that did not indicate that repeated measures were used (52/184) included at least one ANOVA that appeared to require repeated measures. There is no way to distinguish between papers that used the wrong test and papers that failed to clearly specify which test was used. Figure 5 illustrates the differences between these two tests. Failing to account for repeated measures in an ANOVA makes it less likely that investigators will detect an effect, as the variability that can be attributed to individual subjects remains unexplained. To avoid confusion, we recommend that reviewers, editors and journal guidelines encourage authors to specify whether each factor was entered as between or within-subjects factor, even if the paper does not include a repeated measures ANOVA.

Figure 5

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Many of the 179 papers that included a t-test were missing information that was needed to determine what type of t-test was performed, including whether the tests were paired or unpaired, or assumed equal or unequal variance.

Unpaired vs. paired t-tests

Over half of the papers (53%; 95/179) did not specify whether any t-tests were paired or unpaired; a small proportion (2.2%; 4/179) provided this information for some but not all of the t-tests in the paper. 69 of the 95 papers without any information on paired vs. unpaired t-tests reported that the Student’s t-test was used. While the term Student’s t-test traditionally refers to the unpaired t-test for equal variances, we identified numerous instances where authors referred to a paired t-test as a Student’s t-test. Due to this confusion, we did not assume that the Student’s t-test was unpaired unless the authors included additional terms like unpaired t-test or independent samples t-test. Figure 6 illustrates why clear reporting that allows readers to confirm that the correct test was used is essential. Unpaired and paired t-tests interpret the data differently, test different hypotheses, use different information to calculate the test statistic and usually give different results. If the incorrect test is used, the analysis tests the wrong hypothesis and the results may be misleading. Without the original data, it is difficult to determine how the test results would have been different had the appropriate tests been used.For example, differencesbetween the results of the paired and unpaired t-tests depend on the strength of the correlation between paired data points (Figure 7), which is difficult or impossible to determine from line graphs that only show summary statistics.

Figure 6

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Figure 7

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Reporting the test statistic (ANOVA: F-statistic, t-tests: t-statistic), degrees of freedom and exact p-values are important for several reasons. First, these values allow authors, reviewers and editors to confirm that the correct test was used. This is particularly important when the statistical methods do not provide enough information to determine which type of ANOVA or t-test was performed, which was common in our dataset. Second, reporting the degrees of freedom allows readers to confirm that no participants, animals or samples were excluded without explanation. A recent study found that more than two thirds of papers using animal models to study stroke or cancer did not contain sufficient information to determine whether animals were excluded, while 7-8% of papers excluded animals without explanation (Holman et al., 2016). Biased exclusion of animals or observations can substantially increase the probability of false positive results in small sample size studies. Third, this information allows authors and readers to verify the test result. In an analysis of psychology papers, over half reported at least one p-value that did not match the test statistic and degrees of freedom: this error was sufficient to alter the study conclusions in one out of eight papers (Nuijten et al., 2016). Authors and journal editors can eliminate these errors by double checking their results, or using software programs such as statcheck (Eskamp and Nuijten, 2016) to confirm that p-values match the reported test statistic and degrees of freedom. Unfortunately, the information needed to verify the test result is not reported in many papers.

Among the studies in our sample that included ANOVA (Figure 8), more than 95% failed to report the F-statistic or degrees of freedom. Moreover, 77.8% of these papers reported ranges of p-values (i.e., p>0.05, p<0.05, p<0.01), with just 50 papers reporting exact p-values (41 of 225 papers reported exact p-values for some ANOVAs, and 9 papers reported exact p-values for all ANOVAs). Among studies that included t-tests, 16 papers (8.9%) were excluded because abstractors were unable to determine what data were analyzed by t-tests or to identify a two-group comparison. While most papers reported the sample size or degrees of freedom for some (16.6%) or all (76.7%) t-tests, t-statistics were missing from 95.7% of papers (Table 1). Moreover, 79.7% of the papers that included t-tests reported ranges of p-values instead of exact p-values.

Figure 8

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This systematic review demonstrates that t-tests and ANOVA may not be so simple after all, as many papers do not contain sufficient information to determine why a particular test was selected, what type of test was used or to verify the test result. Selecting statistical tests that are not appropriate for the study design may be surprisingly common. Often, it is not possible to determine why statistical tests were selected, or whether other analyses may have provided more insight. Investigators frequently present data using bar or line graphs that only show summary statistics (Weissgerber et al., 2015) and raw data are rarely available. Many journals have recently introduced policies to encourage more informative graphics, such as dot plots, box plots or violin plots, that show the data distribution (Nature, 2017; Fosang and Colbran, 2015; Kidney International, 2017; PLOS Biology, 2016; Teare, 2016) and may provide insight into whether other tests are needed. Non-parametric tests, such as the Mann-Whitney U test, Wilcoxon sign rank test and Kruskal Wallis test, may sometimes be preferable as sample sizes in basic biomedical science research are often too small to determine the data distribution. However, these tests are not commonly used. A systematic review of physiology studies showed that 3.8% used only non-parametric tests to compare continuous data, 13.6% used a combination of parametric and non-parametric tests, and 78.1% of studies used only parametric tests (Weissgerber et al., 2015). A recent primer Hardin and Kloke, 2017 provides a brief overview of common statistical techniques, including non-parametric alternatives to t-tests and ANOVAs.

Recently, fields such as psychology have been moving away from a reliance on t-tests and ANOVAs towards more informative techniques, including effect sizes, confidence intervals and meta-analyses (Cumming, 2014). While p-values focus on whether the difference is statistically significant, effect sizes answer the question: "how big is the difference?" A published tutorial provides more details on how to calculate effect sizes for t-tests and ANOVA (Lakens, 2013). Presenting confidence intervals provides more information about the uncertainty of the estimated statistic (i.e., mean, effect size, correlation coefficient). A guide to robust statistical methods in neuroscience examines a variety of newer methods to address the problems with hypothesis tests, and includes information on techniques that are suitable for studies with small sample sizes (Wilcox and Rousselet, 2018). Small, underpowered studies frequently produce inconclusive results that may appear to be contradictory. Meta-analyses combine these divergent results to provide a comprehensive assessment of the size and direction of the true effect (Cumming, 2014).

The findings of the present study highlight the need for investigators, journal editors and reviewers to work together to improve the quality of statistical reporting in submitted manuscripts. While journal policy changes are a common solution, the effectiveness of policy changes is unclear. In a study of life sciences articles published in Nature journals, the percentage of animal studies reporting the Landis 4 criteria (blinding, randomization, sample size calculation, exclusions) increased from 0% to 16.4% after new guidelines were released (Macleod and The NPQIP Collaborative group, 2017). In contrast, a randomized controlled trial of animal studies submitted to PLoS One demonstrated that asking authors to complete the ARRIVE checklist at the time of submission had no effect (Hair et al., 2018). Some improvements in reporting of confidence intervals, sample size justification and inclusion and exclusion criteria were noted after Psychological Science introduced new policies, although this may have been partially due to widespread changes in the field (Giofrè et al., 2017). A joint editorial series published in the Journal of Physiology and British Journal of Pharmacology did not improve the quality of data presentation or statistical reporting (Diong et al., 2018). Statistical reporting requirements are not standard practice for many fields and journals in basic biomedical science, thus limiting the ability of readers to critically evaluate published research.

Other possible solutions to improve reporting include strengthening and implementing reporting guidelines, and training editors, reviewers and investigators to recognize common problems. Box 2 lists statistical information that should be reported when presenting data that were analyzed by t-tests and ANOVA. Some journals have already begun offering unlimited word counts for methods sections to improve reporting (Nature, 2013), while others suggest putting additional information in supplemental methods. Creating open-source software programs that calculate word counts for the results section after excluding statistical information may also facilitate transparent reporting of statistical results. Encouraging public data archiving or interactive graphics that include all data (Ellis and Merdian, 2015; Weissgerber et al., 2016b; Weissgerber et al., 2017) may also strengthen reporting and reproducibility while facilitating data re-use.

All data from the systematic review has been uploaded with the manuscript, along with the abstraction protocol.

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Thank you for submitting your article 'Why We Need to Report More Than "Data were Analyzed by t-tests or ANOVA"' to eLife for consideration as a Feature Article. Your article has been reviewed by three peer reviewers, including Dawn Teare as the Reviewing Editor and Reviewer #1, and the evaluation has been overseen by Peter Rodgers, the eLife Features Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Andrew Althouse (Reviewer #2); Glenn Begley (Reviewer #3).

The reviewers have discussed the reviews with one another and the Reviewing Editor and Features Editor have drafted this decision to help you prepare a revised submission.

Summary:

This paper is a systematic review of 328 papers published in June 2017 in 21 physiology journals. The authors focused on the use of t-tests and ANOVA. They conclude that key information was routinely absent. Similar studies have been published in the past that describe the problems with statistical analysis of scientific papers. However, with the change in Guidelines to Authors instituted by many journals over recent years, it might have been hoped that the situation had improved. Sadly, that does not appear to be the case. The paper includes several figures that demonstrate the challenges that arise when data is inappropriately analysed: these are very useful. The authors are to be congratulated on a clear, well-written, compelling study.

Essential revisions:

Reviewer #1:

a) Given the authors are stating that reporting initiatives are urgently needed, it is a shame that they did not use the PRISMA guidelines to draft the manuscript. There are many reporting initiatives out there, we don't need new ones but rather we need to know how the existing ones can be improved. This paper has been written without much reference to those other initiatives.

b) The manuscript selects instances where a t-test or an ANOVA have been performed. There is no mention of the use of non-parametric tests. Although there is some discussion of how to optimally use an ANOVA to examine interactions, the work tends to focus on being able to replicate exactly what has been done by providing more details. The article would benefit from some discussion of how to select the optimal analysis strategy given a research hypothesis.

c) The checklist provided in box 2 does not have prompts for effect sizes and confidence intervals to be reported. Many of the new reporting guidelines that have been proposed recently directly encourage these to be reported rather than the F-test values and degrees of freedom. This is also missing from the ANOVA section. Again the article would benefit from some discussion of comparative statistics and confidence intervals.

d) The final section ('Transparency: Where should we draw the line?') is missing the idea of reproducibility. Transparency is important for reproducibility. I would suggest including the following recommendation: There should be sufficient detail in a paper so that: i) a reader can understand why the author has selected the analysis methods they have; ii) a reader can repeat the analysis and get the same answer (if they have the raw data).

e) Please expand the figure captions to better explain what is shown in each figure.

Essential revisions:

Reviewer #1:

a) Given the authors are stating that reporting initiatives are urgently needed, it is a shame that they did not use the PRISMA guidelines to draft the manuscript. There are many reporting initiatives out there, we don't need new ones but rather we need to know how the existing ones can be improved. This paper has been written without much reference to those other initiatives.

We have added a statement to the Materials and methods that the systematic review was conducted in accordance with all relevant aspects of the PRISMA guidelines and included a PRISMA checklist. We have also integrated the SAMPL guidelines for statistical reporting in the Introduction. The SAMPL guidelines are very general and may not include adequate information for scientists with little or no statistical training to determine what details should be reported. This paper is designed to provide basic biomedical scientists with more information about why it is important to include additional information so that readers can determine whether an appropriate type of ANOVA or t-test was performed. While we focus on t-tests and ANOVA because they are the most common, the same principles apply to other types of tests.

We always follow all relevant aspects of the PRISMA guidelines as part of our standard protocol for conducting systematic reviews. However, it is important to note that large portions of the guidelines do not apply to literature surveys or to systematic reviews without a meta-analysis. For example, search terms are not included because no selective electronic search was performed. Journals were identified by selecting the top 25% of journals, according to 2016 impact factor, in the physiology category of the Journal Citation Reports database. Articles were then identified by examining journal websites to identify all articles in issues published in June 2017. This process was completed by two independent reviewers. The PRISMA guidelines recommend a structured Abstract, however this contradicts this journal’s requirements for features articles. Elements such as PICO, risk of bias assessments, and reporting of elements relevant to meta-analyses are not relevant to this literature survey.

b) The manuscript selects instances where a t-test or an ANOVA have been performed. There is no mention of the use of non-parametric tests. Although there is some discussion of how to optimally use an ANOVA to examine interactions, the work tends to focus on being able to replicate exactly what has been done by providing more details. The article would benefit from some discussion of how to select the optimal analysis strategy given a research hypothesis.

We chose to focus on t-tests and ANOVA for two reasons. First, while t-tests and ANOVA are very common, our previous work has shown that non-parametric tests are not. We examined articles published in the top 25% of physiology journals during a three-month period in 2014 (Weissgerber et al., 2015). We found that 78.1% of studies used only parametric tests to compare continuous data (i.e. t-tests and ANOVA), 13.6% used a combination of parametric and non-parametric tests, and 3.8% used only non-parametric tests. We have now described this data in the manuscript. Second, there are many different types of ANOVAs and t-tests; therefore additional detail is needed to determine which test was performed. In contrast, the name of the non-parametric test (i.e. Kruskal-Wallis, Mann Whitney, Wilcoxon Rank Sum, Wilcoxon Signed Rank) is sufficient because these tests do not have variations.

We understand the reviewers’ desire for a single paper that outlines the problems with the reporting of existing analyses, addresses the misconceptions that lead to these reporting errors and shows how to correct them, and also describes how to select more informative or optimal tests. However, it is important to be realistic about what can be accomplished in a single paper designed for basic biomedical scientists, many of whom have limited or no statistical training. There are several papers that address the problems with t-tests and ANOVA and describe how to select more informative alternatives. Although these papers tend to be quite long, the authors frequently note that they are intended to supplement existing statistical knowledge and are not a substitute for statistical training. We have rewritten the last section of the paper to briefly address other approaches and referred readers to existing resources for additional information. A shift away from hypothesis testing in basic biomedical science will require retraining the scientific workforce, which will take time. It is likely that most investigators will continue to perform t-tests and ANOVA in the near future; hence, efforts to improve reporting for these techniques are needed.

c) The checklist provided in box 2 does not have prompts for effect sizes and confidence intervals to be reported. Many of the new reporting guidelines that have been proposed recently directly encourage these to be reported rather than the F-test values and degrees of freedom. This is also missing from the ANOVA section. Again the article would benefit from some discussion of comparative statistics and confidence intervals.

We have updated Box 2 to include effect sizes and confidence intervals and added a section at the end of the manuscript that addresses other statistical approaches and provides links to papers that examine these resources in detail. This includes a citation on how to calculate effect sizes for t-tests and ANOVA.

d) The final section ('Transparency: Where should we draw the line?') is missing the idea of reproducibility. Transparency is important for reproducibility. I would suggest including the following recommendation: There should be sufficient detail in a paper so that: i) a reader can understand why the author has selected the analysis methods they have; ii) a reader can repeat the analysis and get the same answer (if they have the raw data).

These are both included in the SAMPL guidelines, which we have now mentioned in the Introduction. Additionally, these points are also both mentioned in the first sentence of the final section of the paper, which has been extensively revised and is now entitled “Moving towards a more transparent and reproducible future”. This section also includes a brief discussion on more informative analysis techniques and links to resources and integrates the concept of reproducibility.

e) Please expand the figure captions to better explain what is shown in each figure.

We have added additional descriptors to figure legends.

Author details

1. Tracey L Weissgerber

   Tracey L Weissgerber is in the Division of Nephrology & Hypertension, Mayo Clinic, Rochester, Minnesota, United States, and QUEST – Quality | Ethics | Open Science | Translation, Charité - Universitätsmedizin Berlin, Berlin Institutes of Health, Berlin, Germany

   Contribution

   Conceptualization, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Visualization, Methodology, Writing—original draft, Project administration, Writing—review and editing

   For correspondence

   weissgerber.tracey@mayo.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-7490-2600

2. Oscar Garcia-Valencia

   Oscar Garcia-Valencia is in the Division of Nephrology & Hypertension, Mayo Clinic, Rochester, Minnesota, United States

   Contribution

   Investigation, Visualization, Methodology, Writing—review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-0186-9448

3. Vesna D Garovic

   Vesna D Garovic is in the Division of Nephrology & Hypertension, Mayo Clinic, Rochester, Minnesota, United States

   Contribution

   Supervision, Funding acquisition, Writing—review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-6891-0578

4. Natasa M Milic

   Natasa M Milic is in the Division of Nephrology & Hypertension, Mayo Clinic, Rochester, Minnesota, United States and the Department of Medical Statistics & Informatics, Medical Faculty, University of Belgrade, Belgrade, Serbia

   Contribution

   Conceptualization, Validation, Methodology, Writing—review and editing

   Contributed equally with

   Stacey J Winham

   Competing interests

   No competing interests declared

5. Stacey J Winham

   Stacey J Winham is in the Division of Biomedical Statistics & Informatics, Mayo Clinic, Rochester, Minnesota, United States

   Contribution

   Conceptualization, Funding acquisition, Methodology, Writing—review and editing

   Contributed equally with

   Natasa M Milic

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-8492-9102

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