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Determining mean and standard deviation of the strong gravity prior through simulations.

ABSTRACT: Humans expect downwards moving objects to accelerate and upwards moving objects to decelerate. These results have been interpreted as humans maintaining an internal model of gravity. We have previously suggested an interpretation of these results within a Bayesian framework of perception: earth gravity could be represented as a Strong Prior that overrules noisy sensory information (Likelihood) and therefore attracts the final percept (Posterior) very strongly. Based on this framework, we use published data from a timing task involving gravitational motion to determine the mean and the standard deviation of the Strong Earth Gravity Prior. To get its mean, we refine a model of mean timing errors we proposed in a previous paper (Jörges & López-Moliner, 2019), while expanding the range of conditions under which it yields adequate predictions of performance. This underscores our previous conclusion that the gravity prior is likely to be very close to 9.81 m/s2. To obtain the standard deviation, we identify different sources of sensory and motor variability reflected in timing errors. We then model timing responses based on quantitative assumptions about these sensory and motor errors for a range of standard deviations of the earth gravity prior, and find that a standard deviation of around 2 m/s2 makes for the best fit. This value is likely to represent an upper bound, as there are strong theoretical reasons along with supporting empirical evidence for the standard deviation of the earth gravity being lower than this value.

SUBMITTER: Jorges B

PROVIDER: S-EPMC7446919 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Project description:BACKGROUND:Rigorous, informative meta-analyses rely on availability of appropriate summary statistics or individual participant data. For continuous outcomes, especially those with naturally skewed distributions, summary information on the mean or variability often goes unreported. While full reporting of original trial data is the ideal, we sought to identify methods for handling unreported mean or variability summary statistics in meta-analysis. METHODS:We undertook two systematic literature reviews to identify methodological approaches used to deal with missing mean or variability summary statistics. Five electronic databases were searched, in addition to the Cochrane Colloquium abstract books and the Cochrane Statistics Methods Group mailing list archive. We also conducted cited reference searching and emailed topic experts to identify recent methodological developments. Details recorded included the description of the method, the information required to implement the method, any underlying assumptions and whether the method could be readily applied in standard statistical software. We provided a summary description of the methods identified, illustrating selected methods in example meta-analysis scenarios. RESULTS:For missing standard deviations (SDs), following screening of 503 articles, fifteen methods were identified in addition to those reported in a previous review. These included Bayesian hierarchical modelling at the meta-analysis level; summary statistic level imputation based on observed SD values from other trials in the meta-analysis; a practical approximation based on the range; and algebraic estimation of the SD based on other summary statistics. Following screening of 1124 articles for methods estimating the mean, one approximate Bayesian computation approach and three papers based on alternative summary statistics were identified. Illustrative meta-analyses showed that when replacing a missing SD the approximation using the range minimised loss of precision and generally performed better than omitting trials. When estimating missing means, a formula using the median, lower quartile and upper quartile performed best in preserving the precision of the meta-analysis findings, although in some scenarios, omitting trials gave superior results. CONCLUSIONS:Methods based on summary statistics (minimum, maximum, lower quartile, upper quartile, median) reported in the literature facilitate more comprehensive inclusion of randomised controlled trials with missing mean or variability summary statistics within meta-analyses.

Project description:BackgroundIn systematic reviews and meta-analysis, researchers often pool the results of the sample mean and standard deviation from a set of similar clinical trials. A number of the trials, however, reported the study using the median, the minimum and maximum values, and/or the first and third quartiles. Hence, in order to combine results, one may have to estimate the sample mean and standard deviation for such trials.MethodsIn this paper, we propose to improve the existing literature in several directions. First, we show that the sample standard deviation estimation in Hozo et al.'s method (BMC Med Res Methodol 5:13, 2005) has some serious limitations and is always less satisfactory in practice. Inspired by this, we propose a new estimation method by incorporating the sample size. Second, we systematically study the sample mean and standard deviation estimation problem under several other interesting settings where the interquartile range is also available for the trials.ResultsWe demonstrate the performance of the proposed methods through simulation studies for the three frequently encountered scenarios, respectively. For the first two scenarios, our method greatly improves existing methods and provides a nearly unbiased estimate of the true sample standard deviation for normal data and a slightly biased estimate for skewed data. For the third scenario, our method still performs very well for both normal data and skewed data. Furthermore, we compare the estimators of the sample mean and standard deviation under all three scenarios and present some suggestions on which scenario is preferred in real-world applications.ConclusionsIn this paper, we discuss different approximation methods in the estimation of the sample mean and standard deviation and propose some new estimation methods to improve the existing literature. We conclude our work with a summary table (an Excel spread sheet including all formulas) that serves as a comprehensive guidance for performing meta-analysis in different situations.

Project description:IntroductionResponse to treatment, according to Clinical Global Impression-Improvement (CGI-I) scale, is an easily interpretable outcome in clinical trials of autism spectrum disorder (ASD). Yet, the CGI-I rating is sometimes reported as a continuous outcome, and converting it to dichotomous would allow meta-analysis to incorporate more evidence.MethodsClinical trials investigating medications for ASD and presenting both dichotomous and continuous CGI-I data were included. The number of patients with at least much improvement (CGI-I ≤ 2) were imputed from the CGI-I scale, assuming an underlying normal distribution of a latent continuous score using a primary threshold θ = 2.5 instead of θ = 2, which is the original cut-off in the CGI-I scale. The original and imputed values were used to calculate responder rates and odds ratios. The performance of the imputation method was investigated with a concordance correlation coefficient (CCC), linear regression, Bland-Altman plots, and subgroup differences of summary estimates obtained from random-effects meta-analysis.ResultsData from 27 studies, 58 arms, and 1428 participants were used. The imputation method using the primary threshold (θ = 2.5) had good performance for the responder rates (CCC = 0.93 95% confidence intervals [0.86, 0.96]; β of linear regression = 1.04 [0.95, 1.13]; bias and limits of agreements = 4.32% [-8.1%, 16.74%]; no subgroup differences χ2 = 1.24, p-value = 0.266) and odds ratios (CCC = 0.91 [0.86, 0.96]; β = 0.96 [0.78, 1.14]; bias = 0.09 [-0.87, 1.04]; χ2 = 0.02, p-value = 0.894). The imputation method had poorer performance when the secondary threshold (θ = 2) was used.DiscussionAssuming a normal distribution of the CGI-I scale, the number of responders could be imputed from the mean and standard deviation and used in meta-analysis. Due to the wide limits of agreement of the imputation method, sensitivity analysis excluding studies with imputed values should be performed.

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Determining mean and standard deviation of the strong gravity prior through simulations.

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