In meta-analyses, it sometimes happens that smaller trials show different, often larger, treatment effects. One possible reason for such 'small study effects' is publication bias. This is said to occur when the chance of a smaller study being published is increased if it shows a stronger effect. Assuming no other small study effects, under the null hypothesis of no publication bias, there should be no association between effect size and effect precision (e.g. inverse standard error) among the trials in a meta-analysis.A number of tests for small study effects/publication bias have been developed. These use either a non-parametric test or a regression test for association between effect size and precision. However, when the outcome is binary, the effect is summarized by the log-risk ratio or log-odds ratio (log OR). Unfortunately, these measures are not independent of their estimated standard error. Consequently, established tests reject the null hypothesis too frequently. We propose new tests based on the arcsine transformation, which stabilizes the variance of binomial random variables. We report results of a simulation study under the Copas model (on the log OR scale) for publication bias, which evaluates tests so far proposed in the literature. This shows that: (i) the size of one of the new tests is comparable to those of the best existing tests, including those recently published; and (ii) among such tests it has slightly greater power, especially when the effect size is small and heterogeneity is present. Arcsine tests have additional advantages that they can include trials with zero events in both arms and that they can be very easily performed using the existing software for regression tests.
Standard generic inverse variance methods for the combination of single proportions are based on transformed proportions using the logit, arcsine, and Freeman-Tukey double arcsine transformations. Generalized linear mixed models are another more elaborate approach. Irrespective of the approach, meta-analysis results are typically back-transformed to the original scale in order to ease interpretation. Whereas the back-transformation of meta-analysis results is straightforward for most transformations, this is not the case for the Freeman-Tukey double arcsine transformation, albeit possible. In this case study with five studies, we demonstrate how seriously misleading the back-transformation of the Freeman-Tukey double arcsine transformation can be. We conclude that this transformation should only be used with special caution for the meta-analysis of single proportions due to potential problems with the back-transformation. Generalized linear mixed models seem to be a promising alternative.
2.) Let's look at the railroad example from above. If you knew that the train rose 3 vertical miles on a track that was 5 miles long, you could determine the angle of incline of the track using the arcsine.
The arcsine is the inverse function of the sine function. This means that they are opposite functions, and one will cancel out the other. The arcsine is mainly used to determine the measure of an angle when two sides of a right triangle are known. In order to use this function, you must know the hypotenuse and the side opposite the angle you are trying to determine. It has applications in navigation, engineering, and other sciences.
Note that the arcsine transformation only works on values between the range of 0 to 1. So, if we have a vector with values outside of this range then we need to first convert each value to be in the range of 0 to 1.
For a binomial distribution, variance is a function of the mean, reaching a maximum value at a proportion of 0.5, and declining to zero at proportions of zero and one. Variance-stabilizing transformations are used to correct this problem in binomial data, and two of the most common variance-stabilizing transformations are the logit and arcsine transformations. These transformations are also used for percentage data that may not follow a binomial distribution.
The arcsine transformation (also called the arcsine square root transformation, or the angular transformation) is calculated as two times the arcsine of the square root of the proportion. In some cases, the result is not multiplied by two (Sokal and Rohlf 1995). Multiplying by two makes the arcsine scale go from zero to pi; not multiplying by two makes the scale stop at pi/2. The choice is arbitrary.
A large number of processes in the mesoscopic world occur out of equilibrium, where the time evolution of a system becomes immensely important since it is driven principally by dissipative effects. Nonequilibrium steady states (NESS) represent a crucial category in such systems, where relaxation timescales are comparable to the operational timescales. In this study, we employ a model NESS stochastic system, which is comprised of a colloidal microparticle optically trapped in a viscous fluid, externally driven by a temporally correlated noise, and show that time-integrated observables such as the entropic current, the work done on the system or the work dissipated by it, follow the three LÃvy arcsine laws [A. C. Barato et al., Phys. Rev. Lett. 121, 090601 (2018)], in the large time limit. We discover that cumulative distributions converge faster to arcsine distributions when it is near equilibrium and the rate of entropy production is small, because in that case the entropic current has weaker temporal autocorrelation. We study this phenomenon by changing the strength of the added noise as well as by perturbing our system with a flow field produced by a microbubble at close proximity to the trapped particle. We confirm our experimental findings with theoretical simulations of the systems. Our work provides an interesting insight into the NESS statistics of the meso-regime, where stochastic fluctuations play a pivotal role.
Action of a microbubble in close vicinity of the optically trapped probe. (a) Schematic of the experimental probe particle-micobubble system. The microbubble is grown on a preexisting absorbing pattern or trail in the sample chamber (see Methods). The different dimensions of the bubble, bead and the trail are marked in the figure . (b) Histogram of the position fluctuation; clearly it develops a skew in the presence of the flow field generated by the microbubble. (c) CDF of T+ and (d) convergence rates to the first arcsine law for the colloidal probe placed at different distances from the microbubble. (e) Entropy production rate for changing distance of the microbubble (see Ref. [24]).
Three arcsine laws tabulated for entropic currents. The entropic currents computed from our experiments are used to plot the three arcsine distributions for T+, Tlast, and Tmax in red, green, and blue colors, respectively, for both the cases where bubble is present (in circles) and absent (in squares).
The second and third arcsine laws in presence of the bubble: The L1 distance between instantaneous CDF and arcsine distribution is plotted as a function of Ï for the (a) Tlast and (b) Tmax, for various distances to the bubble and also for the case when there is no bubble present.
Arcsine laws tabulated for all the cases. The work dissipated by the stochastic engine as well as the work done in our experiments are used to plot the three arcsine laws for T+, Tlast, and Tmax in red, green, and blue colors, respectively.
According to the Handbook of Biological Statistics, the arcsine squareroot transformation is used for proportional data, constrained at $-1$ and $1$. However, when I use transf.arcsine in R on a dataset ranging from $-1$ to $1$, NaNs are produced because of the square-rooting of a negative number. What is the correct way to transform this data - i.e. how do I use arcsine squareroot transformations on data which include negative numbers?
Zakhar Kabluchko. Vladislav Vysotsky. Dmitry Zaporozhets. "A multidimensional analogue of the arcsine law for the number of positive terms in a random walk." Bernoulli 25 (1) 521 - 548, February 2019. -BEJ996
Keywords: absorption probability , arcsine law , convex cone , Convex hull , distribution-free probability , finite reflection group , hyperplane arrangement , random linear subspace , Random walk , random walk bridge , Weyl chamber
When performing t tests or ANOVA on results that are proportions, statisticians used to recommend transforming the data to equalize variances. The transform is often called "the arcsine" transform. But, when used in this way, the required function really is the arcsine of the square root of the proportion. Prism cannot calculate this with a builtin function. You'd need to write a user defined transform:
The arcsine function (precise definition below) is the best we can do in trying to get an inverse of the sine function.
The arcsine function is actually the inverse of the green piece shown above!
The arcsine is one of the inverse trigonometric functions (antitrigonometric functions) and is the inverse of the sine function. It is sometimes written as sin-1(x), but this notation should be avoided as it can be confused with an exponent notation (power of, raised to the power of). The arcsine is used to obtain an angle from the sine trigonometric ratio, which is the ratio between the side opposite to the angle and the longest side of the triangle.
In a blank column, enter the appropriate function for the transformation you've chosen. For example, if you want to transform numbers that start in cell A2, you'd go to cell B2 and enter =LOG(A2) or =LN(A2) to log transform, =SQRT(A2) to square-root transform, or =ASIN(SQRT(A2)) to arcsine transform. Then copy cell B2 and paste into all the cells in column B that are next to cells in column A that contain data. To copy and paste the transformed values into another spreadsheet, remember to use the "Paste Special..." command, then choose to paste "Values." Using the "Paste Special...Values" command makes Excel copy the numerical result of an equation, rather than the equation itself. (If your spreadsheet is Calc, choose "Paste Special" from the Edit menu, uncheck the boxes labeled "Paste All" and "Formulas," and check the box labeled "Numbers.")
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