The size of a pilot study for a clinical trial should be calculated in relation to considerations of precision and efficiency

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.Electronic supplementary materialThe online version of this article (doi:10.1186/1471-2288-14-135) contains supplementary material, which is available to authorized users.

Statistical inference with confidence intervals

Inference from a sample mean--Part 1.

following statement of the significance of a probable error is often made: The probable error of the mean is a value above and below the mean such that if the test were repeated under the same conditions there would be, on the average, equal chances that the mean would fall within or without this range. probable error is attached to the mean of the sample and it is assumed that the standard deviation of the sample is that of the sampled normal population. This was formerly a very usual explanation of the meaning of probable error by research workers, but it is inaccurate and misleading, especially for samples of 20 or less such as are dealt with in agricultural experiments. inaccuracy of this explanation of the meaning of probable error has been realized for many years by competent statisticians, but no satisfactory treatment has heretofore been devised.' attempted explanation of the probable error in terms of the expected frequency of the occurrence of different size deviations of the means of future samples from the sample mean does raise a very interesting, important, and legitimate question, namely, what is the probability of a second mean lying within a certain multiple of the standard deviation of a first sample of the mean of a first sample? This question is of fundamental concern to those engaged in experimental work. Its answer will indicate to investigators reasonable deviations from the results oftheir first experiments, will form a valid basis for the rejection of doubtful observations or groups of such observations, and will form a basis for a test of the significance of the divergence of results in different experiments. It is found that the usual method of treating the probable error gives an overly optimistic idea of the smallness of the deviations that may be expected in future samples. distribution function of the variable

This publication presents the results of the analysis of the dynamics of changes in the largefruited indicators of the breeding group of minipigs of the ICG SB RAS. The analysis showed that the four large-copious indicators are divided into two pairs. The first pair is made up of sample values of the characteristic: average and maximum. These indicators are characterized by stability throughout the studied period. The second pair includes the sample minimum values and standard deviations of the trait. These two indicators are dynamic: the sample minimum values are characterized by a decrease, and the sample standard deviations are characterized by a uniform increase, described by linear regression equations. It is shown that the dynamic characteristics are related to each other. It is determined that in this complex, the leader is the minimum value, and the follower is the standard deviation. This is explained by the fact that an increase in the standard deviation is associated with a decrease in the minimum value and the stability of the maximum in the studied period of time. The result of this process is the growth of the genetic potential in the breeding group, which is responsible for the high weight of the newborn individual. However, due to the small size of sows in comparison with commercial breeds (60-70 kg), this potential cannot be realized. Nevertheless, its redundancy ensures the stabilization of the maximum and average values of the trait - the mass of a newborn individual in minipigs of the ICG SB RAS. A possible way to increase the realization of the potential of large-copious breeding group is to reduce the multiple fertility of sows, which is quite solvable, but hardly advisable. Thus there is natural selection directed against individuals with a low birth weight in the herd. Natural and artificial selection for live weight of piglets at birth of 700 g or more, both help to stabilize the average value of the trait at the level optimal for the broodstock.

The process capability index (PCI), C pk , one of the widely used tools for assessing the capability of a manufacturing process, expresses the deviation of the process mean from the midpoint of the specification limits. The C pk is known to perform well under the general assumption that the experimental data are normally distributed without contamination. Under this assumption, the sample mean and sample standard deviation are used for the estimation of the PCI. However, the sample mean and sample standard deviation are quite sensitive to data contamination and this will result in underperformance of C pk . Therefore, in this article, we propose alternatives to the conventional method by replacing the sample mean and sample standard deviation with robust location and scale estimators. We also propose a method for constructing a robust PCI C pk confidence interval which lends itself to robust statistical hypothesis testing. The robust hypothesis testing methods based on this confidence interval are shown to be quite efficient when the data are normally distributed yet also outperform the conventional method when data contamination exists.

A method is presented which allows correlation coefficients to be corrected for restriction of range when only the proportion of the population selected is known. The method assumes that the population distribution is normal and that selection has resulted in single truncation. A table is given which provides the ratio of the population and sample standard deviations, the truncation point, and the ordinate in N(0, 1), corresponding to the proportion of the population selected. Correlations can be corrected for the effects of direct or indirect selection by substitution of tabled values in traditional correction formulae. Further, the population mean or standard deviation can be estimated if the censored sample mean or standard deviation is known.

The Shewhart R control chart and s control chart are widely used to monitor shifts in the process spread. One fact is that the distributions of the range and sample standard deviation are highly skewed. Therefore, the R chart and s chart neither provide an in-control average run length (ARL) of approximately 370 nor guarantee the desired type I error of 0.0027. Another disadvantage of these two charts is their failure in detecting an improvement in the process variability. In order to overcome these shortcomings, we propose the improved R chart (IRC) and s chart (ISC) with accurate approximation of the control limits by using cumulative distribution functions of the sample range and standard deviation. Simulation studies show that the IRC and ISC perform very well. We also compare the type II error risks and ARLs of the IRC and ISC and found that the s chart is generally more efficient than the R chart. Examples are given to illustrate the use of the developed charts.

Empirical models are often used in EMP assessments of electronic equipment. Two such sets of models previously developed for prediction of EMP failure levels of discrete silicon bipolar semiconductor devices are evaluated. The sample mean and standard deviation of the ratio of failure model calculated to experimentally measured damage constant for each model and device type form the basis of the evaluation. The sample mean is used to evaluate the predictive accuracy of each model. The sample standard deviation is used to develop error bounds and to evaluate the recommended hierarchy of use of each of the model sets. The computerized data base SUPERSAP2 is the source of device numbers and experimental damage constants. Model input parameters are device electrical characteristics extracted from SUPERSAP2, vendor catalogs, and D.A.T.A. books.

Hypothesis tests

What's New in Orthopaedic Rehabilitation.

INTRODUCTION When conducting a meta-analysis that includes previously published data, differences between treatments reported with P-values, least significant differences (LSD), and other statistics provide no direct estimate of the variance. ESTIMATING STANDARD ERROR FROM OTHER SUMMARY STATISTICS (_P_, _LSD_, _MSD_) In the context of the statistical meta-analysis models that we use, overestimates of variance are okay, because this effectively reduces the weight of a study in the overall analysis relative to an exact estimate, but provides more information than either excluding the study or excluding any estimate of uncertainty (though there are limits to this assumption such as ...). Where available, direct estimates of variance are preferred, including Standard Error (SE), sample Standard Deviation (SD), or Mean Squared Error (MSE). SE is usually presented in the format of mean (±SE). MSE is usually presented in a table. When extracting SE or SD from a figure, measure from the mean to the upper or lower bound. This is different than confidence intervals and range statistics (described below), for which the entire range is collected. If MSE, SD, or SE are not provided, it is possible that LSD, MSD, HSD, or CI will be provided. These are range statistics and the most frequently found range statistics include a Confidence Interval (95%CI), Fisher’s Least Significant Difference (LSD), Tukey’s Honestly Significant Difference (HSD), and Minimum Significant Difference (MSD). Fundamentally, these methods calculate a range that indicates whether two means are different or not, and this range uses different approaches to penalize multiple comparisons. The important point is that these are ranges and that we record the entire range. Another type of statistic is a “test statistic”; most frequently there will be an F-value that can be useful, but this should not be recorded if MSE is available. Only if there is no other information available should you record the P-value.

Fever accelerates host immune system control of pathogens but at a high metabolic cost. The optimal approach to fever management and the optimal temperature thresholds used for treatment in critically ill children are unknown. To determine the feasibility of conducting a definitive randomised controlled trial (RCT) to evaluate the clinical effectiveness and cost-effectiveness of different temperature thresholds for antipyretic management. A mixed-methods feasibility study comprising three linked studies - (1) a qualitative study exploring parent and clinician views, (2) an observational study of the epidemiology of fever in children with infection in paediatric intensive care units (PICUs) and (3) a pilot RCT with an integrated-perspectives study. Participants were recruited from (1) four hospitals in England via social media (for the FEVER qualitative study), (2) 22 PICUs in the UK (for the FEVER observational study) and (3) four PICUs in England (for the FEVER pilot RCT). (1) Parents of children with relevant experience were recruited to the FEVER qualitative study, (2) patients who were unplanned admissions to PICUs were recruited to the FEVER observational study and (3) children admitted with infection requiring mechanical ventilation were recruited to the FEVER pilot RCT. Parents of children and clinicians involved in the pilot RCT. The FEVER qualitative study and the FEVER observational study had no interventions. In the FEVER pilot RCT, children were randomly allocated (1 : 1) using research without prior consent (RWPC) to permissive (39.5 °C) or restrictive (37.5 °C) temperature thresholds for antipyretics during their PICU stay while mechanically ventilated. (1) The acceptability of FEVER, RWPC and potential outcomes (in the FEVER qualitative study), (2) the size of the potentially eligible population and the temperature thresholds used (in the FEVER observational study) and (3) recruitment and retention rates, protocol adherence and separation between groups and distribution of potential outcomes (in the FEVER pilot RCT). In the FEVER qualitative study, 25 parents were interviewed and 56 clinicians took part in focus groups. Both the parents and the clinicians found the study acceptable. Clinicians raised concerns regarding temperature thresholds and not using paracetamol for pain/discomfort. In the FEVER observational study, 1853 children with unplanned admissions and infection were admitted to 22 PICUs between March and August 2017. The recruitment rate was 10.9 per site per month. The majority of critically ill children with a maximum temperature of > 37.5 °C received antipyretics. In the FEVER pilot RCT, 100 eligible patients were randomised between September and December 2017 at a recruitment rate of 11.1 per site per month. Consent was provided for 49 out of 51 participants in the restrictive temperature group, but only for 38 out of 49 participants in the permissive temperature group. A separation of 0.5 °C (95% confidence interval 0.2 °C to 0.8 °C) between groups was achieved. A high completeness of outcome measures was achieved. Sixty parents of 57 children took part in interviews and/or completed questionnaires and 98 clinicians took part in focus groups or completed a survey. Parents and clinicians found the pilot RCT and RWPC acceptable. Concerns about children being in pain/discomfort were cited as reasons for withdrawal and non-consent by parents and non-adherence to the protocol by clinicians. Different recruitment periods for observational and pilot studies may not fully reflect the population that is eligible for a definitive RCT. The results identified barriers to delivering the definitive FEVER RCT, including acceptability of the permissive temperature threshold. The findings also provided insight into how these barriers may be overcome, such as by limiting the patient inclusion criteria to invasive ventilation only and by improved site training. A definitive FEVER RCT using a modified protocol should be conducted, but further work is required to agree important outcome measures for clinical trials among critically ill children. The FEVER observational study is registered as NCT03028818 and the FEVER pilot RCT is registered as Current Controlled Trials ISRCTN16022198. This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 23, No. 5. See the NIHR Journals Library website for further project information.

In the meta-analysis, most individual research provide information in the form of {sample mean, sample standard deviation; sample size}. This is the basis for the estimate of the parameter, its standard error, confidence interval, and hypothesis test. However, in some cases, only ‘five-number summary’ information {minimum, first quartile, median, third quartile, maximum; sample size} is given. In this case, for maximum utilization of meta-information, the work of unifying information must be preceded. In most cases, it is transformed in the form {sample mean, sample standard deviation; sample size}. Several previous studies have already suggested several methods of estimating the population mean and population standard deviation from the five-number summary under the assumption of a normal population. In performance comparison studies of these methods, Lee(2022) recently proposed the maximum likelihood estimation method and showed the superiority of it, but studies on the characteristics of the standard error of the estimates were not presented. Therefore, in this study, in order to estimate the standard error of the maximum likelihood estimate(mle) based on the five-number summary, the log-likelihood function, the score function, and the Fisher information matrix(FIM) are first derived algebraically under the assumption of a normal population, and using these we create a function that computes them easily in R. Through a simulation using these, the characteristics of the standard error of the mle are identified. In addition, after estimating the FIM of the five-number summary, it was compared with the FIM of sufficient statistics and the relative efficiency was examined.

Guidelines for reporting statistics in journals published by the American Physiological Society