A New Definition of P-Value Involving the Maximum Likelihood Estimator

We present here an alternative definition of the P-value for statistical hypothesis test of a real-valued parameter for a continuous random variable X. Our approach uses neither the notion of Type I error nor the assumption that null hypothesis is true. Instead, the new P-value involves the maximum likelihood estimator, which is usually available for a parameter such as the mean μ or standard deviation σ of a random variable X with a common distribution.

One-sided empirical Bayes test for location parameter in Gamma distribution

In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.

GENERALIZED p-VALUES FOR TESTING REGRESSION COEFFICIENTS IN PARTIALLY LINEAR MODELS

The one-sided and two-sided hypotheses about the parametric component in partially linear model are considered in this paper. Generalized p-values are proposed based on fiducial method for testing the two hypotheses at the presence of nonparametric nuisance parameter. Note that the nonparametric component can be approximated by a linear combination of some known functions, thus, the partially linear model can be approximated by a linear model. Thereby, generalized p-values for a linear model are studied first, and then the results are extended to the situation of partially linear model. Small sample frequency properties are analyzed theoretically. Meanwhile, simulations are conducted to assess the finite sample performance of the tests based on the proposed p-values.

Hypothesis testing of Poisson rates in COVID-19 offspring distributions

In the present study,we undertake the task of hypothesis testing in the context of Poissondistributed data.The primary objective of our investigation is to ascertain whether two distinct sets of discrete data share the same Poisson rate.We delve into a comprehensive review and comparative analysis of various frequentist and Bayesian methodologies specifically designed to address this problem.Among these are the conditional test,the likelihood ratio test,and the Bayes factor.Additionally,we employ the posterior predictive p-value in our analysis,coupled with its corresponding calibration procedures.As the culmination of our investigation,we apply these diverse methodologies to test both simulated datasets and real-world data.The latter consists of the offspring distributions linked to COVID-19 cases in two disparate geographies-Hong Kong and Rwanda.This allows us to provide a practical demonstration of the methodologies’applications and their potential implications in the field of epidemiology.

Comparison between Distractor Application on Both Radial &Ulnar Side and Radial Side Only for Fracture Distal Radius with Ulnar Styloid Fracture

Background: Fracture of distal radius with involvement of the ulnar styloid process is a common clinical problem. It can be treated conservatively, usually involving wrist immobilization in plaster cast or surgically. A key method of surgical fixation is external fixation by distractor. Distractor can be applied either only on the radial side or on both ulnar and radial sides. Materials and Methods: A prospective randomized and comparative study of 1 year duration was conducted on 32 patients admitted in the Department of Orthopaedics of BSMC & H in the age group of 20 to 75 years old with AO types B and C distal radius fracture along with involvement of the ulnar styloid process. The parameters studied were restoration of radial length, restoration of radial angle, intracarpal step-off and palmar tilt which were statistically evaluated and Fisher’s exact test was performed. The two tailed P-value was calculated and both the groups were statistically compared. Results: In our study, 37.5% patients in Group A and 81.25% in Group B had a radial difference Table 1, Chart 1). 43.75% patients in Group A and 87.5% in Group B had radial angle Table 2, Chart 2). 31.25% in Group A and 75% had intra carpal step off Table 3, Chart 3). 62.5% had an abnormal palmar tilt in Group A while only 6.25% had an abnormal palmar tilt in Group B which is extremely statistically significant. On an average, 2 mm of distraction was required in 75% patients of Group A while only 30% patients in Group B required distraction (Table 4, Chart 4). Conclusion: In our study, the radial difference, radial angle, intra carpal step off and palmar tilt returned significantly to normal in the patients treated with distractor on radial side only when compared with distractor application on both radial and ulnar sides for distal radius fracture with ulnar styloid process involvement. Also post-operative distraction required under image intensifier was higher in the group treated with distractor on either side than those with distractor only on radial side.

Inverted Simulations Demonstrating Strong Ecological Fallacies in Cohort Studies

We start with a description of the statistical inferential framework and the duality between observed data and the true state of nature that underlies it. We demonstrate here that the usual testing of dueling hypotheses and the acceptance of one and the rejection of the other is a framework which can often be faulty when such inferences are applied to individual subjects. This follows from noting that the statistical inferential framework is predominantly based on conclusions drawn for aggregates and noting that what is true in the aggregate frequently does not hold for individuals, an ecological fallacy. Such a fallacy is usually seen as problematic when each data record represents aggregate statistics for counties or districts and not data for individuals. Here we demonstrate strong ecological fallacies even when using subject data. Inverted simulations, of trials rightly sized to detect meaningful differences, yielding a statistically significant p-value of 0.000001 （1 in a million） and associated with clinically meaningful differences between a hypothetical new therapy and a standard therapy, had a proportion of instances of subjects with standard therapy effect better than new therapy effects close to 30%. A ―winner take all‖ choice between two hypotheses may not be supported by statistically significant differences based on stochastic data. We also argue the incorrectness across many individuals of other summaries such as correlations, density estimates, standard deviations and predictions based on machine learning models. Despite artifacts we support the use of prospective clinical trials and careful unbiased model building as necessary first steps. In health care, high touch personalized care based on patient level data will remain relevant even as we adopt more high tech data-intensive personalized therapeutic strategies based on aggregates.

FDR Control for Pairwise Comparisons of Normal Means Based on Goodness of Fit Test

This study is undertaken to apply a bootstrap method of controlling the false discovery rate （FDR） when performing pairwise comparisons of normal means. Due to the dependency of test statistics in pairwise comparisons, many conventional multiple testing procedures can＇t be employed directly. Some modified pro- cedures that control FDR with dependent test statistics are too conservative. In the paper, by bootstrap and goodness-of-fit methods, we produce independent p-values for pairwise comparisons. Based on these indepen- dent p-values, plenty of procedures can be used, and two typical FDR controlling procedures are applied here. An example is provided to illustrate the proposed approach. Extensive simulations show the satisfactory FDR control and power performance of our approach. In addition, the proposed approach can be easily extended to more than two normal, or non-normal, balance or unbalance cases.