Estimation of population parameters using sample extremes from nonconstant sample sizes

Sleep improvement is a promising target for preventing and modifying many health problems. Hypnosis is considered a cost-effective and safe intervention with reported benefits for multiple health conditions. There is a growing body of research assessing the efficacy of hypnosis for various health conditions in which sleep was targeted as a primary or secondary outcome. This review aimed to investigate the effects of hypnosis interventions on sleep, to describe the hypnotic procedures, and to evaluate potential adverse effects of hypnosis. We reviewed studies (prior to January 2017) using hypnosis in adults for sleep problems and other conditions comorbid with sleep problems, with at least one sleep outcome measure. Randomized controlled trials and other prospective studies were included. One hundred thirty-nine nonduplicate abstracts were screened, and 24 of the reviewed papers were included for qualitative analysis. Overall, 58.3% of the included studies reported hypnosis benefit on sleep outcomes, with 12.5% reporting mixed results, and 29.2% reporting no hypnosis benefit; when only studies with lower risk of bias were reviewed the patterns were similar. Hypnosis intervention procedures were summarized and incidence of adverse experiences assessed. Hypnosis for sleep problems is a promising treatment that merits further investigation. Available evidence suggests low incidence of adverse events. The current evidence is limited because of few studies assessing populations with sleep complaints, small samples, and low methodological quality of the included studies. Our review points out some beneficial hypnosis effects on sleep but more high-quality studies on this topic are warranted.

Some Thoughts About Data Type, Distribution, and Statistical Significance

The electronics industry has heavily prioritized enhancing the quality, lifetime and conforming rate (conforming to specifications) of electronic components. Various methods have been developed for assessing quality performance. In practice, process capability indices (PCIs) are used as a means of measuring process potential and performance. Moreover, most PCIs have been developed or investigated under the assumption that electronic components have a lifetime with a normal distribution. However, PCIs for non‐normal distributions have seldom been discussed. Nevertheless, the lifetime of electronic components generally may possess an exponential, gamma or Weibull distribution and so forth. Under an exponential distribution, some properties of the PCIs and their estimators differ from those in a normal distribution. To utilize the PCIs more reasonably and accurately in assessing the lifetime performance of electronic components, this study constructs a uniformly minimum variance unbiased (UMVU) estimator of their lifetime performance index under an exponential distribution. The UMVU estimator of the lifetime performance index is then utilized to develop the hypothesis testing procedure. The purchasers can then employ the testing procedure to determine whether the lifetime of the electronic components adheres to the required level. Manufacturers can also utilize this procedure to enhance process capability.

We deal with the design problem of early phase dose-finding clinical trials with monotone biologic endpoints, such as biological measurements, laboratory values of serum level, and gene expression. A specific objective of this type of trial is to identify the minimum dose that exhibits adequate drug activity and shifts the mean of the endpoint from a zero dose to the so-called minimum effective dose. Stepwise test procedures for dose finding have been well studied in the context of nonhuman studies where the sampling plan is done in one stage. In this article, we extend the notion of stepwise testing to a two-stage enrollment plan in an attempt to reduce the potential sample size requirement by shutting down unpromising doses in a futility interim. In particular, we examine four two-stage designs and apply them to design a statin trial with four doses and a placebo in patients with Hodgkin's disease. We discuss the calibration of the design parameters and the implementation of these proposed methods. In the context of the statin trial, a calibrated two-stage design can reduce the average total sample size up to 38% (from 125 to 78) from a one-stage step-down test, while maintaining comparable error rates and probability of correct selection. The price for the reduction in the average sample size is the slight increase in the maximum total sample size from 125 to 130.

This paper is concerned with tests of distribution free methods in sequential form. One of the most outstanding features of this methods is the broad field of application, we don’t need almost any assumption about the distribution function of the random variable that we study. Unfortunately this distribution free methods need a large sample size to get the neccessary accuracy, so the usefulness of sequential methods that have great savings in average sample size. The distribution free test in sequential form has two very important proprieties, broad field of application and a small average sample size. In the first chapter the author give a test S for the median of any distribution, that, in the case of normal distribution has one relative efficiency of 60% againts Wald sequential test, and about 120% against current most powerful test. So we can use this test S instead of the most powerful test with advantage in sample size and in numerical calculus, because the test S is very simple. In the second chapter, the previous tests S is adapted to “two sample problem”, in first time with alternative hypothesis of differences in location, and then generalized to any alternative. With normal distribution and alternative hypothesis of differences in location the test presented by the author is most powerful and smaller in sample size than other usual tests, Wilcoxon, Wald and Wolfowitz, Epstein, Tsao. In the chapter three the author study the tests of randomness in a similar way.

A return on investment analysis of applying health monitoring to LED lighting systems

BackgroundA typical antipsychotics for neuropsychiatric symptoms in dementia have been tested in much larger trials than the older conventional drugs. The advantage of larger sample sizes is that negative findings become less likely and the effect estimates more precise. However, as sample sizes increase, the trials also get more expensive and time consuming while exposing more patients to drugs with unknown safety profiles. Moreover, a large sample size might yield a statistically significant effect that is not necessarily clinically relevant.ObjectiveTo assess (1) the variation in sample size and sample size calculations of antipsychotic trials in dementia, (2) the size of reported treatment effects and related statistical significance, and (3) general study characteristics that might be related to sample size.Study Design and SettingWe performed a meta-epidemiological study of randomized trials that tested antipsychotics for neuropsychiatric symptoms in dementia. The trials compared conventional or atypical antipsychotics with placebo or another antipsychotic. Two reviewers independently extracted sample size, sample size calculations, reported treatment effects with p-values, and general study characteristics (drug type, trial duration, type of funding). We calculated a reference sample size of 83 and 433 per study group for the placebo-controlled and head-to-head trials respectively.ResultsWe identified 33 placebo-controlled trials, and 18 head-to-head trials. Only 14 (42%) and 2 (11%), respectively, reported a sample size calculation. The average sample size per arm was 34 (range 6–179) in placebo-controlled trials testing conventional drugs, 107 (8–237) in such trials testing atypical drugs, and 104 (95–115) in such trials testing both drug types; it was 31 (10–88) in head-to-head trials. Thirteen out of 18 trials with sample sizes larger than required (72%) reported a statistically significant treatment effect, of which two (15%) were clinically relevant. None of the head-to-head trials reported a statistically significant treatment effect, even though some suggested non-inferiority. In placebo-controlled trials of atypical drugs, longer trial duration (>6 weeks) and commercial funding were associated with higher sample size.ConclusionSample size calculations were poorly reported in antipsychotic trials for dementia. Placebo-controlled trials of atypical antipsychotics showed large sample size fallacy while head-to-head trials were massively underpowered.

Objective: In past years, the focus of genetic-epidemiological studies has shifted to analyzing complex diseases. Here, single genes often contribute only little to the manifestation of traits so that many probands have to be included in a study to reliably detect small effects. To reduce the number of required phenotypings and genotypings and thus facilitate analyzing complex traits, sequential study designs can be applied. Methods: For sequential analyses of complex diseases in association studies, we compare the procedure by Sobell et al. (Am J Med Genet 1993;48:28–35) with the adaptation of formal group sequential study designs by Pampallona and Tsiatis (J Stat Plan Inf 1994;42:19–35). Error rates and average sample sizes are investigated by Monte-Carlo simulations. Results: Formal sequential designs have a higher power regardless of underlying genetic effects. In addition, compared with conventional designs with fixed samples, average sample sizes are reduced considerably; under the null hypothesis of no association, up to 50% of the required sample size can be spared. Conclusions: To increase the efficiency of genetic-epidemiological case-control studies, we recommend using formal group sequential study designs. The tremendous savings in average sample sizes are expected to affect both cost and time spent on large-scale studies.

The primary focus of the paper is to establish both numerical and experimental methods to control the concentration of samples in a microreactor well. The concentration of the reacting samples is controlled by varying the initial sample size and electric field. Further, the paper numerically investigates the feasibility of mixing and reacting nanoliter samples with a wide variation in reaction rates in the microreactor driven by electro-osmotic pumping. Two discrete samples are measured and transported to the microreactor simultaneously by electro-osmotic pinching and switching. The transported samples are mixed in the microreactor and floated for 4.5 s for reaction to occur. It is seen that the normalized concentration of the product increases from 0.25 to 0.45 during that period. Also the effects of sample size and applied electric field on sample concentration during the switching process are studied. It is found that the normalized final sample concentration increases from 0.03 to 0.11 with an increase in sample size from 60 to 150 µm, at a constant electric field. Further, by increasing the electric field from 100 to 1000 V cm−1, at a constant sample size, there is a significant decrease in the final concentration of the sample from 0.14 to 0.04. Our studies also show that the normalized product concentration depends on the reaction rate and increases from 0.28 to 0.48 as the reaction rate increases from 10 L mol−1 s−1 to 105 L mol−1 s−1. However, the increase in the reaction rate beyond 105 L mol−1 s−1 does not influence the product concentration for the present design of the microreactor. Our microreactor with improved mixing can be used for assessing reactions of biological samples. The optimized sample size along with a controlled electric field for sample injection forms the basis for developing a prototype of a microreactor device for high throughput drug screening.

Random sampling is a fundamental primitive in modern algorithms, statistics, and machine learning, used as a generic method to obtain a small yet subset of the data. In this work, we investigate the robustness of sampling against adaptive adversarial attacks in a streaming setting: An adversary sends a stream of elements from a universe U to a sampling algorithm (e.g., Bernoulli sampling or reservoir sampling), with the goal of making the sample unrepresentative of the underlying data stream. The adversary is fully adaptive in the sense that it knows the exact content of the sample at any given point along the stream, and can choose which element to send next accordingly, in an online manner. Well-known results in the static setting indicate that if the full stream is chosen in advance (non-adaptively), then a random sample of size Ω(d/e2) is an e-approximation of the full data with good probability, where d is the VC-dimension of the underlying set system (U, R). Does this sample size suffice for robustness against an adaptive adversary? The simplistic answer is negative : We demonstrate a set system where a constant sample size (corresponding to a VC-dimension of 1) suffices in the static setting, yet an adaptive adversary can make the sample very unrepresentative, as long as the sample size is (strongly) sublinear in the stream length, using a simple and easy-to-implement attack. However, this attack is theoretical only, requiring the set system size to (essentially) be exponential in the stream length. This is not a coincidence: We show that in order to make the sampling algorithm robust against adaptive adversaries, the modification required is solely to replace the VC-dimension term d in the sample size with the cardinality term log |R|. That is, the Bernoulli and reservoir sampling algorithms with sample size Ω(log |R|/e2) output a representative sample of the stream with good probability, even in the presence of an adaptive adversary. This nearly matches the bound imposed by the attack.

Поставлено і розв’язано для деяких окремих випадків, важливих в практичній діяльності, обернену задачу побудови толерантних інтервалів. Розв’язок отримано для планування експерименту в непараметричному випадку, а також для рівномірного розподілу, показникового розподілу, розподілу Вейбулла, нормального розподілу, логарифмічно нормального розподілу. Запропоновано чисельні методи розв’язання поставлених задач, доступних для найбільш поширених програмних продуктів. Прямою задачею побудови толерантних інтервалів в параметричному випадку названо задачу, в якій при заданому об'ємі вибірки, відомому закону розподілу і його параметрів, визначених за вибірковими даними, заданому рівні довіри (статистичній надійності) необхідно визначити межі можливих значень випадкової величини, в яких може знаходитися задана частка вибірки. За відсутності відомостей про вид закону розподілу вибірки розглянуто розв’язок задачі в непараметричному випадку. При виконанні розрахунків чисельних прикладів прийнято наступні умови. Для частки генеральної сукупності прийнято стандартні умови: 0,75; 0,90; 0,95; 0,99; для заданої статистичної надійності прийнято значення: 0,90; 0,95; 0,99. Прийнято, що вибірка містить не менш ніж 30 спостережень. Обмеження на об'єм вибірки обумовлені тим, що, по-перше, при меншому об'ємі вибірки необхідне створення спеціалізованих програмних продуктів, по-друге, обробка даних, отриманих по вибірках меншого об’єму, не завжди має змістовний сенс. При розв’язанні задачі в непараметричному випадку отримано таблицю, яка дозволяє обрати розв’язок поставленої задачі для заданих умов. Показано, що вибірки більше, ніж 300 спостережень не дають істотних змін у розв’язку задачі. Для всіх перерахованих розподілів визначені, для нижнього і верхнього значень меж толерантних інтервалів, об'єми вибірок, що забезпечують необхідні ймовірнісні характеристики: частку вибірки в генеральній сукупності і її статистичну надійність. Для нормального розподілу поставлена задача вирішена для варіанту двостороннього толерантного інтервалу.

Abstract. Exponential family statistical distributions, including the well-known normal, binomial, Poisson, and exponential distributions, are overwhelmingly used in data analysis. In the presence of covariates, an exponential family distributional assumption for the response random variables results in a generalized linear model. However, it is rarely ensured that the parameters of the assumed distributions are stable through the entire duration of the data collection process. A failure of stability leads to nonsmoothness and nonlinearity in the physical processes that result in the data. In this paper, we propose testing for stability of parameters of exponential family distributions and generalized linear models. A rejection of the hypothesis of stable parameters leads to change detection. We derive the related likelihood ratio test statistic. We compare the performance of this test statistic to the popular normal distributional assumption dependent cumulative sum (Gaussian CUSUM) statistic in change detection problems. We study Atlantic tropical storms using the techniques developed here, so to understand whether the nature of these tropical storms has remained stable over the last few decades.

In randomised controlled trials that have non-compliance with the treatment assigned, policy makers require unbiased estimates of the causal effect of the treatment received.Instrumental variable (IV) approaches provide complier average causal effects (CACE) estimates.Common IV methods such as two-stage least squares (2SLS) have not been extended to settings with multivariate outcomes.We propose a three-stage least squares (3SLS) regression approach, whereby estimates from the first stage regression of treatment received conditional on assignment, feed into a seemingly unrelated regression (SUR) system of equations that recognise the correlation between the outcomes.We also develop Bayesian IV approaches which jointly model the effects of random assignment on treatment received, and the bivariate outcome, which here is assume to be cost-effectiveness.We also apply 2SLS individually to each outcome, for comparison.We consider the performance of these methods in a simulation study, where costs are assumed to follow Normal or Gamma distributions, to have positive and negative correlation with health outcomes, the instrument is strong (30% non-compliance) or weak (70% noncompliance), and the sample size, moderate (n=1,000) or small (n=100).We find that the proposed IV methods generally perform well.For example, in scenarios with Normally distributed cost data and a strong instrument, each method reports unbiased estimates.However, in these settings the 2SLS approach reports levels of Confidence Interval (CI) coverage that are above (positive correlation) and below (negative correlation) nominal levels.By contrast both the 3SLS and Bayesian methods report CI coverage close to nominal levels.

Srivastava (1966) has proposed two classes of asymptotically efficient sequential procedures for selecting the population with the largest mean when nothing is assumed about the form of the distribution functions except for the finiteness of unknown variance. In order to choose between these two classes, it seems desirable to study the performance of these two classes of sequential procedures for moderate sample sizes. In this paper, assuming that these populations are normal, the average sample sizes and the error probabilities actually obtained are computed to compare the two procedures. Results of calculation show that Procedure B (see Section 2) is better than Procedure A in that the average sample size is smaller while the error probabilities are almost the same (the superiority of procedure B was suggested by Srivastava (1966) for a different intuitive reason). At the same time the calculation helps to show the closeness of the error probability (both cases) to $\alpha$. The calculation is on the lines of Ray (1957) and Robbins (1959) by generalizing a problem of the latter. Starr (1966) has recently carried out calculations to study the performance of a sequential procedure for finding fixed-width confidence bounds for the normal mean (see also Chow and Robbins, 1965).

In testing hypotheses about an exponential distribution with probability density function $p(x; \theta, A) = (1/\theta)e^{-(x - A)/\theta},\quad \text{ for } x \geqq A,\\= 0,\quad \text{ for } x < A,$ where $\theta > 0$, the following questions arise: (1) Are certain linear forms in the order statistics of a random sample of size $n$ from this distribution distributed as chi-square random variables? (2) Are certain linear forms in the order statistics stochastically independent? The first two theorems in Section 2 answer these questions. As a consequence of these two theorems, several results follow which are similar to those pertaining to quadratic forms in normally distributed variables. The characterization theorem in Section 3 was suggested by a result for normally distributed variables. Lukacs [4] proved that if a random sample is taken from a continuous type distribution with finite variance, then the independence of the sample mean and the sample variance characterizes the normal distribution. That is, the independence of the estimates of the two parameters of the normal distribution characterizes that distribution. Now if $X_1 < X_2 < \cdots < X_n$ are the order statistics of a random sample from the exponential distribution $p(x; \theta, A)$, then $X_1$ and $(1/n) \sum^n_{i = 1} (X_i - X_1)$ are estimates of the parameters $A$ and $\theta$, respectively. In Section 3, we prove that the independence of these two statistics characterizes this exponential distribution.