Sequential Methods In Statistics Research Articles

Sequential Probability Ratio Tests: Conservative and Robust

In practice, most computers generate simulation outputs sequentially, so it is attractive to analyze these outputs through sequential statistical methods such as sequential probability ratio tests (SPRTs). We investigate several SPRTs for choosing between two hypothesized values for the mean output (response). One SPRT is published in Wald (1945), and allows general distribution types. For a normal (Gaussian) distribution this SPRT assumes a known variance, but in our modified SPRT we estimate the variance. Another SPRT is published in Hall (1962), and assumes a normal distribution with an unknown variance estimated from a pilot sample. We also investigate a modification, replacing this pilot-sample estimator by a fully sequential estimator. We present a sequence of Monte Carlo experiments for quantifying the performance of these SPRTs. In experiment #1 the simulation outputs are normal. This experiment suggests that Wald (1945)’s SPRT with estimated variance gives significantly high error rates. Hall (1962)’s original and modified SPRTs are conservative; i.e., the actual error rates are much smaller than the prespecified (nominal) rates. The most efficient SPRT is our modified Hall (1962) SPRT. In experiment #2 we examine the robustness of the various SPRTs in case of nonnormal output. If we know that the output has a specific nonnormal distribution such as the exponential distribution, then we may also apply Wald (1945)’s original SPRT. Throughout our investigation we pay special attention to the design and analysis of these experiments.

Rekurencyjna estymacja gęstości prawdopodobieństwa

In the paper a survey of the asymptotic theory of recursive estimation of probability densities is given. Stress is laid on pointwise properties. In particular, asymptotic unbiasedness and consistency under possibly minimal assumptions and the rates of convergence of the mean square error, laws of theiterated logarithm and Berry-Esseen type theorems under suitably stronger assumptions are discussed for the estimators in question. The paper is a slightly modified version of an earlier paper of the second author (to appear in Sequential methods in statistics, R.Zielinski fed.J, Banach Center Publications, vol. 16 , PVN - Polish Scientific Publishers)

Determination of Sample Size for Two Stage Sequential Designs in Bioequivalence Studies under 2x2 Crossover Design

Sequential design is an adaptive design that allows for pre-mature termination of a trial due to efficacy or futility based on the interim analyses. The concept of sequential statistical methods was originally motivated by the need to obtain clinical benefits under certain economic constraints. That is for a trial for a positive results, early stopping ensures that a new drug product can exploited sooner, while negative results indicated, early stopping avoids wastage of resources. In short, the right drug at the right time for the right patient. Furthermore, the possible implication of two stage sequential design/ sample size re-estimation is to adjust the sample size based on the observed variance estimated from the first stage. The purpose of this work was to determine the minimum number of sample size required to proceed the second stage of sequential design, and the simulation is done through R ve. 3.0.3 Statistical software package. In general, from our simulation study, we can understand that, for highly variable drugs (CV ≥30), the appropriate GMR value is between (0.95, 1.05), which is also appropriate for low variable drugs to achieve the minimum sample size required to conduct any clinical trials.

Statistical optimisation of cell growth and carotenoid production by Rhodotorula mucilaginosa

Sequential statistical methods were used to maximise carotenoid production by a strain of Rhodotorula mucilaginosa, isolated from the Brazilian ecosystem. Initially, a factorial 2(5-1) experimental design was used, and the variables were pH and the levels of glucose, yeast extract, MgSO4.7H2O and KH2PO4. The nitrogen source (yeast extract) was the most important variable in enhancing carotenoid production; MgSO4.7H2O and KH2PO4 had a negative influence. The initial pH had no significant effect on carotenoid and cell productions. We further investigated the effects of glucose and yeast extract effects, using a second-order central composite design (CCD) to optimise carotenoid production, which was adequately approximated with a full quadratic equation obtained from a two-factor-2-level design. The analysis of quadratic surfaces showed that after 5 days of cultivation at 25 °C, the maximum carotenoid concentration (745 µg l(-1)) was obtained with 15 g l(-1) of yeast extract and 20 g l(-1) of glucose. The maximum carotenoid production (152 µg g(-1)) was obtained with 5 g l(-1) yeast extract and 10 g l(-1) glucose. Carotenoid formation was more sensitive to changes in yeast extract concentration than to changes in glucose concentration. Maximum cell production was achieved with 15-17 g l(-1) of yeast extract and 15-20 g l(-1) of glucose.

Signal identification and evaluation for risk of febrile seizures in children following trivalent inactivated influenza vaccine in the Vaccine Safety Datalink Project, 2010–2011

In fall 2010 in the southern hemisphere, an increased risk of febrile seizures was noted in young children in Australia in the 24 h after receipt of trivalent inactivated influenza vaccine (TIV) manufactured by CSL Biotherapies. Although the CSL TIV vaccine was not recommended for use in young children in the US, during the 2010-2011 influenza season near real-time surveillance was conducted for febrile seizures in the 0-1 days following first dose TIV in a cohort of 206,174 vaccinated children ages 6 through 59 months in the Vaccine Safety Datalink Project. On a weekly basis, surveillance was conducted with the primary approach of a self-controlled risk interval design and the secondary approach of a current vs. historical vaccinee design. Sequential statistical methods were employed to account for repeated analyses of accumulating data. Signals for seizures based on computerized data were identified in mid November 2010 using a current vs. historical design and in late December 2010 using a self-controlled risk interval design. Further signal evaluation was conducted with chart-confirmed febrile seizure cases using only data from the primary approach (i.e. self-controlled risk interval design). The magnitude of the incidence rate ratio and risk difference comparing risk of seizures in the 0-1 days vs. 14-20 days following TIV differed by receipt of concomitant 13-valent pneumococcal conjugate vaccine (PCV13). Among children 6-59 months of age, the incidence rate ratio (IRR) for TIV adjusted for concomitant PCV13 was 2.4 (95% CI 1.2, 4.7) while the IRR for PCV13 adjusted for concomitant TIV was 2.5 (95% CI 1.3, 4.7). The IRR for concomitant TIV and PCV13 was 5.9 (95% CI 3.1, 11.3). Risk difference estimates varied by age due to the varying baseline risk for seizures in young children, with the highest estimates occurring at 16 months (12.5 per 100,000 doses for TIV without concomitant PCV13, 13.7 per 100,000 doses for PCV13 without concomitant TIV, and 44.9 per 100,000 doses for concomitant TIV and PCV13) and the lowest estimates occurring at 59 months (1.1 per 100,000 doses for TIV without concomitant PCV13, 1.2 per 100,000 doses for PCV13 without concomitant TIV, and 4.0 per 100,000 doses for concomitant TIV and PCV13). Incidence rate ratio and risk difference estimates were lower for children receiving TIV without concomitant PCV13 or PCV13 without concomitant TIV. Because of the importance of preventing influenza and pneumococcal infections and associated complications, our findings should be placed in a benefit-risk framework to ensure that population health benefits are maximized.

Statistical optimisation of cell growth and carotenoid production by rhodotorula mucilaginosa

Sequential statistical methods were used to maximise carotenoid production by a strain of Rhodotorula mucilaginosa, isolated from the Brazilian ecosystem. Initially, a factorial 25–1 experimental design was used, and the variables were pH and the levels of glucose, yeast extract, MgSO4.7H2O and KH2PO4. The nitrogen source (yeast extract) was the most important variable in enhancing carotenoid production; MgSO4.7H2O and KH2PO4 had a negative influence. The initial pH had no significant effect on carotenoid and cell productions. We further investigated the effects of glucose and yeast extract effects, using a second-order central composite design (CCD) to optimise carotenoid production, which was adequately approximated with a full quadratic equation obtained from a two-factor-2-level design. The analysis of quadratic surfaces showed that after 5 days of cultivation at 25 °C, the maximum carotenoid concentration (745 µg l-1) was obtained with 15 g l-1 of yeast extract and 20 g l-1 of glucose. The maximum carotenoid production (152 µg g-1) was obtained with 5 g l-1 yeast extract and 10 g l-1 glucose. Carotenoid formation was more sensitive to changes in yeast extract concentration than to changes in glucose concentration. Maximum cell production was achieved with 15–17 g l-1 of yeast extract and 15–20 g l-1 of glucose.

C-B5-02: H1N1 Vaccine Safety Monitoring in the Vaccine Safety Datalink Project: New Challenges and Useful Lessons

Background and Aims: The worldwide introduction of influenza A (H1N1) vaccines in fall 2009 has raised widespread public questions about the safety of these new vaccines. The Vaccine Safety Datalink Project, a collaboration among CDC and eight health care systems in the HMORN, began accelerated monitoring of this vaccine’s safety in early fall 2009. Methods: The VSD Project conducts near real-time monitoring of potential adverse events following vaccination for all new vaccines. Each week, each site updates dynamic data files, and the coordinating center analyzes all data cumulatively. Repeated analysis of the same data requires adjustment for multiple testing. To address this issue, VSD uses sequential statistical methods. Evaluation of H1N1 vaccine safety poses special challenges, including confounding by indication, seasonality, and new priority groups including pregnant women. We are using several analytic methods, including: Self-controlled case-series, which compares exposed vs. unexposed time windows within the same individual; Poisson, which compares the outcomes during the current season with expected rates based on historical data for seasonal influenza vaccine; and Difference-in-difference, which compares the relative risk in exposed vs. unexposed time windows for H1N1 vaccine during the current season with the relative risk for seasonal influenza vaccine during cumulative prior seasons. Results: Pre-specified outcomes of interest include: Guillain-Barre syndrome, neuropathies, seizures, encephalitis, Bell’s palsy, ataxia, anaphylaxis, spontaneous abortion, pre-eclampsia, stroke, myocarditis and wheezing. Historical rates of these outcomes were calculated for time windows after seasonal influenza vaccination in prior seasons (2000/01–2008/09). The sequential analysis methods above will be used, and relative and absolute risks will be estimated for each outcome. For outcomes found associated with vaccination in preliminary analyses, additional evaluation will be conducted using temporal scan analyses, logistic regression, and when appropriate, medical record review.

The MRC superficial bladder cancer trial of intravesical mytomicin-c after complete surgical resection. Sequential statistical methods applied to survival data from a randomised clinical trial

Reduction in the duration of a study and in the number of patients required can be obtained when we adopt a sequential design. In this paper we re-analyse a trial completed by the British Medical Research Council on the effects of chemotherapy to prevent the recurrence of surgically removed superficial bladder cancer as if it had been monitored sequentially. The aim is to illustrate the use and benefits of sequential designs (stopping rules) and to highlight how to handle some potential problems when the assumptions of the statistical model are not satisfied. These problems are not exclusive to the sequential design, but are also present when a conventional design is used.

Early Stopping Rules in Clinical Trials Based on Sequential Monitoring of Serious Adverse Events

Several multistage or group sequential statistical methods have been developed for defining stopping rules in terms of efficacy in phase II and III clinical trials, but they rely on interim analyses after the inclusion of a fixed number of patients. These methods, however, need to be adapted for the evaluation of serious adverse events (SAEs), which can occur relatively early in the trial. A high frequency of their occurrence may require the trial to close early. The methods developed here define stopping rules after the occurrence of each SAE by comparing the number of patients included to the number of patients satisfying maximum SAE criteria. The nominal type I error, power, and average sample number (ASN) under specific hypotheses are obtained through simulations. Data from a clinical trial are presented as an example.

MULTIVARIATE CONTROL CHARTS FOR ECOLOGICAL AND ENVIRONMENTAL MONITORING

Ecological and environmental monitoring has become increasingly important, with increasing threats from human disturbances. Monitoring usually involves sampling from several sites of a similar habitat at regular (or irregular) intervals through time. The purpose of monitoring is to determine where and when an impact may have occurred or, once detected, may still be occurring. Sequential statistical methods, including control charts, as developed for industrial applications, offer some promise in this regard. These provide a way of identifying when a system (e.g., in a factory) is going “out of control,” so as to trigger an alarm to stop the system and employ appropriate remedial measures. Such techniques clearly would be useful in the context of environmental monitoring. Traditional control charts, however, cannot be used for many ecological applications because they do not handle multivariate data, and individual counts of species abundances do not generally fulfill the necessary statistical assumptions. A distance-based multivariate control chart method is described here, with some examples of its use in monitoring coral reef fish assemblages of the Great Barrier Reef, Australia. The method is flexible, as it can be based on any dissimilarity measure of choice, and useful, as it does not require any specific assumptions regarding distributions of variables. Bootstrapping techniques are used to provide control-chart limits for an appropriate multivariate distance-based criterion through time. The method is designed to identify impacts at individual sites as quickly as possible, thus triggering an “alarm bell” in the context of ecological monitoring. It can also be applied at several spatial scales in hierarchical designs.

Research Recommendations from a Lung Cancer Screening Workshop

The National Cancer Institute and the American Cancer Society cosponsored a workshop on March 7–8, 2001, in Rockville, Md, to discuss rapidly emerging technology used in screening for lung cancer; the various research methods that can be used to evaluate performance of the screening technology; and the data systems, infrastructure needs, and mechanisms for facilitating such research activities. The conclusions and recommendations from that workshop are given herein. Group 1 was asked to examine the impact of technology changes on screening studies. For example, how can the presumed future changes in low-dose helical computed tomographic technology be most effectively managed in the clinical trials setting? How do we deal, from a scientific and research point of view, with the fact that technology is changing faster than we can study it? What are the potential issues associated with the integration of computer-aided diagnosis into screening technologies. Group 1’s conclusions and recommendations were as follows: (a) Investigators should explore and develop clinical trial designs that can adapt to changing information. For example, draw sequential statistical methods and Bayesian methods from the existing statistical literature on adaptive designs. Plan for changing technology during the course of a trial, and characterize technology in an ongoing way. (b) Observer performance may dominate technology differences and the effects of screening. Therefore, measure early and train observers appropriately. (c) Consider modest, shortterm, intermediate end points to allow cutting losses early. (d) Researchers should do modeling for overall evaluation at variable times depending on goal and with detailed data on lead time, length time, and survival characteristics by cell type for patients treated and not treated. (e) Trialists should consider measuring costs during screening trials; cost-effectiveness analysis will be worthwhile if effects are present and “large.” (f) Investigators must be aggressive about quality assurance. Group 2 was asked to assess the various methodologic approaches to evaluating screening performance, efficacy, and other aspects of new screening technologies in trials and observational data. Their conclusions and recommendations were as follows: (a) Studies should be designed and performed to answer practice-relevant questions (eg, What should be done with small lesions?). (b) Models need to be developed to evaluate varying screening and treatment strategies and risk/outcome in terms of cost and effectiveness. (c) There is a need for coordinated and standardized surveillance of both screening and treatment in the community with emphasis on quality assurance. (d) All prospective studies of lung cancer screening should be organized to achieve a multidisciplinary, stateof-the-art approach to detection, treatment, and follow-up. (e) Screening programs provide a unique opportunity to educate patients on risk factors such as smoking. There is a need to evaluate different strategies to reduce smoking. Group 3 was charged with evaluating issues of data standardization and informatics. The type of comparisons to be made across studies will dictate the degree of data standardization required for various factors, such as study population, criteria for entry, follow-up, and intervention. What types of comparisons are feasible across studies? What will be the influence of rapidly evolving use of computerized systems for management of data in research and in clinical practice? Group 3’s conclusions and recommendations were as follows: (a) Support is needed for the development of a repository of standard data elements with an explicit data dictioAcad Radiol 2001; 8:942–943

Biopharmaceutical Sequential Statistical Applications.

Focusing on group sequential procedures, summarizes the sequential statistical methods used in anticancer, antiviral, cardiovascular, and gastrointestinal drug research and screening. The clinical and preclinical applications are mainly presented as case studies, many of which form part of New Drug

Biopharmaceutical Sequential Statistical Applications.

Focusing on group sequential procedures, summarizes the sequential statistical methods used in anticancer, antiviral, cardiovascular, and gastrointestinal drug research and screening. The clinical and preclinical applications are mainly presented as case studies, many of which form part of New Drug

How to Use Sequential Statistical Methods

How to Use Sequential Statistical Methods

Discussion of the Papers by Hinkley and Diciccio and Romano

Discussion of the Papers by Hinkley and Diciccio and Romano

Sequential Methods in Statistics

Sequential Methods in Statistics

Sequential Methods in Statistics.

Sequential Methods in Statistics.

Sequential Methods in Statistics.

Sequential Methods in Statistics.

Sequential Methods in Statistics (G. Barrie Wetherill)

Sequential Methods in Statistics (G. Barrie Wetherill)

Sequential Methods in Statistics.

Sequential Methods in Statistics.