Asymptotic confidence interval construction for risk difference under inverse sampling

2009 ◽  
Vol 53 (3) ◽  
pp. 621-631 ◽  
Author(s):  
Man-Lai Tang ◽  
Maozai Tian
Keyword(s):  
Confidence Interval ◽  
Risk Difference ◽  
Inverse Sampling ◽  
Asymptotic Confidence Interval

scholarly journals Coverage versus Confidence

2021 ◽  
Vol 23 ◽  
Author(s):  
Peyton Cook
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Coverage Probability ◽  
Negative Binomial ◽  
Asymptotic Confidence Interval ◽  
Population Proportion ◽  
Coverage Probabilities ◽  
The Mean

This article is intended to help students understand the concept of a coverage probability involving confidence intervals. Mathematica is used as a language for describing an algorithm to compute the coverage probability for a simple confidence interval based on the binomial distribution. Then, higher-level functions are used to compute probabilities of expressions in order to obtain coverage probabilities. Several examples are presented: two confidence intervals for a population proportion based on the binomial distribution, an asymptotic confidence interval for the mean of the Poisson distribution, and an asymptotic confidence interval for a population proportion based on the negative binomial distribution.

Common risk difference test and interval estimation of risk difference for stratified bilateral correlated data

2018 ◽  
Vol 28 (8) ◽  
pp. 2418-2438
Author(s):  
Xi Shen ◽  
Chang-Xing Ma ◽  
Kam C Yuen ◽  
Guo-Liang Tian
Keyword(s):  
Data Analysis ◽  
Confidence Interval ◽  
Score Test ◽  
Real Data ◽  
Risk Difference ◽  
Error Rates ◽  
Correlated Data ◽  
Test Statistic ◽  
Data Set ◽  
Intra Class Correlation

Bilateral correlated data are often encountered in medical researches such as ophthalmologic (or otolaryngologic) studies, in which each unit contributes information from paired organs to the data analysis, and the measurements from such paired organs are generally highly correlated. Various statistical methods have been developed to tackle intra-class correlation on bilateral correlated data analysis. In practice, it is very important to adjust the effect of confounder on statistical inferences, since either ignoring the intra-class correlation or confounding effect may lead to biased results. In this article, we propose three approaches for testing common risk difference for stratified bilateral correlated data under the assumption of equal correlation. Five confidence intervals of common difference of two proportions are derived. The performance of the proposed test methods and confidence interval estimations is evaluated by Monte Carlo simulations. The simulation results show that the score test statistic outperforms other statistics in the sense that the former has robust type [Formula: see text] error rates with high powers. The score confidence interval induced from the score test statistic performs satisfactorily in terms of coverage probabilities with reasonable interval widths. A real data set from an otolaryngologic study is used to illustrate the proposed methodologies.

A Randomized Study of the Effects of Gabapentin on Postamputation Pain

2006 ◽  
Vol 105 (5) ◽  
pp. 1008-1015 ◽  
Author(s):  
Lone Nikolajsen ◽  
Nanna B. Finnerup ◽  
Steffen Kramp ◽  
Anne-Sofie Vimtrup ◽  
Johnny Keller ◽  
...  
Keyword(s):  
Confidence Interval ◽  
Rating Scale ◽  
Day Treatment ◽  
Randomized Study ◽  
Placebo Treatment ◽  
Risk Difference ◽  
Postoperative Treatment ◽  
Limb Amputation ◽  
Phantom Pain ◽  
Postamputation Pain

Background Pain after amputation is common but difficult to treat. Therefore, the authors examined whether postoperative treatment with gabapentin could reduce postamputation stump and phantom pain. Methods Forty-six patients scheduled to undergo lower limb amputation were randomly assigned to receive oral gabapentin or placebo. Treatment was started on the first postoperative day and continued for 30 days. The daily dose of gabapentin or placebo was gradually increased to 2,400 mg/day. The intensity of stump and phantom pain was recorded every day on a numeric rating scale (0-10) during the 30-day treatment period. Five interviews were performed after 7, 14, and 30 days and after 3 and 6 months. Results Results from 41 patients were included in the data analysis. The risk of phantom pain (gabapentin vs. placebo) was 55.0% versus 52.6% (risk difference, 2.4%; 95% confidence interval, -28.9 to 33.7%; P = 0.88; 30 days) and 58.8% versus 50.0% (risk difference, 8.8%; 95% confidence interval, -23.3 to 40.9%; P = 0.59; 6 months). The median intensity of phantom pain (gabapentin vs. placebo) was 1.5 (range, 0-9.0) versus 1.2 (range, 0-6.6) (P = 0.60; 30 days) and 1.0 (range, 0-6.0) versus 0.5 (range, 0-5.0) (P = 0.77; 6 months). The median intensity of stump pain was 0.85 (range, 0-8.2) versus 1.0 (range, 0-5.4) (P = 0.68; 30 days) and 0 (range, 0-8.0) versus 0 (range, 0-5.0) (P = 0.58; 6 months). Conclusion Gabapentin administered in the first 30 postoperative days after amputation does not reduce the incidence or intensity of postamputation pain.

Estimation of the parameters of a branching process from migrating binomial observations

1998 ◽  
Vol 30 (4) ◽  
pp. 948-967 ◽  
Author(s):  
C. Jacob ◽  
J. Peccoud
Keyword(s):  
Confidence Interval ◽  
Asymptotic Behaviour ◽  
Population Size ◽  
Branching Process ◽  
Total Population ◽  
Initial Population ◽  
Asymptotic Confidence Interval ◽  
Total Population Size ◽  
Initial Population Size ◽  
Watson Process

This paper considers a branching process generated by an offspring distribution F with mean m < ∞ and variance σ2 < ∞ and such that, at each generation n, there is an observed δ-migration, according to a binomial law Bpvn*Nnbef which depends on the total population size Nnbef. The δ-migration is defined as an emigration, an immigration or a null migration, depending on the value of δ, which is assumed constant throughout the different generations. The process with δ-migration is a generation-dependent Galton-Watson process, whereas the observed process is not in general a martingale. Under the assumption that the process with δ-migration is supercritical, we generalize for the observed migrating process the results relative to the Galton-Watson supercritical case that concern the asymptotic behaviour of the process and the estimation of m and σ2, as n → ∞. Moreover, an asymptotic confidence interval of the initial population size is given.

scholarly journals The Effects of Including Aerobic Exercise in the Treatment Protocol of Concussions: A Systemic Review and Meta-analysis

2019 ◽  
Vol 7 (4) ◽  
pp. 33
Author(s):  
Sofie De Wandel ◽  
Tracey Sulak ◽  
Darryn S. Willoughby
Keyword(s):  
Physical Activity ◽  
Confidence Interval ◽  
Aerobic Exercise ◽  
Children And Adolescents ◽  
Effect Size ◽  
Meta Analysis ◽  
Risk Difference ◽  
Systemic Review ◽  
Significant Difference ◽  
The Mean

Background of Study: More research studies are being completed advocating for the use of exercise as an intervention and form of treatment for concussions. However, exercise can include many forms of physical activity, intensities, and durations. This systemic review and meta-analysis focused on the use of aerobic exercise, such as cycling or walking, as an intervention and form of treatment for children and young adults suffering from a concussion. Objective: The purpose of this systematic review and meta-analysis was to determine if the addition of aerobic exercise to an individual concussion treatment makes a significant difference when compared to treatments using flexibility as a form of physical activity or traditional methods of treatment following guidelines from the 2016 Berlin Consensus Statement on Concussion in Sport. Method: The search conducted for articles generated 472 studies. Out of these, 5 studies were selected based from the inclusion criteria. Results: Aerobic exercise was shown to significantly decrease the absolute risk difference for the development of prolonged post-concussion symptoms in children and adolescents with concussions when compared to those who reported no physical activity. The mean risk difference for the independent variable (IV) was -0.12 with a 95% confidence interval was reported to be -0.17 to -0.07 and an effect size of Z = 4.94 (P < 0.00001). Aerobic exercise was also shown to have an effect on the change in post-concussion symptom scale scores. The mean IV difference was 8.7 with a 95% confidence interval of 2.05 to 14.35 and an effect size of Z=3.02 (p=0.003). Conclusion: In conclusion, while there is evidence that aerobic exercise is beneficial for children and adolescents with a concussion, more studies need to be completed focusing on this age group and the effects of aerobic exercise on concussion recovery.

scholarly journals Association between high blood pressure and long term cardiovascular events in young adults: systematic review and meta-analysis

BMJ ◽  
2020 ◽  
pp. m3222 ◽  
Author(s):  
Dongling Luo ◽  
Yunjiu Cheng ◽  
Haifeng Zhang ◽  
Mingchuan Ba ◽  
Pengyuan Chen ◽  
...  
Keyword(s):  
Systematic Review ◽  
Blood Pressure ◽  
Young Adults ◽  
Confidence Interval ◽  
Cardiovascular Events ◽  
Meta Analysis ◽  
Risk Difference ◽  
Normal Blood ◽  
Normal Blood Pressure ◽  
Increased Risk

AbstractObjectiveTo evaluate and quantify the future risk of cardiovascular events in young adults with high blood pressure.DesignSystematic review and meta-analysis.Data sourcesMedline, Embase, and Web of Science were searched from inception to 6 March 2020. Relative risks were pooled using a random effects model and expressed with 95% confidence intervals. Absolute risk difference was calculated. Dose-response relations between blood pressure and individual outcomes were assessed by a restricted cubic spline model.Eligibility criteria for selecting studiesStudies were selected that investigated the adverse outcomes of adults aged 18-45 with raised blood pressure. The primary study outcome was a composite of total cardiovascular events. Coronary heart disease, stroke, and all cause mortality were examined as secondary outcomes.ResultsSeventeen observational cohorts consisting of approximately 4.5 million young adults were included in the analysis. The average follow-up was 14.7 years. Young adults with normal blood pressure had increased risk of cardiovascular events compared with those with optimal blood pressure (relative risk 1.19, 95% confidence interval 1.08 to 1.31; risk difference 0.37, 95% confidence interval 0.16 to 0.61 per 1000 person years). A graded, progressive association was found between blood pressure categories and increased risk of cardiovascular events (high normal blood pressure: relative risk 1.35, 95% confidence interval 1.22 to 1.49; risk difference 0.69, 95% confidence interval 0.43 to 0.97 per 1000 person years; grade 1 hypertension: 1.92, 1.68 to 2.19; 1.81, 1.34 to 2.34; grade 2 hypertension: 3.15, 2.31 to 4.29; 4.24, 2.58 to 6.48). Similar results were observed for coronary heart disease and stroke. Generally, the population attributable fraction for cardiovascular events associated with raised blood pressure was 23.8% (95% confidence interval 17.9% to 28.8%). The number needed to treat for one year to prevent one cardiovascular event was estimated at 2672 (95% confidence interval 1639 to 6250) for participants with normal blood pressure, 1450 (1031 to 2326) for those with high normal blood pressure, 552 (427 to 746) for those with grade 1 hypertension, and 236 (154 to 388) for those with grade 2 hypertension.ConclusionsYoung adults with raised blood pressure might have a slightly increased risk of cardiovascular events in later life. Because the evidence for blood pressure lowering is limited, active interventions should be cautious and warrant further investigation.

Treatment with Antithrombin or Thrombomodulin and Mortality from Heatstroke-Induced Disseminated Intravascular Coagulation: A Nationwide Observational Study

2019 ◽  
Vol 45 (08) ◽  
pp. 760-766
Author(s):  
Hiroyuki Ohbe ◽  
Shunsuke Isogai ◽  
Taisuke Jo ◽  
Hiroki Matsui ◽  
Kiyohide Fushimi ◽  
...  
Keyword(s):  
Treatment Group ◽  
Confidence Interval ◽  
Hospital Mortality ◽  
Disseminated Intravascular Coagulation ◽  
Risk Difference ◽  
Control Group ◽  
Robust Analysis ◽  
Intravascular Coagulation ◽  
Doubly Robust ◽  
Inpatient Database

AbstractHeatstroke-induced disseminated intravascular coagulation represents potential targets for specific intensive treatments. However, the effect of antithrombin or thrombomodulin treatment remains uncertain. Using a large nationwide inpatient database in Japan, this study aimed to evaluate whether treatment with antithrombin or thrombomodulin could reduce mortality among patients with heatstroke-induced disseminated intravascular coagulation. Using the Japanese Diagnosis Procedure Combination inpatient database from April 2014 to March 2017, we identified heatstroke patients who developed disseminated intravascular coagulation. We allocated patients who started treatment with antithrombin or thrombomodulin within 2 days after admission to the treatment group and allocated others to the control group. A primary outcome was in-hospital mortality. We used a doubly robust analysis to ensure the robustness of our findings. We also conducted two sensitivity analyses for thrombomodulin versus others and antithrombin versus others. We identified 1,606 eligible patients during the 81-month study period. Of these, 556 (35%) received antithrombin or thrombomodulin. The doubly robust analysis demonstrated that in-hospital mortality was significantly lower among patients in the treatment group than among those in the control group (risk difference −6.5%; 95% confidence interval: −12 to −1.4%). In-hospital mortality was significantly lower in patients with thrombomodulin than in others (risk difference −5.5%; 95% confidence interval: −9.5 to −1.6%). There was no significant difference in in-hospital mortality between patients with antithrombin and others (risk difference −4.2%; 95% confidence interval: −9.3 to 0.9%). Treatment with recombinant human thrombomodulin may be associated with lower in-hospital mortality among patients with heatstroke-induced disseminated intravascular coagulation.

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