Efficient confidence intervals for the difference of two Bernoulli distributions’ success parameters

Cluster randomization trials, in which intact social units are randomized to different interventions, have become popular in the last 25 years. Outcomes from these trials in many cases are positively skewed, following approximately lognormal distributions. When inference is focused on the difference between treatment arm arithmetic means, existent confidence interval procedures either make restricting assumptions or are complex to implement. We approach this problem by assuming log-transformed outcomes from each treatment arm follow a one-way random effects model. The treatment arm means are functions of multiple parameters for which separate confidence intervals are readily available, suggesting that the method of variance estimates recovery may be applied to obtain closed-form confidence intervals. A simulation study showed that this simple approach performs well in small sample sizes in terms of empirical coverage, relatively balanced tail errors, and interval widths as compared to existing methods. The methods are illustrated using data arising from a cluster randomization trial investigating a critical pathway for the treatment of community acquired pneumonia.

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Comment on "Quantitative performance metrics for stratospheric-resolving chemistry-climate models" by Waugh and Eyring (2008)

Atmospheric Chemistry and Physics ◽

10.5194/acp-9-9101-2009 ◽

2009 ◽

Vol 9 (23) ◽

pp. 9101-9110 ◽

Cited By ~ 9

Author(s):

V. Grewe ◽

R. Sausen

Keyword(s):

Observational Data ◽

Confidence Intervals ◽

Climate Models ◽

Performance Metrics ◽

Statistical Tests ◽

Low Grade ◽

Perfect Model ◽

Special Cases ◽

Quantitative Performance ◽

The Difference

Abstract. This comment focuses on the statistical limitations of a model grading, as applied by D. Waugh and V. Eyring (2008) (WE08). The grade g is calculated for a specific diagnostic, which basically relates the difference of means of model and observational data to the standard deviation in the observational dataset. We performed Monte Carlo simulations, which show that this method has the potential to lead to large 95%-confidence intervals for the grade. Moreover, the difference between two model grades often has to be very large to become statistically significant. Since the confidence intervals were not considered in detail for all diagnostics, the grading in WE08 cannot be interpreted, without further analysis. The results of the statistical tests performed in WE08 agree with our findings. However, most of those tests are based on special cases, which implicitely assume that observations are available without any errors and that the interannual variability of the observational data and the model data are equal. Without these assumptions, the 95%-confidence intervals become even larger. Hence, the case, where we assumed perfect observations (ignored errors), provides a good estimate for an upper boundary of the threshold, below that a grade becomes statistically significant. Examples have shown that the 95%-confidence interval may even span the whole grading interval [0, 1]. Without considering confidence intervals, the grades presented in WE08 do not allow to decide whether a model result significantly deviates from reality. Neither in WE08 nor in our comment it is pointed out, which of the grades presented in WE08 inhibits such kind of significant deviation. However, our analysis of the grading method demonstrates the unacceptably high potential for these grades to be insignificant. This implies that the grades given by WE08 can not be interpreted by the reader. We further show that the inclusion of confidence intervals into the grading approach is necessary, since otherwise even a perfect model may get a low grade.

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Uncertainty and Inference for Verification Measures

Weather and Forecasting ◽

10.1175/waf989.1 ◽

2007 ◽

Vol 22 (3) ◽

pp. 637-650 ◽

Cited By ~ 74

Author(s):

Ian T. Jolliffe

Keyword(s):

Hypothesis Testing ◽

Confidence Intervals ◽

Multiple Testing ◽

Prediction Intervals ◽

Hypothesis Tests ◽

Statistical Inferences ◽

The Difference ◽

Main Ideas

Abstract When a forecast is assessed, a single value for a verification measure is often quoted. This is of limited use, as it needs to be complemented by some idea of the uncertainty associated with the value. If this uncertainty can be quantified, it is then possible to make statistical inferences based on the value observed. There are two main types of inference: confidence intervals can be constructed for an underlying “population” value of the measure, or hypotheses can be tested regarding the underlying value. This paper will review the main ideas of confidence intervals and hypothesis tests, together with the less well known “prediction intervals,” concentrating on aspects that are often poorly understood. Comparisons will be made between different methods of constructing confidence intervals—exact, asymptotic, bootstrap, and Bayesian—and the difference between prediction intervals and confidence intervals will be explained. For hypothesis testing, multiple testing will be briefly discussed, together with connections between hypothesis testing, prediction intervals, and confidence intervals.

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Hacer estimaciones estadísticas

ENERO-JUNIO 2021 - Revista Innovaciones de Negocios ◽

10.29105/rinn5.10-10 ◽

2017 ◽

Vol 5 (10) ◽

Author(s):

M. H Badii

Keyword(s):

Confidence Intervals ◽

Statistical Estimation ◽

Good Estimator ◽

The Mean ◽

The Difference

Keywords: Estimations, sampling, statisticsAbstract. The notion of statistical estimation both in terms of point and interval is described. The criteria of a good estimator are noted. The procedures to calculate the intervals for the mean, proportions and the difference among two means as well as the confidence intervals for the probable errors in statistics are provided.Palabras clave: Estadística, estimación, muestreoResumen. En la presente investigación se describen la noción de la estimación estadística, tanto de tipo puntual con de forma de intervalo. Se presentan los criterios que debe reunir un estimador bueno. Se notan con ejemplos, la forma de calcular la estimación del intervalo para la media, la proporción y de la diferencia entre dos medias y los intervalos de confianza para los errores probables.

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Bootstrap-calibrated empirical likelihood confidence intervals for the difference between two Gini indexes

The Journal of Economic Inequality ◽

10.1007/s10888-017-9348-8 ◽

2017 ◽

Vol 15 (2) ◽

pp. 195-216 ◽

Cited By ~ 2

Author(s):

Xiaofeng Lv ◽

Gupeng Zhang ◽

Xinkuo Xu ◽

Qinghai Li

Keyword(s):

Confidence Intervals ◽

Empirical Likelihood ◽

The Difference

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Effect of Sodium-Transport Inhibitors on Bronchial Reactivity in Vivo

Clinical Science ◽

10.1042/cs0790325 ◽

1990 ◽

Vol 79 (4) ◽

pp. 325-330 ◽

Cited By ~ 11

Author(s):

Alan J. Knox ◽

John R. Britton ◽

Anne E. Tattersfield

Keyword(s):

Confidence Intervals ◽

Sodium Transport ◽

Geometric Mean ◽

Normal Subjects ◽

Bronchial Reactivity ◽

Mean Values ◽

Doubling Dose ◽

The Difference

1. We have recently shown that ouabain, an inhibitor of Na+/K+-adenosine triphosphatase, causes contraction of bovine and human airways in vitro, and that amiloride causes relaxation and inhibits receptor-operated contraction in bovine trachealis. 2. To determine whether such drugs alter bronchial reactivity in vivo, we have studied the effect of oral digoxin (an inhibitor of Na+/K+-adenosine triphosphatase) and oral and inhaled amiloride on bronchial reactivity to histamine in three double-blind, placebo-controlled studies. 3. Histamine reactivity was measured as the provocative dose causing a 20% reduction in the forced expiratory volume in 1 s (PD20FEV1) or, when normal subjects were included, the provocative dose causing a 35% reduction in the specific airways conductance (PD35sGaw); the results are given as geometric mean values. 4. In study 1, 13 atopic asthmatic subjects were given 20 mg of oral amiloride or placebo on separate days. Two hours after the drug, the geometric mean PD20FEV1 for histamine was 0.43 μmol after amiloride and 0.54 μmol after placebo (95% confidence intervals for the difference: 0.9 to −0.2 doubling doses of histamine; P = 0.2). 5. In study 2, six normal and 24 atopic asthmatic men inhaled 10 ml of 10−2 mol/l amiloride or diluent control in a crossover study. The mean values of PD35sGaw for histamine immediately after inhalation of amiloride and placebo were 3.0 μmol and 4.3 μmol, respectively, in the normal subjects (95% confidence intervals for the difference: −0.53 to 1.52 doubling doses, P = 0.2), and 0.33 μmol and 0.29 μmol in the asthmatic subjects (95% confidence intervals for the difference: −0.95 to 0.57 doubling doses; P = 0.6). 6. In study 3, 24 atopic asthmatic men were treated for 7 days with placebo or oral digoxin (1.5 mg loading dose plus 0.25 mg twice daily for 6 days). The PD20FEV1 for histamine was measured before, 12 h after the loading dose and on day 7 of treatment. The change in PD20FEV1 did not differ significantly after digoxin and placebo, after either 1 day's treatment [mean (95% confidence intervals) difference: 0.56 doubling dose (−0.37 to 1.5 doubling dose)] or 7 day's treatment [mean (95% confidence intervals) difference: 0.3 doubling dose (−1.23 to 1.8 doubling doses)]. 7. Although our work in vitro has suggested that membrane sodium transport may play an important role in determining airway smooth muscle contractility, we have been unable to demonstrate any effect of the sodium-transport inhibitors amiloride and digoxin on histamine reactivity in these studies.

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Involvement of Workers in Closed and Semiclosed Institutions in Outbreaks of Acute Gastroenteritis Due to Norovirus

Viruses ◽

10.3390/v12121392 ◽

2020 ◽

Vol 12 (12) ◽

pp. 1392

Author(s):

Ignacio Parrón ◽

Irene Barrabeig ◽

Miquel Alseda ◽

Thais Cornejo-Sánchez ◽

Susana Guix ◽

...

Keyword(s):

Prospective Study ◽

Confidence Intervals ◽

Personal Hygiene ◽

Occupational Category ◽

Hygiene Measures ◽

The Mean ◽

The Difference ◽

Rate Ratios ◽

A Prospective Study ◽

Mean Cycle

Norovirus outbreaks frequently occur in closed or semiclosed institutions. Recent studies in Catalonia and various countries indicate that, during outbreaks in these institutions, norovirus is detected in between 23% and 60% of workers, and the prevalence of infection in asymptomatic workers involved in outbreaks ranges from 17% to 40%. In this work, we carried out a prospective study to investigate the involvement of workers in closed and semiclosed institutions during outbreaks. The attack rates (ARs) and the rate ratios (RRs) were calculated according to the type of transmission and occupational category. The RRs and 95% confidence intervals (CIs) between workers and users were calculated. The mean cycle of quantification (Cq) values were compared according to the genogroup and the presence of symptoms. ARs were higher in person-to-person transmission than in common vehicle outbreaks, and 38.8% of workers were symptomatic. The RR between workers and users was 0.46 (95% CI 0.41–0.52). The ARs in workers were high, particularly in workers with closer contact with users. The mean Cq was lower in patients than in asymptomatic infected persons, although the difference was only significant for genogroup I (GI). The frequency of asymptomatic infected persons suggests that personal hygiene measures should be followed by all workers in the centers affected.

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