A Geometric Comparison of the Delta and Fieller Confidence Intervals

Background Determining the incidence, disease-associated serotypes and antimicrobial susceptibility of invasive pneumococcal disease (IPD) among children in Africa is essential in order to monitor the impact of these infections prior to widespread introduction of the pneumococcal conjugate vaccine (PCV). Methods To provide updated estimates of the incidence, serotype distribution, and antimicrobial susceptibility profile of Streptococcus pneumoniae causing disease in Africa, we performed a systematic review of articles published from 2000–2015 using Ovid Medline and Embase. We included prospective and surveillance studies that applied predefined diagnostic criteria. Meta-analysis for all pooled analyses was based on random-effects models. Results We included 38 studies consisting of 386,880 participants in 21 countries over a total of 350,613 person-years. The pooled incidence of IPD was 62.6 (95% CI 16.9, 226.5) per 100,000 person-years, including meningitis which had a pooled incidence of 24.7 (95% CI 11.9, 51.6) per 100,000 person-years. The pooled prevalence of penicillin susceptibility was 78.1% (95% CI 61.9, 89.2). Cumulatively, PCV10 and PCV13 included 66.9% (95% CI 55.9, 76.7) and 80.6% (95% CI 66.3, 90.5) of IPD serotypes, respectively. Conclusions Our study provides an integrated and robust summary of incidence data, serotype distribution and antimicrobial susceptibility for S. pneumoniae in children ≤5 years of age in Africa prior to widespread introduction of PCV on the continent. The heterogeneity of studies and wide range of incidence rates across the continent indicate that surveillance efforts should be intensified in all regions of Africa to improve the integrity of epidemiologic data, vaccine impact and cost benefit. Although the incidence of IPD in young children in Africa is substantial, currently available conjugate vaccines are estimated to cover the majority of invasive disease-causing pneumococcal serotypes. These data provide a reliable baseline from which to monitor the impact of the broad introduction of PCV.

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“…Fieller’s method was used to calculate the 95% CI for the percentage of cases attributable to meningitis as part of IPD overall. 13 …”

Section: Methodsmentioning

confidence: 99%

Childhood pneumococcal disease in Africa – A systematic review and meta-analysis of incidence, serotype distribution, and antimicrobial susceptibility

Tam

Thielen

Obaro

et al. 2017

Vaccine

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“…(4) is easier to implement than (2), and is in fact the limit of (2) in the large sample case, because as n → ∞, we have t α /2 (r ) → z α /2 , → 0, and Var(X ) ∼ O(1/n). Although Fieller's confidence interval can be more accurate for small samples [30], this benefit appears rather limited for big data. Moreover, the Delta method can also be easily extended for a better approximation by using Edgeworth expansion [5,29].…”

Section: Delta Methods and Edgeworth Correctionmentioning

confidence: 99%

Applying the Delta Method in Metric Analytics

Deng

Knoblich

2018

Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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During the last decade, the information technology industry has adopted a data-driven culture, relying on online metrics to measure and monitor business performance. Under the setting of big data, the majority of such metrics approximately follow normal distributions, opening up potential opportunities to model them directly without extra model assumptions and solve big data problems via closed-form formulas using distributed algorithms at a fraction of the cost of simulation-based procedures like bootstrap. However, certain attributes of the metrics, such as their corresponding data generating processes and aggregation levels, pose numerous challenges for constructing trustworthy estimation and inference procedures. Motivated by four real-life examples in metric development and analytics for large-scale A/B testing, we provide a practical guide to applying the Delta method, one of the most important tools from the classic statistics literature, to address the aforementioned challenges. We emphasize the central role of the Delta method in metric analytics by highlighting both its classic and novel applications.

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“…An alternative method for the construction of CIs for ratios is Fieller's (1954) proposal. This approach has been shown to be superior to the application of the Delta method in several applications (e.g., Hirschberg and Lye ). This superiority has been found in the coverage of the resulting tests where the estimated

100 (1 - α) %

interval from the Fieller method more closely coincides with the theoretical interval than the alternate Delta interval .…”

Section: Introductionmentioning

confidence: 99%

“…See Hirschberg and Lye () for more details on the nature of the relationship between the CIs for both methods. In general, when the denominator is significantly different from zero and the correlation between the denominator and the numerator is the same sign as the ratio, the Delta and the Fieller will tend to coincide.…”

mentioning

confidence: 99%

Ratios of Parameters: Some Econometric Examples

Lye¹,

Hirschberg²

2018

Australian Economic Review

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Ratios of parameter estimates are often used in econometric applications. However, constructing confidence intervals (CIs) for these ratios can cause difficulties since the ratio of asymptotically normally distributed random variables are Cauchy distributed and thus have no finite moments. This article presents a method for the estimation of CIs based on the Fieller approach that has been shown to be preferable to the usual Delta method. Using example applications in Stata and R, we demonstrate that a few extra steps in the examination of the estimate of the ratio can provide a CI with superior coverage.

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A Geometric Comparison of the Delta and Fieller Confidence Intervals

Cited by 35 publications

References 20 publications

Childhood pneumococcal disease in Africa – A systematic review and meta-analysis of incidence, serotype distribution, and antimicrobial susceptibility

Childhood pneumococcal disease in Africa – A systematic review and meta-analysis of incidence, serotype distribution, and antimicrobial susceptibility

Applying the Delta Method in Metric Analytics

Ratios of Parameters: Some Econometric Examples

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