Efficient estimation of smooth distributions from coarsely grouped data
Open accessAbstract
Ungrouping binned data can be desirable for many reasons: Bins can be too coarse to allow for accurate analysis; comparisons can be hindered when different grouping approaches are used in different histograms; and the last interval is often wide and open-ended and, thus, covers a lot of information in the tail area. Age group-specific disease incidence rates and abridged life tables are examples of binned data. We propose a versatile method for ungrouping histograms that assumes that only the underlying distribution is smooth. Because of this modest assumption, the approach is suitable for most applications. The method is based on the composite link model, with a penalty added to ensure the smoothness of the target distribution. Estimates are obtained by maximizing a penalized likelihood. This maximization is performed efficiently by a version of the iteratively reweighted least-squares algorithm. Optimal values of the smoothing parameter are chosen by minimizing Akaike's Information Criterion. We demonstrate the performance of this method in a simulation study and provide several examples that illustrate the approach. Wide, open-ended intervals can be handled properly. The method can be extended to the estimation of rates when both the event counts and the exposures to risk are grouped.
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The authors dealt with potential death registration delays by harmonizing and smoothing death counts with a PCLM shown to provide reliable estimates of mortality for all countries in the study and by adjusting person-years exposed.
“We deal with these potential issues by harmonizing and smoothing death counts with a PCLM that has been shown to provide reliable estimates of mortality for all countries in our study26 and by adjusting the person-years exposed.”
From Quantifying impacts of the COVID-19 pandemic through life-expectancy losses: a population-level study of 29 countries (2022) · cites this paper as [26]
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Projected Aging Among People With HIV in the US
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- Authors
- Rizzi, S., Gampe, J., & Eilers, P. H. C.
- Affiliations
- University of Southern Denmark (DK)
- Max Planck Institute for Demographic Research (DE)
- Corresponding author
- Rizzi, Silvia
- Venue
- American Journal of Epidemiology
- Publisher
- Oxford University Press (OUP)
- Published
- 2015-06-16
- Volume
- 182
- Issue
- 2
- Pages
- 138-147
- ISSN
- 0002-9262 (ISSN-L)
- 1476-6256
- PMC
- PMC4493979
- OpenAlex
- W2148091099
- Cited by
- 98
- References
- 19
- Citations by year
- 2026: 14 · 2025: 11 · 2024: 17 · 2023: 9 · 2022: 12 · 2021: 8 · 2020: 12 · 2019: 3 · 2018: 4 · 2017: 2 · 2016: 5 · 2015: 1
- FWCI
- 3.86
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- cc-by-nc
- Locations
- American Journal of Epidemiology (publishedVersion, cc-by-nc)
- Europe PMC (PubMed Central) (publishedVersion, cc-by-nc)
- PubMed Central (publishedVersion, cc-by-nc)
- PubMed (publishedVersion)
- EUR Research Repository (Erasmus University Rotterdam) (publishedVersion)
- University of Southern Denmark Research Portal (University of Southern Denmark) (publishedVersion)
- EUR Research Repository (Erasmus University Rotterdam) (submittedVersion)
- Funders
- Innovative Research Group Project of the National Natural Science Foundation of China
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- histogram smoothing, penalized likelihood, iteratively reweighted least squares, Akaike information criterion, bandwidth selection, age-specific incidence, abridged life tables
- MeSH terms
- Epidemiologic Methods, Statistics as Topic
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