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Efficient estimation of smooth distributions from coarsely grouped data.

Rizzi S, Gampe J, Eilers PH - Am. J. Epidemiol. (2015)

Bottom Line: 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.

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Ungrouping of the age-at-death distribution for diseases of the circulatory system, United States, 2009. The original data taken from the Centers for Disease Control and Prevention database were grouped in 5-year bins plus a wide class for ages ≥85 years. An additional bin with 0 counts between ages 115 and 130 years was added. This histogram was ungrouped by the penalized composite link model. A) Grouped histogram, original data (black line with overplotted points) and ungrouped data (solid gray line). B) The value of the smoothing parameter λ was chosen by minimizing Akaike's Information Criterion (AIC); λ varied on a fine grid, and the value that gave the minimum of AIC led to log10(λ) = 5.5.
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KWV020F2: Ungrouping of the age-at-death distribution for diseases of the circulatory system, United States, 2009. The original data taken from the Centers for Disease Control and Prevention database were grouped in 5-year bins plus a wide class for ages ≥85 years. An additional bin with 0 counts between ages 115 and 130 years was added. This histogram was ungrouped by the penalized composite link model. A) Grouped histogram, original data (black line with overplotted points) and ungrouped data (solid gray line). B) The value of the smoothing parameter λ was chosen by minimizing Akaike's Information Criterion (AIC); λ varied on a fine grid, and the value that gave the minimum of AIC led to log10(λ) = 5.5.

Mentions: We first apply the approach to deaths from diseases of the circulatory system. The results are shown in Figure 2. The open-ended age class collects the observations made for individuals older than the starting age for the interval (here, age 85 years). Although in theory the tail area could be unlimited, in most applications there is a maximal number beyond which no observation is expected or is even possible. As the penalized composite link model smoothly redistributes the grouped observations into the tail area, such information, if available, should be provided. For the present application, the age of 115 years was set as the maximum, and the histogram was complemented with an age group from 115 to 130 years with 0 counts. The penalized composite link model can easily deal with longer stretches of 0 counts.Figure 2.


Efficient estimation of smooth distributions from coarsely grouped data.

Rizzi S, Gampe J, Eilers PH - Am. J. Epidemiol. (2015)

Ungrouping of the age-at-death distribution for diseases of the circulatory system, United States, 2009. The original data taken from the Centers for Disease Control and Prevention database were grouped in 5-year bins plus a wide class for ages ≥85 years. An additional bin with 0 counts between ages 115 and 130 years was added. This histogram was ungrouped by the penalized composite link model. A) Grouped histogram, original data (black line with overplotted points) and ungrouped data (solid gray line). B) The value of the smoothing parameter λ was chosen by minimizing Akaike's Information Criterion (AIC); λ varied on a fine grid, and the value that gave the minimum of AIC led to log10(λ) = 5.5.
© Copyright Policy - creative-commons
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4493979&req=5

KWV020F2: Ungrouping of the age-at-death distribution for diseases of the circulatory system, United States, 2009. The original data taken from the Centers for Disease Control and Prevention database were grouped in 5-year bins plus a wide class for ages ≥85 years. An additional bin with 0 counts between ages 115 and 130 years was added. This histogram was ungrouped by the penalized composite link model. A) Grouped histogram, original data (black line with overplotted points) and ungrouped data (solid gray line). B) The value of the smoothing parameter λ was chosen by minimizing Akaike's Information Criterion (AIC); λ varied on a fine grid, and the value that gave the minimum of AIC led to log10(λ) = 5.5.
Mentions: We first apply the approach to deaths from diseases of the circulatory system. The results are shown in Figure 2. The open-ended age class collects the observations made for individuals older than the starting age for the interval (here, age 85 years). Although in theory the tail area could be unlimited, in most applications there is a maximal number beyond which no observation is expected or is even possible. As the penalized composite link model smoothly redistributes the grouped observations into the tail area, such information, if available, should be provided. For the present application, the age of 115 years was set as the maximum, and the histogram was complemented with an age group from 115 to 130 years with 0 counts. The penalized composite link model can easily deal with longer stretches of 0 counts.Figure 2.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Show MeSH
Related in: MedlinePlus