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A note on obtaining correct marginal predictions from a random intercepts model for binary outcomes

Overview of attention for article published in BMC Medical Research Methodology, August 2015
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  • In the top 25% of all research outputs scored by Altmetric
  • High Attention Score compared to outputs of the same age (86th percentile)

Mentioned by

blogs
1 blog
twitter
8 tweeters

Citations

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25 Dimensions

Readers on

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38 Mendeley
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Title
A note on obtaining correct marginal predictions from a random intercepts model for binary outcomes
Published in
BMC Medical Research Methodology, August 2015
DOI 10.1186/s12874-015-0046-6
Pubmed ID
Authors

Menelaos Pavlou, Gareth Ambler, Shaun Seaman, Rumana Z. Omar

Abstract

Clustered data with binary outcomes are often analysed using random intercepts models or generalised estimating equations (GEE) resulting in cluster-specific or 'population-average' inference, respectively. When a random effects model is fitted to clustered data, predictions may be produced for a member of an existing cluster by using estimates of the fixed effects (regression coefficients) and the random effect for the cluster (conditional risk calculation), or for a member of a new cluster (marginal risk calculation). We focus on the second. Marginal risk calculation from a random effects model is obtained by integrating over the distribution of random effects. However, in practice marginal risks are often obtained, incorrectly, using only estimates of the fixed effects (i.e. by effectively setting the random effects to zero). We compare these two approaches to marginal risk calculation in terms of model calibration. In simulation studies, it has been seen that use of the incorrect marginal risk calculation from random effects models results in poorly calibrated overall marginal predictions (calibration slope <1 and calibration in the large ≠ 0) with mis-calibration becoming worse with higher degrees of clustering. We clarify that this was due to the incorrect calculation of marginal predictions from a random intercepts model and explain intuitively why this approach is incorrect. We show via simulation that the correct calculation of marginal risks from a random intercepts model results in predictions with excellent calibration. The logistic random intercepts model can be used to obtain valid marginal predictions by integrating over the distribution of random effects.

Twitter Demographics

The data shown below were collected from the profiles of 8 tweeters who shared this research output. Click here to find out more about how the information was compiled.

Mendeley readers

The data shown below were compiled from readership statistics for 38 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
United States 2 5%
Finland 1 3%
Switzerland 1 3%
Unknown 34 89%

Demographic breakdown

Readers by professional status Count As %
Researcher 12 32%
Student > Ph. D. Student 11 29%
Other 4 11%
Student > Master 3 8%
Student > Doctoral Student 2 5%
Other 1 3%
Unknown 5 13%
Readers by discipline Count As %
Medicine and Dentistry 6 16%
Mathematics 6 16%
Environmental Science 3 8%
Computer Science 3 8%
Agricultural and Biological Sciences 2 5%
Other 7 18%
Unknown 11 29%

Attention Score in Context

This research output has an Altmetric Attention Score of 16. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 25 April 2022.
All research outputs
#1,819,771
of 21,749,011 outputs
Outputs from BMC Medical Research Methodology
#282
of 1,922 outputs
Outputs of similar age
#41,191
of 299,584 outputs
Outputs of similar age from BMC Medical Research Methodology
#1
of 1 outputs
Altmetric has tracked 21,749,011 research outputs across all sources so far. Compared to these this one has done particularly well and is in the 91st percentile: it's in the top 10% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 1,922 research outputs from this source. They typically receive a lot more attention than average, with a mean Attention Score of 10.4. This one has done well, scoring higher than 85% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 299,584 tracked outputs that were published within six weeks on either side of this one in any source. This one has done well, scoring higher than 86% of its contemporaries.
We're also able to compare this research output to 1 others from the same source and published within six weeks on either side of this one. This one has scored higher than all of them