Varying cluster sizes in trials with clusters in one treatment arm: Sample size adjustments when testing treatment effects with linear mixed models

AbstractThe effective sample size (ESS) is a quantity estimated in genome-wide association studies (GWAS) with related individuals and/or linear mixed models used in analysis. ESS originally measured relative power in family-based GWAS and has recently become important for correcting GWAS summary statistics in post-GWAS analyses. However, existing ESS approaches have been overlooked and based on empirical estimation. This work presents an analytical form of ESS in mixed-model GWAS of quantitative traits, which is derived using the expectation of quadratic form and validated in extensive simulations. We illustrate the performance and relevance of our ESS estimator in common GWAS scenarios and analytically show that (i) family-based studies are consistently underpowered compared to studies of unrelated individuals of the same sample size; (ii) conditioning on polygenic genetic effect by linear mixed models boosts power; and (iii) power of detecting gene-environment interaction can be substantially gained or lost in family-based designs depending on exposure distribution. We further analyze UK Biobank dataset in two samples of 336,347 unrelated and 68,910 related individuals. Analysis in unrelated individuals reveals a high accuracy of our ESS estimator compared to the existing empirical approach; and analysis of related individuals suggests that the loss in effective sample size due to relatedness is at most 0.94x. Overall, we provide an analytical form of ESS for guiding GWAS designs and processing summary statistics in post-GWAS analyses.

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Heat, Hills and the High Season: A Model-Based Comparative Analysis of Spatio-Temporal Factors Affecting Shared Bicycle Use in Three Southern European Islands

Sustainability ◽

10.3390/su13063274 ◽

2021 ◽

Vol 13 (6) ◽

pp. 3274

Author(s):

Suzanne Maas ◽

Paraskevas Nikolaou ◽

Maria Attard ◽

Loukas Dimitriou

Keyword(s):

Correlation Analysis ◽

Mixed Models ◽

Linear Mixed Models ◽

Positive Association ◽

Sustainable Mobility ◽

Weather Factors ◽

Gran Canaria ◽

Bivariate Correlation ◽

Temporal Factors

Bicycle sharing systems (BSSs) have been implemented in cities worldwide in an attempt to promote cycling. Despite exhibiting characteristics considered to be barriers to cycling, such as hot summers, hilliness and car-oriented infrastructure, Southern European island cities and tourist destinations Limassol (Cyprus), Las Palmas de Gran Canaria (Canary Islands, Spain) and the Valletta conurbation (Malta) are all experiencing the implementation of BSSs and policies to promote cycling. In this study, a year of trip data and secondary datasets are used to analyze dock-based BSS usage in the three case-study cities. How land use, socio-economic, network and temporal factors influence BSS use at station locations, both as an origin and as a destination, was examined using bivariate correlation analysis and through the development of linear mixed models for each case study. Bivariate correlations showed significant positive associations with the number of cafes and restaurants, vicinity to the beach or promenade and the percentage of foreign population at the BSS station locations in all cities. A positive relation with cycling infrastructure was evident in Limassol and Las Palmas de Gran Canaria, but not in Malta, as no cycling infrastructure is present in the island’s conurbation, where the BSS is primarily operational. Elevation had a negative association with BSS use in all three cities. In Limassol and Malta, where seasonality in weather patterns is strongest, a negative effect of rainfall and a positive effect of higher temperature were observed. Although there was a positive association between BSS use and the number of visiting tourists in Limassol and Malta, this is predominantly explained through the multi-collinearity with weather factors rather than by intensive use of the BSS by tourists. The linear mixed models showed more fine-grained results and explained differences in BSS use at stations, including differences for station use as an origin and as a destination. The insights from the correlation analysis and linear mixed models can be used to inform policies promoting cycling and BSS use and support sustainable mobility policies in the case-study cities and cities with similar characteristics.

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Confidence, prediction, and tolerance in linear mixed models

Statistics in Medicine ◽

10.1002/sim.8386 ◽

2019 ◽

Vol 38 (30) ◽

pp. 5603-5622 ◽

Cited By ~ 3

Author(s):

Bernard G. Francq ◽

Dan Lin ◽

Walter Hoyer

Keyword(s):

Mixed Models ◽

Linear Mixed Models

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