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Table S3 Table S3a. Bias results for main genetic effect assessment comparing ordinary statistical methods (OLR and OLMM) with family-based methods (AQTDTM and ALMM) under homogeneous (HP) and stratified (SP) m populations. Each time, n cases were simulated with parameters β1 = α5 = 0.5. Simulations are based on the recessive genetic model. † = number that identifies each model in the paper.

From: Gene-environment interaction tests for family studies with quantitative phenotypes: A review and extension to longitudinal measures

 

OLR (16) †

AQTDTM (17)

OLMM (19)

ALMM (20)

n

β ^ 1 - β 1

α ^ 5 - α 5

 

HP

SP

HP

SP

HP

SP

HP

SP

100

-0.010

-0.505

-0.012

-0.049

-0.026

-0.508

-0.023

-0.052

200

-0.022

-0.507

-0.049

-0.040

-0.019

-0.494

-0.031

-0.023

300

-0.002

-0.500

-0.003

0.028

-0.010

-0.505

-0.004

0.025

400

-0.020

-0.499

-0.018

0.002

-0.008

-0.496

-0.012

0.006

500

0.007

-0.494

0.012

0.004

0.005

-0.495

0.006

-0.002

600

0.000

-0.496

0.010

0.003

-0.001

-0.499

0.001

0.001

Table S3b. Bias results for gene-environment effect assessment comparing ordinary statistical methods (OLR and OLMM) with family-based methods (AQTDT M and ALMM) under homogeneous (HP) and stratified (SP) populations. Each time, n cases were simulated with parameters β 3 = α 7 = 1. Simulations are based on the recessive genetic model. † = number that identifies each model in the paper.

n

β ^ 3 - β 3

α ^ 7 - α 7

 

OLR (21) †

AQTDTM (22)

OLMM (23)

ALMM (24)

 

HP

SP

HP

SP

HP

SP

HP

SP

100

0.008

-0.962

0.001

0.048

0.006

-1.003

0.017

0.027

200

-0.008

-1.042

0.020

-0.007

-0.001

-1.024

0.019

-0.006

300

0.011

-1.005

0.048

0.001

0.009

-1.004

0.012

0.010

400

0.014

-1.001

0.019

0.022

0.001

-0.988

-0.009

0.034

500

0.011

-1.010

0.000

-0.028

-0.002

-1.010

-0.012

-0.006

600

0.016

-0.967

0.016

0.033

0.015

-0.973

0.008

0.032

  1. OLR, ordinary linear regression; OLMM, ordinary linear mixed models; ALMM, adjusted linear mixed models; AQTDTM, adjusted quantitative transmission disequilibrium test with mating type indicators