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Table 1 Type I error rates for case-only and case–control designs

From: The case-only design is a powerful approach to detect interactions but should be used with caution

Disease prevalence

\(\boldsymbol{\alpha }\)

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

5.0%

10.0%

15.0%

20.0%

(a) Two main effects

 case–control

0.001

0.000962

0.000970

0.001041

0.001009

0.000983

0.000958

0.000994

0.000983

0.000970

0.000976

0.000978

0.000997

 case-only

0.001

0.001015

0.000942

0.000983

0.001038

0.000990

0.000995

0.001098

0.001067

0.001083

0.001390

0.001667

0.002091

 case–control

0.05

0.050330

0.049824

0.049887

0.049905

0.050113

0.050161

0.049653

0.050160

0.049735

0.049845

0.049912

0.050371

 case-only

0.05

0.050132

0.050603

0.049854

0.050842

0.050614

0.051195

0.051387

0.052100

0.052221

0.057378

0.063536

0.070049

(b) Only a genetic main effect

 case–control

0.001

0.001005

0.000929

0.001021

0.001002

0.000976

0.000999

0.001016

0.001030

0.000981

0.000958

0.000973

0.001068

 case-only

0.001

0.001009

0.000969

0.000979

0.000990

0.000995

0.000940

0.001023

0.001030

0.001014

0.000966

0.000986

0.000984

 case–control

0.05

0.049911

0.049822

0.050093

0.050012

0.049857

0.049930

0.049642

0.050276

0.050018

0.049894

0.049908

0.050146

 case-only

0.05

0.050315

0.049506

0.050062

0.049971

0.049997

0.049994

0.049793

0.050205

0.049727

0.049807

0.049933

0.049700

(c) Only an environment main effect

 case–control

0.001

0.000998

0.000981

0.000997

0.000971

0.001026

0.000980

0.000973

0.000951

0.001022

0.001015

0.000960

0.000984

 case-only

0.001

0.000952

0.000998

0.000936

0.000968

0.000975

0.001012

0.000962

0.001046

0.000995

0.000998

0.000961

0.000940

 case–control

0.05

0.050296

0.050185

0.050248

0.049903

0.050320

0.049931

0.049868

0.049853

0.049658

0.049894

0.049753

0.049896

 case-only

0.05

0.049769

0.049906

0.049880

0.050149

0.049980

0.050189

0.049935

0.049731

0.049396

0.049929

0.049621

0.050153

(d) No main effects

 case–control

0.001

0.001010

0.000981

0.000929

0.001040

0.000940

0.000984

0.000959

0.000999

0.001019

0.001012

0.000977

0.001056

 case-only

0.001

0.000997

0.000904

0.000899

0.000930

0.000952

0.000959

0.000953

0.000959

0.001036

0.000958

0.000941

0.001027

 case–control

0.05

0.049769

0.050132

0.049922

0.050361

0.050121

0.050052

0.049907

0.050104

0.050338

0.049919

0.049874

0.050470

 case-only

0.05

0.049667

0.049608

0.049764

0.049975

0.050096

0.050202

0.049683

0.050152

0.050234

0.050031

0.049877

0.050120

  1. Data were generated under the null with no interaction for four scenarios: (a) two main effects [\({\beta }_{G}=\ln(1.2)\) and \({\beta }_{E}=\ln(2)\)]; (b) only a genetic main effect [\({\beta }_{G}=\ln(1.2)\) and \({\beta }_{E}=0\)]; (c) only an environmental main effect [\({\beta }_{G}=0\) and \({\beta }_{E}=\ln(2)\)]; and (d) no main effects \([{\beta }_{G}=0\text{ and }{\beta }_{E}=0]\). The MAF for the genetic variant is 0.2 and the frequency of the environmental exposure is 0.1. The sample sizes are N = 10,000 cases for both the case-only and case–control designs and additionally for the case–control design there are N = 10,000 controls. Type I error is calculated as the proportion of instances that the null hypothesis is rejected among all 1,000,000 replicates. Type I errors exceeding 5% of the alpha level are highlighted in bold in the table
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BMC Genomics

ISSN: 1471-2164

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