From: A multi-marker test based on family data in genome-wide association study
Logistic model
Values of the parameters
Model I
log p 1 − p = β 0 + β 1 x 1 + β 123 x 1 x 2 x 3 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacyGGSbaBcqGGVbWBcqGGNbWzdaWcaaqaaiabdchaWbqaaiabigdaXiabgkHiTiabdchaWbaacqGH9aqpiiGacqWFYoGydaWgaaWcbaGaeGimaadabeaakiabgUcaRiab=j7aInaaBaaaleaacqaIXaqmaeqaaOGaemiEaG3aaSbaaSqaaiabigdaXaqabaGccqGHRaWkcqWFYoGydaWgaaWcbaGaeGymaeJaeGOmaiJaeG4mamdabeaakiabdIha4naaBaaaleaacqaIXaqmaeqaaOGaemiEaG3aaSbaaSqaaiabikdaYaqabaGccqWG4baEdaWgaaWcbaGaeG4mamdabeaaaaa@4D01@
β1 = log(2), β123 = log(5)
Model II
log p 1 − p = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacyGGSbaBcqGGVbWBcqGGNbWzdaWcaaqaaiabdchaWbqaaiabigdaXiabgkHiTiabdchaWbaacqGH9aqpiiGacqWFYoGydaWgaaWcbaGaeGimaadabeaakiabgUcaRiab=j7aInaaBaaaleaacqaIXaqmaeqaaOGaemiEaG3aaSbaaSqaaiabigdaXaqabaGccqGHRaWkcqWFYoGydaWgaaWcbaGaeGOmaidabeaakiabdIha4naaBaaaleaacqaIYaGmaeqaaOGaey4kaSIae8NSdi2aaSbaaSqaaiabiodaZaqabaGccqWG4baEdaWgaaWcbaGaeG4mamdabeaaaaa@4C26@
β1 = β2 = β3 = log(2)
Model III
log p 1 − p = β 0 + ∑ i = 1 6 β i x i + β 7 x 7 x 8 + β 8 x 9 x 10 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacyGGSbaBcqGGVbWBcqGGNbWzdaWcaaqaaiabdchaWbqaaiabigdaXiabgkHiTiabdchaWbaacqGH9aqpiiGacqWFYoGydaWgaaWcbaGaeGimaadabeaakiabgUcaRmaaqahabaGae8NSdi2aaSbaaSqaaiabdMgaPbqabaGccqWG4baEdaWgaaWcbaGaemyAaKgabeaaaeaacqWGPbqAcqGH9aqpcqaIXaqmaeaacqaI2aGna0GaeyyeIuoaiiaakiab+TcaRiab=j7aInaaBaaaleaacqaI3aWnaeqaaOGaemiEaG3aaSbaaSqaaiabiEda3aqabaGccqWG4baEdaWgaaWcbaGaeGioaGdabeaakiabgUcaRiab=j7aInaaBaaaleaacqaI4aaoaeqaaOGaemiEaG3aaSbaaSqaaiabiMda5aqabaGccqWG4baEdaWgaaWcbaGaeGymaeJaeGimaadabeaaaaa@59E4@
β i = log(2), i = 1,..., 6; β7 = β8 = log(3)
Model IV
log p 1 − p = β 0 + ∑ i = 1 10 β i x i MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacyGGSbaBcqGGVbWBcqGGNbWzdaWcaaqaaiabdchaWbqaaiabigdaXiabgkHiTiabdchaWbaacqGH9aqpiiGacqWFYoGydaWgaaWcbaGaeGimaadabeaakiabgUcaRmaaqahabaGae8NSdi2aaSbaaSqaaiabdMgaPbqabaGccqWG4baEdaWgaaWcbaGaemyAaKgabeaaaeaacqWGPbqAcqGH9aqpcqaIXaqmaeaacqaIXaqmcqaIWaama0GaeyyeIuoaaaa@47D0@
β i = log(2), i = 1,..., 10