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Table 2 Model definitions

From: Low dose radiation risks for women surviving the a-bombs in Japan: generalized additive model

Model

Family

ϕ

Model

Family

ϕ

Terms

P0

poisson

1

Q0

quasipoisson

>0

offset(log(py))+(fd+fc)ˆ2+ti(logage) +ti(birth)+ti(logage,birth)

P1e

poisson

1

Q1e

quasipoisson

>0

.+ecdos

P2e

poisson

1

Q2e

quasipoisson

>0

.+ti(ecdos)

P3e

poisson

1

Q3e

quasipoisson

>0

.+ti(ecdos)+ti(ecdos,logage)

P4ae

poisson

1

Q4ae

quasipoisson

>0

.+ti(ecdos)+ti(ecdos,agex)

P4se

poisson

1

Q4se

quasipoisson

>0

.+ti(ecdos)+ti(ecdos,since)

P5ae

poisson

1

Q5ae

quasipoisson

>0

.+ti(ecdos)+ti(ecdos,logage) +ti(agex)+ti(ecdos,agex)

P5se

poisson

1

Q5se

quasipoisson

>0

.+ti(ecdos)+ti(ecdos,logage) +ti(since)+ti(ecdos,since)

P1d

poisson

1

Q1d

quasipoisson

>0

.+dose

P2d

poisson

1

Q2d

quasipoisson

>0

.+ti(dose)

P3d

poisson

1

Q3d

quasipoisson

>0

.+ti(dose)+ti(dose,logage)

P4ad

poisson

1

Q4ad

quasipoisson

>0

.+ti(dose)+ti(dose,agex)

P4sd

poisson

1

Q4sd

quasipoisson

>0

.+ti(dose)+ti(dose,since)

P5ad

poisson

1

Q5ad

quasipoisson

>0

.+ti(dose)+ti(dose,logage) +ti(agex)+ti(dose,agex)

P5sd

poisson

1

Q5sd

quasipoisson

>0

.+ti(dose)+ti(dose,logage) +ti(since)+ti(dose,since)

  1. Models use cubic regression (cr) splines, with basis dimension 10
  2. Model fitting by method ML
  3. “.+” : augment the initial model P0 (or Q0) by the terms which follow
  4. ti refers to a smooth term on the enclosed covariate(s)