Appendix
Appendix Figures
Appendix Figure 1: Correlations between maternal smoking during pregnancy and outcomes in offspring and parts of the correlations
explained by different sources of variance
Note: These are the results from the full models, without model fitting steps performed. Due to computational issues the model for the association
between SDP and preterm birth, as well as with being born small for gestational age, was fitted in three steps; first SDP and outcomes were fitted
separately, then the results from model fitting were used in the cross-phenotype analyses.
Appendix Figure 2: Path diagram representations for each variance source separately.
A covariance
C covariance
M covariance
P covariance
E covariance
Note: gm, genetic relation of mothers. go, genetic relation of siblings in offspring generation. Sub-index 11
refers to offspring 1 in nuclear family 1, sub-index 21 refers to offspring 1 in nuclear family 2, and subindex 22 refers to offspring 2 in nuclear family 2.
Appendix Tables
Appendix Table 1: ACMPE univariate modelled parameters [parameter estimate (standard error)]
Maternal phenotype
Maternal smoking during
pregnancya
Offspring phenotype
Birth weight
Preterm birth
Born small for gestational age
Low academic achievement
General cognitive ability
Criminal convictions
Violent criminal convictions
Drug/alcohol misuse
𝒂𝒔
𝒄𝒔
𝒎𝒔
𝒑𝒔
𝒆𝒔
.831 (.007)
.171 (.021)
.197 (.010)
.396 (.004)
𝒂𝒐
𝒄𝒐
𝒎𝒐
𝒑𝒐
𝒆𝒐
.392 (.005)
.221 (.003)
.147 (.002)
.000 (.014)
.288 (.003)
.517 (.039)
.492 (.015)
.276 (.014)
.001 (.078)
.643
.658 (.035)
.398 (.022)
.270 (.015)
.002 (.068)
.579
.927 (.023)
.107 (.041)
.349 (.010)
.057 (.046)
.067
1.058 (.028)
.816 (.052)
.000 (.114)
.218 (.197)
1.258 (.014)
.627 (.023)
.140 (.051)
.208 (.027)
.000 (.117)
.737
.793 (.050)
.129 (.139)
.254 (.055)
.001 (.390)
.539
.290
.591 (.023)
.241 (.020)
.159 (.023)
.110 (.014)
.745
Note: The e-parameters for binary phenotypes are defined as remaining variance after estimation of other
parameters and are therefore void of standard errors.
a Calculated using the full 1983-2009 cohort.
Appendix Table 2: ACMPE full model results [parameter estimate (standard error)]
Within SDP
Within outcome
Between phenotypes
𝒂𝒔
𝒄𝒔
𝒎𝒔
𝒑𝒔
𝒆𝒔
𝒂𝒐
𝒄𝒐
𝒎𝒐
𝒑𝒐
𝒆𝒐
𝒓𝑨
𝒓𝑪
𝒓𝑴
𝒓𝑷
𝒓𝑬
0.823
(0.003)
0.828
(0.008)
0.828
(0.008)
0.262
(0.003)
0.183
(0.015)
0.183
(0.015)
0.213
(0.003)
0.202
(0.017)
0.202
(0.017)
0.354
(0.003)
0.394
(0.003)
0.394
(0.003)
0.288
0.394
(0.003)
0.514
(0.048)
0.660
(0.015)
0.207
(0.003)
0.494
(0.019)
0.396
(0.015)
0.147
(0.001)
0.277
(0.015)
0.270
(0.011)
0.035
(0.003)
0.002
(0.075)
0.002
(0.075)
0.300
(0.003)
0.644
-0.046
(0.003)
NA
-0.773
(0.001)
NA
-0.679
(0.003)
NA
-1.000
(0.005)
NA
-0.244
(0.001)
NA
0.578
NA
NA
NA
NA
NA
Low
academic
achievement
General
cognitive
ability
0.810
(0.000)
0.344
(0.000)
0.267
(0.000)
0.296
(0.000)
0.258
0.893
(0.000)
0.154
(0.000)
0.366
(0.000)
0.105
(0.000)
0.185
0.598
(0.001)
0.024
(0.006)
0.623
(0.001)
0.494
(0.009)
-0.018
(0.001)
0.813
(0.022)
0.263
(0.020)
0.307
(0.019)
0.313
(0.016)
0.278
1.076
(0.033)
0.819
(0.023)
0.097
(0.019)
0.212
(0.012)
1.244
(0.016)
-0.536
(0.010)
-0.071
(0.014)
-0.327
(0.008)
-0.980
(0.010)
-0.030
(0.010)
Criminality
0.802
(0.029)
0.782
(0.017)
0.835
(0.001)
0.351
(0.030)
0.370
(0.020)
0.293
(0.001)
0.290
(0.038)
0.314
(0.019)
0.260
(0.001)
0.291
(0.011)
0.297
(0.012)
0.296
(0.001)
0.254
0.573
(0.024)
0.795
(0.061)
0.600
(0.001)
0.203
(0.024)
0.000
(0.155)
0.256
(0.001)
0.222
(0.018)
0.272
(0.042)
0.146
(0.000)
0.076
(0.030)
0.057
(0.073)
0.088
(0.000)
0.759
1.000
(0.099)
0.654
(0.228)
0.591
(0.001)
-0.693
(0.090)
0.795
(0.147)
0.190
(0.000)
0.009
(0.120)
0.421
(0.481)
0.743
(0.001)
0.511
(0.498)
0.522
(0.816)
0.182
(0.000)
0.000
(0.016)
0.024
(0.039)
0.000
(0.000)
Birth weight
Preterm
birtha
Born small
for
gestational
agea
Violent
criminality
Drug misuse
0.290
0.290
0.255
0.250
0.538
0.738
Abbreviations: SDP, maternal smoking during pregnancy. NA, not applicable.
Note: Standard errors may be misleading due to constraints put on the optimizer when fitting the model. The e-parameters for binary phenotypes
are defined as remaining variance after estimation of other parameters and are therefore void of standard errors.
a Due to computational issues SDP and outcome were fitted separately.
Appendix Table 3: ACMPE best-fitting model results [parameter estimate (standard error)]
Within SDP
Within outcome
Between phenotypes
𝑎𝑠
𝑐𝑠
𝑚𝑠
𝒑𝒔
𝒆𝒔
𝒂𝒐
𝒄𝒐
𝒎𝒐
𝒑𝒐
𝒆𝒐
𝒓𝑨
𝒓𝑪
𝒓𝑴
𝒓𝑷
𝒓𝑬
0.823
(0.003)
0.828
(0.008)
0.828
(0.008)
0.262
(0.003)
0.183
(0.015)
0.183
(0.015)
0.213
(0.003)
0.202
(0.017)
0.202
(0.017)
0.354
(0.003)
0.394
(0.003)
0.394
(0.003)
0.288
0.394
(0.003)
0.514
(1.314)
0.660
(0.006)
0.207
(0.003)
0.494
(0.003)
0.396
(0.004)
0.147
(0.001)
0.277
(0.002)
0.270
(0.005)
0.035
(0.003)
0
0.300
(0.003)
0.644
0.578
-0.773
(0.001)
0.212
(0.170)
1.000
(1.414)
-0.679
(0.003)
0.385
(0.248)
-0.138
(3.247)
-1.000
(0.005)
0
0
-0.046
(0.003)
0.045
(0.131)
0.536
(1.321)
-0.244
(0.001)
0.048
(0.012)
0.172
(0.706)
Low
academic
achievementb
General
cognitive
ability
0.810
0.344
0.267
0.296
0.258
0.893
0.154
0.366
0.105
0.185
0.598
0
0.623
0.494
-0.018
0.820
(0.047)
0.283
(0.071)
0.295
(0.070)
0.289
(0.027)
0.278
1.114
(0.026)
0.825
(0.020)
0
0
1.228
(0.014)
-0.555
(0.048)
-0.301
(0.093)
0
0
-0.034
(0.020)
Criminality
0.808
(0.006)
0.802
(0.028)
0.850
(0.005)
0.344
(0.006)
0.349
(0.030)
0.290
(0.005)
0.282
(0.006)
0.286
(0.036)
0.229
(0.005)
0.293
(0.006)
0.297
(0.010)
0.281
(0.005)
0.254
0.585
(0.006)
0.899
(0.018)
0.730
(0.005)
0.192
(0.006)
0
0.227
(0.020)
0
0
0.755
0
0.438
-0.687
(0.017)
0
0
0
0
0
0
0
0
0.683
1.000
(0.002)
0.691
(0.027)
0.635
(0.005)
0
0
0
-0.001
(0.013)
0.026
(0.019)
-0.002
(0.005)
Birth weight
Preterm
birtha
Born small
for
gestational
agea
Violent
criminality
Drug misuse
0.290
0.290
0.255
0.249
0
Abbreviations: SDP, maternal smoking during pregnancy.
Note: Standard errors may be misleading due to constraints put on the optimizer when fitting the model. The e-parameters for binary phenotypes
are defined as remaining variance after estimation of other parameters and are therefore void of standard errors. All values significant, on a 5%level, except when a “0” is stated, where they are non-significant in a likelihood ratio test and have been removed from model. e-parameters are
not subject to significance tests. 𝑟𝐸 is included in final model regardless of significance.
a Due to computational issues the model was fitted in three steps; first SDP and outcome were fitted separately, then the results from model fitting
were used in the cross-phenotype analyses.
b No valid standard errors could be obtained from the optimization.
8
Appendix Table 4a: Likelihood ratio tests for smoking during pregnancy and birth weight
Model name
Number of
estimated
parameters
-2 log
likelihood
ACMPE – ACMPE
ACME – ACME
ACPE – ACPE
AMPE – AMPE
CMPE – CMPE
ACMPE – CMPE
ACMPE – ACPE
ACMPE – ACME
ACMPE – AMPE
ACMPE – ACMP
40
38
38
38
38
39
39
39
39
39
4108980.3
4109054.1
4109917.0
4109821.6
4109241.9
4108984.5
4108998.2
4109054.3
4109070.6
4111042.7
P-value; test again
previous model with
more estimated
parameters
NA
<0.001
<0.001
<0.001
<0.001
0.039
<0.001
<0.001
<0.001
<0.001
Abbreviations: NA, not applicable.
Note: “Best-fitting model” marked in bold letters. Each model is tested against previous model with more
estimated parameters. The model name implies which parameters that are included, it is stated as
ACMPE – ACMPE, where the first five letters tells us which of the variance parameters in birth weight that
are included (i.e., 𝑎𝑜2 , 𝑐𝑜2 , 𝑚𝑜2 , 𝑝𝑜2 , and 𝑒𝑜2 ), and the five last letters tells us which of the cross-phenotype
parameters that are included (i.e., 𝑟𝐴 , 𝑟𝐶 , 𝑟𝑀 , 𝑟𝑃 , and 𝑟𝐸 ). All of the variance parameters in maternal smoking
during pregnancy are included in all models.
Appendix Table 4b: Likelihood ratio tests for preterm birth
Model name
Number of
estimated
parameters
-2 log
likelihood
ACMPE
ACME
ACE
AME
CME
17
16
15
15
15
714467.6
714467.6
714554.3
714644.1
714501.1
P-value; test again
previous model with
more estimated
parameters
NA
1
<0.001
<0.001
<0.001
Abbreviations: NA, not applicable.
Note: “Best-fitting model” marked in bold letters. Due to computational issues only the outcome
phenotype was tested for significance. Each model is tested against previous model with more estimated
parameters. The model name implies which parameters that are included, it is stated as ACMPE, where
the letters tells us which of the variance parameters in preterm birth that are included (i.e., 𝑎𝑜2 , 𝑐𝑜2 , 𝑚𝑜2 , 𝑝𝑜2 ,
and 𝑒𝑜2 ).
Appendix Table 4c: Likelihood ratio tests for being born small for gestational age
Model name
Number of
estimated
parameters
-2 log
likelihood
P-value; test again
previous model with
more estimated
9
ACMPE
ACME
ACE
AME
CME
17
16
15
15
15
808894.7
808894.7
808986.0
808975.9
808994.6
parameters
NA
1
<0.001
<0.001
<0.001
Abbreviations: NA, not applicable.
Note: “Best-fitting model” marked in bold letters. Due to computational issues only the outcome
phenotype was tested for significance. Each model is tested against previous model with more estimated
parameters. The model name implies which parameters that are included, it is stated as ACMPE, where
the letters tells us which of the variance parameters in being born small for gestational age that are
included (i.e., 𝑎𝑜2 , 𝑐𝑜2 , 𝑚𝑜2 , 𝑝𝑜2 , and 𝑒𝑜2 ).
Appendix Table 4d: Likelihood ratio tests for smoking during pregnancy and low academic
achievement
Model name
Number of
estimated
parameters
-2 log
likelihood
ACMPE – ACMPE
ACME – ACME
AMPE – AMPE
ACPE – ACPE
CMPE – CMPE
ACMPE – AMPE
ACMPE – AME
ACMPE – MPE
ACMPE – APE
ACMPE – AMP
39
37
37
37
37
38
37
37
37
37
1298228.9
1298279.4
1298270.4
1298563.5
1298296.0
1298229.9
1298283.1
1298425.3
1298295.3
1298229.9
P-value; test again
previous model with
more estimated
parameters
NA
<0.001
<0.001
<0.001
<0.001
0.900
<0.001
<0.001
<0.001
1
Abbreviations: NA, not applicable.
Note: “Best-fitting model” marked in bold letters. Each model is tested against previous model with more
estimated parameters. The model name implies which parameters that are included, it is stated as
ACMPE – ACMPE, where the first five letters tells us which of the variance parameters in low academic
achievement that are included (i.e., 𝑎𝑜2 , 𝑐𝑜2 , 𝑚𝑜2 , 𝑝𝑜2 , and 𝑒𝑜2 ), and the five last letters tells us which of the
cross-phenotype parameters that are included (i.e., 𝑟𝐴 , 𝑟𝐶 , 𝑟𝑀 , 𝑟𝑃 , and 𝑟𝐸 ). All of the variance parameters in
maternal smoking during pregnancy are included in all models.
Appendix Table 4e: Likelihood ratio tests for smoking during pregnancy and general cognitive
functioning
Model name
Number of
estimated
parameters
-2 log
likelihood
ACMPE – ACMPE
38
1154273.6
P-value; test again
previous model with
more estimated
parameters
NA
10
ACPE – ACPE
ACE – ACE
AE – AE
CE – CE
ACE – AE
ACE – CE
ACE – AC
36
34
32
32
33
33
33
1154275.8
1154278.3
1154790.9
1154927.5
1154339.4
1154626.1
1154321.9
0.327
0.289
<0.001
<0.001
<0.001
<0.001
<0.001
Abbreviations: NA, not applicable.
Note: “Best-fitting model” marked in bold letters. Each model is tested against previous model with more
estimated parameters. The model name implies which parameters that are included, it is stated as
ACMPE – ACMPE, where the first five letters tells us which of the variance parameters in general
cognitive functioning that are included (i.e., 𝑎𝑜2 , 𝑐𝑜2 , 𝑚𝑜2 , 𝑝𝑜2 , and 𝑒𝑜2 ), and the five last letters tells us which of
the cross-phenotype parameters that are included (i.e., 𝑟𝐴 , 𝑟𝐶 , 𝑟𝑀 , 𝑟𝑃 , and 𝑟𝐸 ). All of the variance
parameters in maternal smoking during pregnancy are included in all models.
Appendix Table 4f: Likelihood ratio tests for smoking during pregnancy and criminal convictions
Model name
Number of
estimated
parameters
-2 log
likelihood
ACMPE – ACMPE
ACME - ACME
AME – AME
ACE – ACE
CME – CME
ACME – ACE
ACME – AE
ACME – CE
ACME – AC
39
37
35
35
35
36
35
35
35
847607.1
847607.9
847877.4
847675.9
847640.0
847607.9
847619.3
847976.4
847607.9
P-value; test again
previous model with
more estimated
parameters
NA
0.692
<0.001
<0.001
<0.001
1
<0.001
<0.001
1
Abbreviations: NA, not applicable.
Note: “Best-fitting model” marked in bold letters. Each model is tested against previous model with more
estimated parameters. The model name implies which parameters that are included, it is stated as
ACMPE – ACMPE, where the first five letters tells us which of the variance parameters in criminal
convictions that are included (i.e., 𝑎𝑜2 , 𝑐𝑜2 , 𝑚𝑜2 , 𝑝𝑜2 , and 𝑒𝑜2 ), and the five last letters tells us which of the
cross-phenotype parameters that are included (i.e., 𝑟𝐴 , 𝑟𝐶 , 𝑟𝑀 , 𝑟𝑃 , and 𝑟𝐸 ). All of the variance parameters in
maternal smoking during pregnancy are included in all models.
Appendix Table 4g: Likelihood ratio tests for smoking during pregnancy and violent criminal
convictions
Model name
Number of
estimated
parameters
-2 log
likelihood
ACMPE – ACMPE
AMPE – AMPE
AME – AME
AE – AE
E –E
39
37
35
33
31
624094.2
624094.2
624098.1
624101.1
625980.3
P-value; test again
previous model with
more estimated
parameters
NA
1
0.142
0.224
<0.001
11
AE –E
AE – A
32
32
625594.2
624101.1
<0.001
0.975
Abbreviations: NA, not applicable.
Note: “Best-fitting model” marked in bold letters. Each model is tested against previous model with more
estimated parameters. The model name implies which parameters that are included, it is stated as
ACMPE – ACMPE, where the first five letters tells us which of the variance parameters in violent criminal
convictions that are included (i.e., 𝑎𝑜2 , 𝑐𝑜2 , 𝑚𝑜2 , 𝑝𝑜2 , and 𝑒𝑜2 ), and the five last letters tells us which of the
cross-phenotype parameters that are included (i.e., 𝑟𝐴 , 𝑟𝐶 , 𝑟𝑀 , 𝑟𝑃 , and 𝑟𝐸 ). All of the variance parameters in
maternal smoking during pregnancy are included in all models.
Appendix Table 4h: Likelihood ratio tests for smoking during pregnancy and drug/alcohol misuse
Model name
Number of
estimated
parameters
-2 log
likelihood
ACMPE – ACMPE
ACME – ACME
ACE – ACE
AME – AME
AE - AE
AE – E
AE – A
39
37
35
35
33
32
32
573109.2
573109.2
573115.3
573111.9
573112.3
574303.7
573112.3
P-value; test again
previous model with
more estimated
parameters
NA
1
0.049
0.262
0.827
<0.001
0.803
Abbreviations: NA, not applicable.
Note: “Best-fitting model” marked in bold letters. Each model is tested against previous model with more
estimated parameters. The model name implies which parameters that are included, it is stated as
ACMPE – ACMPE, where the first five letters tells us which of the variance parameters in drug/alcohol
misuse that are included (i.e., 𝑎𝑜2 , 𝑐𝑜2 , 𝑚𝑜2 , 𝑝𝑜2 , and 𝑒𝑜2 ), and the five last letters tells us which of the crossphenotype parameters that are included (i.e., 𝑟𝐴 , 𝑟𝐶 , 𝑟𝑀 , 𝑟𝑃 , and 𝑟𝐸 ). All of the variance parameters in
maternal smoking during pregnancy are included in all models.
12
Appendix Table 5. Covariance between random effects, within and across phenotypes, for different relations as stated in terms of offspring
Within subject
A
𝑨𝑺𝑫𝑷
𝒊𝒋𝒌
𝑎𝑠2
𝑨𝑺𝑫𝑷
𝒊𝒋𝒌
𝑨𝑶𝑼𝑻
𝒊𝒋𝒌
1
𝑎𝑎 𝑟
2 𝑠 𝑜 𝐴
Full sibs
Half sibs
Mothers MZ
twins
Mothers DZ
twins
Mothers full
sibs
Mothers
maternal half
sibs
Mothers
paternal half
sibs
𝑨𝑶𝑼𝑻
𝒊𝒋𝒌
𝑨𝑺𝑫𝑷
𝒊𝒋𝒌′
𝑨𝑶𝑼𝑻
𝒊𝒋𝒌′
𝑨𝑺𝑫𝑷
𝒊𝒋𝒌′
𝑨𝑶𝑼𝑻
𝒊𝒋𝒌′
𝑨𝑺𝑫𝑷
𝒊𝒋′⋅
𝑨𝑶𝑼𝑻
𝒊𝒋′⋅
𝑨𝑺𝑫𝑷
𝒊𝒋′⋅
𝑨𝑶𝑼𝑻
𝒊𝒋′⋅
𝑨𝑺𝑫𝑷
𝒊𝒋′⋅
𝑨𝑶𝑼𝑻
𝒊𝒋′⋅
𝑨𝑺𝑫𝑷
𝒊𝒋′⋅
𝑨𝑶𝑼𝑻
𝒊𝒋′⋅
𝑨𝑺𝑫𝑷
𝒊𝒋′ ⋅
1
𝑎𝑎 𝑟
2 𝑠 𝑜 𝐴
𝑎𝑜2
𝑎𝑠2
𝑎𝑠2
1
𝑎𝑎 𝑟
8 𝑠 𝑜 𝐴
1
𝑎𝑎 𝑟
8 𝑠 𝑜 𝐴
1 2
𝑎
16 𝑜
1 2
𝑎
4 𝑠
1
𝑎𝑎 𝑟
4 𝑠 𝑜 𝐴
1
𝑎𝑎 𝑟
4 𝑠 𝑜 𝐴
1 2
𝑎
8 𝑜
1 2
𝑎
4 𝑠
1
𝑎𝑎 𝑟
4 𝑠 𝑜 𝐴
1
𝑎𝑎 𝑟
4 𝑠 𝑜 𝐴
1 2
𝑎
8 𝑜
1 2
𝑎
2 𝑠
1
𝑎𝑎 𝑟
2 𝑠 𝑜 𝐴
1
𝑎𝑎 𝑟
2 𝑠 𝑜 𝐴
1 2
𝑎
4 𝑜
1 2
𝑎
2 𝑠
1
𝑎𝑎 𝑟
2 𝑠 𝑜 𝐴
1
𝑎𝑎 𝑟
2 𝑠 𝑜 𝐴
1 2
𝑎
4 𝑜
𝑎𝑠2
1
𝑎𝑎 𝑟
2 𝑠 𝑜 𝐴
1
𝑎𝑎 𝑟
2 𝑠 𝑜 𝐴
1 2
𝑎
2 𝑜
𝑪𝑺𝑫𝑷
𝒊𝒋′ ⋅
𝑪𝑶𝑼𝑻
𝒊𝒋′⋅
𝑪𝑺𝑫𝑷
𝒊𝒋′ ⋅
𝑪𝑶𝑼𝑻
𝒊𝒋′⋅
𝑪𝑺𝑫𝑷
𝒊𝒋′ ⋅
𝑪𝑶𝑼𝑻
𝒊𝒋′⋅
𝑪𝑺𝑫𝑷
𝒊𝒋′ ⋅
𝑪𝑶𝑼𝑻
𝒊𝒋′⋅
𝑨𝑶𝑼𝑻
𝒊𝒋′⋅
1
𝑎𝑎 𝑟
8 𝑠 𝑜 𝐴
1
1 2
𝑎𝑎 𝑟
𝑎
8 𝑠 𝑜 𝐴 16 𝑜
𝑪𝑺𝑫𝑷
𝒊𝒋𝒌
𝑪𝑶𝑼𝑻
𝒊𝒋𝒌
𝑪𝑺𝑫𝑷
𝒊𝒋𝒌′
𝑪𝑶𝑼𝑻
𝒊𝒋𝒌′
𝑪𝑺𝑫𝑷
𝒊𝒋𝒌′
𝑪𝑶𝑼𝑻
𝒊𝒋𝒌′
𝑪𝑺𝑫𝑷
𝒊𝒋𝒌
𝑐𝑠2
𝑐𝑠 𝑐𝑜 𝑟𝐶
𝑐𝑠2
𝑐𝑠 𝑐𝑜 𝑟𝐶
𝑐𝑠2
𝑐𝑠 𝑐𝑜 𝑟𝐶
0
0
0
0
0
0
0
0
0
0
𝑪𝑶𝑼𝑻
𝒊𝒋𝒌
𝑐𝑠 𝑐𝑜 𝑟𝐶
𝑐𝑜2
𝑐𝑠 𝑐𝑜 𝑟𝐶
𝑐𝑜2
𝑐𝑠 𝑐𝑜 𝑟𝐶
𝑐𝑜2
0
0
0
0
0
0
0
0
0
0
M
𝑴𝑺𝑫𝑷
𝒊𝒋𝒌
𝑴𝑶𝑼𝑻
𝒊𝒋𝒌
𝑴𝑺𝑫𝑷
𝒊𝒋𝒌′
𝑴𝑶𝑼𝑻
𝒊𝒋𝒌′
𝑴𝑺𝑫𝑷
𝒊𝒋𝒌′
𝑴𝑶𝑼𝑻
𝒊𝒋𝒌′
𝑴𝑺𝑫𝑷
𝒊𝒋′ ⋅
𝑴𝑶𝑼𝑻
𝒊𝒋′⋅
𝑴𝑺𝑫𝑷
𝒊𝒋′ ⋅
𝑴𝑶𝑼𝑻
𝒊𝒋′⋅
𝑴𝑺𝑫𝑷
𝒊𝒋′ ⋅
𝑴𝑶𝑼𝑻
𝒊𝒋′⋅
𝑴𝑺𝑫𝑷
𝒊𝒋′ ⋅
𝑴𝑺𝑫𝑷
𝒊𝒋′⋅
𝑴𝑶𝑼𝑻
𝒊𝒋′⋅
𝑚𝑠2
𝑚𝑠 𝑚𝑜 𝑟𝑀
𝑚𝑠2
𝑚𝑠 𝑚𝑜 𝑟𝑀
𝑚𝑠2
𝑚𝑠 𝑚𝑜 𝑟𝑀
𝑚𝑠2
𝑚𝑠 𝑚𝑜 𝑟𝑀
𝑚𝑠2
𝑚𝑠 𝑚𝑜 𝑟𝑀
𝑚𝑠2
𝑚𝑠 𝑚𝑜 𝑟𝑀
𝑚𝑠2
𝑚𝑜2
𝑚𝑠 𝑚𝑜 𝑟𝑀
𝑚𝑜2
𝑚𝑠 𝑚𝑜 𝑟𝑀
𝑚𝑜2
𝑚𝑠 𝑚𝑜 𝑟𝑀
𝑚𝑜2
𝑚𝑠 𝑚𝑜 𝑟𝑀
𝑚𝑜2
𝑚𝑠 𝑚𝑜 𝑟𝑀
𝑚𝑜2
𝑚𝑠 𝑚𝑜 𝑟𝑀
𝑚𝑜2
𝑷𝑺𝑫𝑷
𝒊𝒋𝒌
𝑷𝑶𝑼𝑻
𝒊𝒋𝒌
𝑷𝑺𝑫𝑷
𝒊𝒋𝒌′
𝑷𝑶𝑼𝑻
𝒊𝒋𝒌′
𝑷𝑺𝑫𝑷
𝒊𝒋𝒌′
𝑷𝑶𝑼𝑻
𝒊𝒋𝒌′
𝑷𝑺𝑫𝑷
𝒊𝒋′⋅
𝑷𝑶𝑼𝑻
𝒊𝒋′ ⋅
𝑷𝑺𝑫𝑷
𝒊𝒋′⋅
𝑷𝑶𝑼𝑻
𝒊𝒋′ ⋅
𝑷𝑺𝑫𝑷
𝒊𝒋′⋅
𝑷𝑶𝑼𝑻
𝒊𝒋′ ⋅
𝑷𝑺𝑫𝑷
𝒊𝒋′⋅
𝑷𝑶𝑼𝑻
𝒊𝒋′ ⋅
𝑝𝑠2
𝑝𝑠 𝑝𝑜 𝑟𝑃
𝑝𝑠2
𝑝𝑠 𝑝𝑜 𝑟𝑃
0
0
0
0
0
0
0
0
0
0
0
0
𝑝𝑜2
𝑝𝑠 𝑝𝑜 𝑟𝑃
𝑝𝑜2
0
0
0
0
0
0
0
0
0
0
0
0
𝑬𝑺𝑫𝑷
𝒊𝒋𝒌
𝑬𝑶𝑼𝑻
𝒊𝒋𝒌
𝑬𝑺𝑫𝑷
𝒊𝒋𝒌′
𝑬𝑶𝑼𝑻
𝒊𝒋𝒌′
𝑒𝑠2
𝑒𝑠 𝑒𝑜 𝑟𝐸
0
0
0
0
0
0
0
0
0
0
0
0
0
0
𝑒𝑠 𝑒𝑜 𝑟𝐸
𝑒𝑜2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C
𝑴𝑺𝑫𝑷
𝒊𝒋𝒌
𝑚𝑠 𝑚𝑜 𝑟𝑀
𝑴𝑶𝑼𝑻
𝒊𝒋𝒌
P
𝑷𝑺𝑫𝑷
𝒊𝒋𝒌
𝑝𝑠 𝑝𝑜 𝑟𝑃
𝑷𝑶𝑼𝑻
𝒊𝒋𝒌
E
𝑬𝑺𝑫𝑷
𝒊𝒋𝒌
𝑬𝑶𝑼𝑻
𝒊𝒋𝒌
𝑬𝑺𝑫𝑷
𝒊𝒋𝒌′
𝑬𝑶𝑼𝑻
𝒊𝒋𝒌′
𝑬𝑺𝑫𝑷
𝒊𝒋′ ⋅
𝑬𝑶𝑼𝑻
𝒊𝒋′ ⋅
𝑬𝑺𝑫𝑷
𝒊𝒋′ ⋅
𝑬𝑶𝑼𝑻
𝒊𝒋′ ⋅
𝑬𝑺𝑫𝑷
𝒊𝒋′ ⋅
𝑬𝑶𝑼𝑻
𝒊𝒋′ ⋅
𝑬𝑺𝑫𝑷
𝒊𝒋′ ⋅
𝑴𝑶𝑼𝑻
𝒊𝒋′⋅
𝑪𝑺𝑫𝑷
𝒊𝒋′⋅
𝑚𝑠 𝑚𝑜 𝑟𝑀 0
𝑬𝑶𝑼𝑻
𝒊𝒋′ ⋅
0
𝑷𝑺𝑫𝑷
𝒊𝒋′ ⋅
𝑬𝑺𝑫𝑷
𝒊𝒋′⋅
𝑪𝑶𝑼𝑻
𝒊𝒋′⋅
0
0
𝑷𝑶𝑼𝑻
𝒊𝒋′⋅
𝑬𝑶𝑼𝑻
𝒊𝒋′⋅
Abbreviations: SDP, smoking during pregnancy – the exposure. OUT, outcome. A, additive genetic effects. C, shared environment between
siblings in offspring generation. M, shared environment between siblings in parental generation. P, paternal/spouse effect. E, unique environment
in offspring generation. The 𝑘 ′ and 𝑗 ′ subscript are the compliments of 𝑘 and 𝑗, respectively. The “⋅” is used to indicate any of possible values at
subscript.
13
Appendix Table 6a: Observed means of birth weight in different exposure-combination groups
Birth weight
SDP status
First
pregnancy
Any value
0
1
Any value
Any value
0
1
0
1
Second
pregnancy
Any value
Any value
Any value
0
1
0
0
1
1
Mean birth weight in grams and
number of individuals
First
Second
N
pregnancy
pregnancy
3461
3625
1,360,988
3486
3651
1,129,312
3344
3498
231,674
3482
3654
1,173,284
3334
3443
187,702
3487
3654
1,098,770
3411
3643
74,514
3446
3516
30,542
3312
3429
157,160
Appendix Table 6b: Observed prevalences of pre-term birth in different exposure-combination groups
Pre-term birth
SDP status
First
pregnancy
Any value
0
1
Any value
Any value
0
1
0
1
Second
pregnancy
Any value
Any value
Any value
0
1
0
0
1
1
Prevalences and number of
individuals
First
Second
N
pregnancy
pregnancy
5.63%
3.61%
1,360,988
5.53%
3.41%
1,129,312
6.14%
4.62%
231,674
5.54%
3.39%
1,173,284
6.23%
4.99%
187,702
5.52%
3.38%
1,098,770
5.80%
3.56%
74,514
5.88%
4.33%
30,542
6.30%
5.12%
157,160
Appendix Table 6c: Observed prevalences of being born small for gestational age in different
exposure-combination groups
Born small for gestational age
SDP status
Prevalences and number of
individuals
14
First
pregnancy
Any value
0
1
Any value
Any value
0
1
0
1
Second
pregnancy
Any value
Any value
Any value
0
1
0
0
1
1
First
pregnancy
7.95%
6.87%
13.22%
7.07%
13.46%
6.82%
10.85%
8.91%
14.35%
Second
pregnancy
4.40%
3.62%
8.18%
3.60%
9.37%
3.52%
4.75%
7.16%
9.80%
N
1,360,988
1,129,312
231,674
1,173,284
187,702
1,098,770
74,514
30,542
157,160
Appendix Table 6d: Observed prevalences of low academic achievement in different exposurecombination groups
Low academic achievement
SDP status
First
pregnancy
Any value
0
1
Any value
Any value
0
1
0
1
Second
pregnancy
Any value
Any value
Any value
0
1
0
0
1
1
Prevalences and number of
individuals
First
Second
N
pregnancy
pregnancy
7.80%
9.30%
453,806
5.73%
6.87%
341,492
14.08%
16.66%
112,314
5.76%
6.93%
356,552
15.26%
17.97%
97,254
5.44%
6.51%
327,628
9.38%
11.68%
28,924
12.58%
15.41%
13,864
15.71%
18.39%
83,390
Appendix Table 6e: Observed means of general cognitive ability in different exposure-combination
groups
General cognitive ability
SDP status
First
pregnancy
Any value
0
1
Second
pregnancy
Any value
Any value
Any value
Means (on a nine-point scale) and
number of individuals
First
Second
N
pregnancy
pregnancy
5.44
5.08
31,614
5.59
5.22
23,836
4.99
4.64
7,778
15
Any value
Any value
0
1
0
1
0
1
0
0
1
1
5.58
4.94
5.62
5.17
5.05
4.92
5.21
4.59
5.25
4.80
4.68
4.57
25,064
6,550
22,928
2,136
908
5,642
Appendix Table 6f: Observed prevalences of criminal convictions in different exposure-combination
groups
Crime
SDP status
First
pregnancy
Any value
0
1
Any value
Any value
0
1
0
1
Second
pregnancy
Any value
Any value
Any value
0
1
0
0
1
1
Prevalences and number of
individuals
First
Second
N
pregnancy
pregnancy
9.14%
10.20%
197,130
7.46%
8.37%
143,608
13.64%
15.10%
53,522
7.55%
8.51%
150,956
14.35%
15.74%
46,174
7.25%
8.16%
137,532
10.58%
12.02%
13,424
12.21%
13.17%
6,076
14.67%
16.13%
40,098
16
Appendix Table 6g: Observed prevalences of violent criminal convictions in different exposurecombination groups
Violent crime
SDP status
First
pregnancy
Any value
0
1
Any value
Any value
0
1
0
1
Second
pregnancy
Any value
Any value
Any value
0
1
0
0
1
1
Prevalences and number of
individuals
First
Second
N
pregnancy
pregnancy
1.76%
2.06%
196,726
1.17%
1.32%
143,370
3.36%
4.06%
53,356
1.20%
1.37%
150,704
3.59%
4.34%
46,022
1.09%
1.25%
137,310
2.33%
2.57%
13,394
2.84%
2.90%
6,060
3.71%
4.56%
39,962
Appendix Table 6h: Observed prevalences of drug/alcohol misuse in different exposure-combination
groups
Drug/alcohol misuse
SDP status
First
pregnancy
Any value
0
1
Any value
Any value
0
1
0
1
Second
pregnancy
Any value
Any value
Any value
0
1
0
0
1
1
Prevalences and number of
individuals
First
Second
N
pregnancy
pregnancy
4.69%
5.88%
94,470
3.61%
4.70%
68,242
7.50%
8.97%
26,228
3.69%
4.72%
71,848
7.88%
9.57%
22,622
3.49%
4.53%
65,386
5.66%
6.62%
6,462
6.37%
8.40%
2,856
8.09%
9.73%
19,766
Appendix Table 7: Expected/observed means or proportions of mothers concordant and discordant
for smoking during pregnancy for each outcome
17
Birth weight
Pre-term birth
Born small for
gestational age
Low academic
achievement
General cognitive
ability
Criminal
conviction
Violent criminal
conviction
Drug/alcohol
misuse
Observed
concordant
not SDP
Observed
concordant
SDP
Observed
discordant in
SDP
3514
4.80%
7.87%
Expected
discordant
SDP,
additivea
3471
5.08%
8.62%
Expected
discordant
SDP,
multiplicativea
NA
5.04%
7.96%
3571
4.45%
5.17%
3371
5.71%
12.08%
5.98%
17.05%
11.65%
11.51%
10.26%
5.43
4.75
4.95
5.09
NA
7.71%
15.40%
11.73%
11.55%
10.98%
1.17%
4.13%
2.58%
2.65%
2.21%
4.01%
8.91%
6.53%
6.46%
6.01 %
Abbreviation: NA, not applicable.
a Expected discordant SDP refers to assuming that the effect of SDP has a linear effect on both siblings
outcomes, i.e. discordant pairs have half the effect of the concordant smoking pairs effect relative to the
concordant non-smoking pairs.
18
Appendix Table 8: Test of carry-over and contagion effects.
Outcome
Birth-weight
Pre-term birth
Born small for
gestational age
Low academic
achievement
General
cognitive ability
Crime
Violent crime
Drug/alcohol
misuse
Effect estimates (standard error)
SDP1 on OUT2
SDP2 on OUT1
-152.5 (1.7)
0.32 (0.02)
0.86 (0.01)
-148.4 (1.9)
0.13 (0.02)
0.72 (0.01)
Interaction
effect;
p-value
0.110
<0.001
<0.001
1.00 (0.02)
1.08 (0.02)
<0.001
-0.59 (0.03)
-0.64 (0.04)
0.282
0.67 (0.02)
1.15 (0.05)
0.69 (0.03)
0.72 (0.02)
1.12 (0.05)
0.80 (0.05)
0.098
0.624
0.064
19
Appendix A: Description of the ACMPE model
Each phenotype, either exposure or outcome, is assumed to be caused by the variance sources A, C, M,
P, E and possible some covariates. Let i (=1, 2,…, N; N=number of extended families) be extended family
𝑆𝐷𝑃
number, j (=1, 2) be nuclear family number, and k (=1, 2) be offspring number. Let 𝑦𝑖𝑗𝑘
be maternal
𝑂𝑈𝑇
𝑆𝐷𝑃
smoking during pregnancy and 𝑦𝑖𝑗𝑘
be the outcome and 𝒙𝑖𝑗𝑘
and 𝒙𝑂𝑈𝑇
𝑖𝑗𝑘 be covariates, for individual k
within nuclear family j and extended family i. Let 𝑆𝐷𝑃𝑖𝑗𝑘 and 𝑂𝑈𝑇𝑖𝑗𝑘 be the residuals; the unexplained
𝑆𝐷𝑃
𝑂𝑈𝑇
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
variance in 𝑦𝑖𝑗𝑘
and 𝑦𝑖𝑗𝑘
when adjusted for covariates 𝒙𝑖𝑗𝑘
and 𝒙𝑂𝑈𝑇
𝑖𝑗𝑘 . Furthermore, let 𝐴𝑖𝑗𝑘 , 𝐶𝑖𝑗𝑘 ,
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑀𝑖𝑗𝑘
, 𝑃𝑖𝑗𝑘
, and 𝐸𝑖𝑗𝑘
be random effects representing the previously defined variance sources for SDP
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇
(the exposure), and 𝐴𝑂𝑈𝑇
𝑖𝑗𝑘 , 𝐶𝑖𝑗𝑘 , 𝑀𝑖𝑗𝑘 , 𝑃𝑖𝑗𝑘 , and 𝐸𝑖𝑗𝑘 be random effects representing the variance
sources for the outcome. These random effects are assumed normally distributed with mean zero.
Finally, let 𝜷𝑆𝐷𝑃 and 𝜷𝑂𝑈𝑇 be regression coefficients for the covariates on the phenotypic values
respectively. For brevity the model is here described using the unity link, as used for continuous
variables; however for binary variables the liability threshold model is used (similar to using a probit
link), the model generalizes to this situation. The observed phenotypes within an individual are defined
by the equation
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑦𝑖𝑗𝑘
𝒙𝑖𝑗𝑘
𝜷𝑆𝐷𝑃 + 𝑆𝐷𝑃𝑖𝑗𝑘
[ 𝑂𝑈𝑇 ] = [ 𝑂𝑈𝑇
],
𝑦𝑖𝑗𝑘
𝒙𝑖𝑗𝑘 𝜷𝑂𝑈𝑇 + 𝑂𝑈𝑇𝑖𝑗𝑘
where the residuals 𝑆𝐷𝑃𝑖𝑗𝑘 and 𝑂𝑈𝑇𝑖𝑗𝑘 are decomposed into random effects:
[
𝑂
𝑆𝐷𝑃𝑖𝑗𝑘
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝐴𝑖𝑗𝑘
+ 𝐶𝑖𝑗𝑘
+ 𝑀𝑖𝑗𝑘
+ 𝑃𝑖𝑗𝑘
+ 𝐸𝑖𝑗𝑘
]
=
[
𝑂
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇 ].
𝑂𝑈𝑇𝑖𝑗𝑘
𝐴𝑂𝑈𝑇
𝑖𝑗𝑘 + 𝐶𝑖𝑗𝑘 + 𝑀𝑖𝑗𝑘 + 𝑃𝑖𝑗𝑘 + 𝐸𝑖𝑗𝑘
Intercepts may depend on extended and nuclear family types, if so then indicators of family types are
included in 𝒙𝑖𝑗𝑘 , and the intercepts regression coefficients are included in the 𝜷-vectors. It should be
noted that these parameters are estimated simultaneously with the random effects.
We use extended families consisting of two nuclear families, and each nuclear family consists of one or
two offspring of the same mother. Thus an extended family may consist of 4 individuals, each with two
phenotypes:
𝑂
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃𝑖11
𝐴𝑖11
+ 𝐶𝑖11
+ 𝑀𝑖11
+ 𝑃𝑖11
+ 𝐸𝑖11
𝑂
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇𝑖11
𝐴𝑂𝑈𝑇
𝑖11 + 𝐶𝑖11 + 𝑀𝑖11 + 𝑃𝑖11 + 𝐸𝑖11
𝑂
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃𝑖12
𝐴𝑖12
+ 𝐶𝑖12
+ 𝑀𝑖12
+ 𝑃𝑖12
+ 𝐸𝑖12
𝑂
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇𝑖12
𝐴𝑂𝑈𝑇
𝑖12 + 𝐶𝑖12 + 𝑀𝑖12 + 𝑃𝑖12 + 𝐸𝑖12
=
𝑂
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃 .
𝑆𝐷𝑃𝑖21
𝐴𝑖21
+ 𝐶𝑖21
+ 𝑀𝑖21
+ 𝑃𝑖21
+ 𝐸𝑖21
𝑂
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇𝑖21
𝐴𝑂𝑈𝑇
𝑖21 + 𝐶𝑖21 + 𝑀𝑖21 + 𝑃𝑖21 + 𝐸𝑖21
𝑂
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃𝑖22
𝐴𝑖22
+ 𝐶𝑖22
+ 𝑀𝑖22
+ 𝑃𝑖22
+ 𝐸𝑖22
𝑂
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇
𝑂𝑈𝑇
[𝑂𝑈𝑇𝑖22
] [𝐴𝑂𝑈𝑇
𝑖22 + 𝐶𝑖22 + 𝑀𝑖22 + 𝑃𝑖22 + 𝐸𝑖22 ]
20
The covariance between subjects, both within and across phenotypes, is dependent on their relation,
both genetic and environmental. In Appendix Table 5 the correlation between random variables 𝐴, 𝐶,
𝑆𝐷𝑃
𝑀, 𝑃, and 𝐸 within and across phenotypes are tabulated. Here 𝑎𝑠2 is the variance of 𝐴𝑖𝑗𝑘
, 𝑎𝑜2 ditto for
𝑆𝐷𝑃 2
𝑂𝑈𝑇
2
𝐴𝑂𝑈𝑇
𝑖𝑗𝑘 , 𝑐𝑠 is the variance of 𝐶𝑖𝑗𝑘 , 𝑐𝑜 ditto for 𝐶𝑖𝑗𝑘 , et cetera. The parameter 𝑟𝐴 captures the genetic
overlap between exposure and outcome, 𝑟𝐶 captures the overlap for environmental 𝐶 part, et cetera.
Appendix Table 5 shows covariance within individual and across relatives, both within each phenotype
and across phenotypes. It can be seen that environments are assumed shared across phenotypes, and
therefore across generations, by simple prolongation of how it looks within each generation. Note that
all covariances between variance sources, both within and across phenotypes, are assumed to be zero,
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑆𝐷𝑃
𝑂𝑈𝑇
𝑂𝑈𝑇 𝑂𝑈𝑇
e.g. 𝐶𝑜𝑣(𝐴𝑖𝑗𝑘
, 𝐶𝑖𝑗𝑘
, 𝑀𝑖𝑗𝑘
, 𝑃𝑖𝑗𝑘 ) ≡ 0. The SEM is shown in
) ≡ 0, 𝐶𝑜𝑣(𝐶𝑖𝑗𝑘
) ≡ 0, and 𝐶𝑜𝑣(𝑀𝑖𝑗𝑘
part as path diagrams in Appendix Figure 2 where an extended family structure of a family with one
offspring in “Nuclear family 1” and a family with two offspring in “Nuclear family 2” are depicted. Each
variance source is shown separately; however, they are simultaneously estimated.
In the SEM an expected covariance matrix is specified, this covariance matrix is specific to any
combination of siblings in nuclear families with any combination of mothers who are siblings in
extended families. Since we allow for one to four individuals in the offspring generation (one: mothers
without siblings with one offspring; four: two mothers who are siblings, each mother with two offspring)
the extended families may be accompanied by an expected covariance matrix of dimensions ranging
from 2x2 to 8x8.
We can derive all covariances between phenotypes in one subject with that of another in the same
extended family using Appendix Table 5 (or Appendix Figure 2), both between and within phenotypes;
Within an individual, note that off-diagonals are symmetric:
𝑉𝑎𝑟(𝑆𝐷𝑃𝑖𝑗𝑘 )
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗𝑘 )
[
]=
𝐶𝑜𝑣(𝑂𝑈𝑇𝑖𝑗𝑘 , 𝑆𝐷𝑃𝑖𝑗𝑘 )
𝑉𝑎𝑟(𝑂𝑈𝑇𝑖𝑗𝑘 )
𝑎𝑠2 + 𝑐𝑠2 + 𝑚𝑠2 + 𝑝𝑠2 + 𝑒𝑠2
[1
].
𝑎𝑠 𝑎𝑜 𝑟𝐴 + 𝑐𝑠 𝑐𝑜 𝑟𝐶 + 𝑚𝑠 𝑚𝑜 𝑟𝑀 + 𝑝𝑠 𝑝𝑜 𝑟𝑃 + 𝑒𝑠 𝑒𝑜 𝑟𝐸 𝑎𝑜2 + 𝑐𝑜2 + 𝑚𝑜2 + 𝑝𝑜2 + 𝑒𝑜2
2
Between full siblings, the 𝑘 ′ sub-index is the complement of 𝑘:
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑆𝐷𝑃𝑖𝑗𝑘 ′ ) 𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗𝑘 ′ )
[
]=
𝐶𝑜𝑣(𝑂𝑈𝑇𝑖𝑗𝑘 , 𝑆𝐷𝑃𝑖𝑗𝑘 ′ ) 𝐶𝑜𝑣(𝑂𝑈𝑇𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗𝑘 ′ )
[1
𝑎𝑠2 + 𝑐𝑠2 + 𝑚𝑠2 + 𝑝𝑠2
𝑎 𝑎 𝑟 + 𝑐𝑠 𝑐𝑜 𝑟𝐶 + 𝑚𝑠 𝑚𝑜 𝑟𝑀 + 𝑝𝑠 𝑝𝑜 𝑟𝑃
2 𝑠 𝑜 𝐴
1 2
𝑎
2 𝑜
+ 𝑐𝑜2 + 𝑚𝑜2 + 𝑝𝑜2
].
Between half siblings:
𝑎𝑠2 + 𝑐𝑠2 + 𝑚𝑠2
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑆𝐷𝑃𝑖𝑗𝑘 ′ ) 𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗𝑘 ′ )
[
] = [1
𝑎 𝑎 𝑟 + 𝑐𝑠 𝑐𝑜 𝑟𝐶 + 𝑚𝑠 𝑚𝑜 𝑟𝑀
𝐶𝑜𝑣(𝑂𝑈𝑇𝑖𝑗𝑘 , 𝑆𝐷𝑃𝑖𝑗𝑘 ′ ) 𝐶𝑜𝑣(𝑂𝑈𝑇𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗𝑘 ′ )
2 𝑠 𝑜 𝐴
1 2
𝑎
4 𝑜
+ 𝑐𝑜2 + 𝑚𝑜2
].
Between cousins where mothers are MZ twins, the 𝑗 ′ sub-index is the complement of 𝑗, and “⋅” is used
to indicate any of possible values at sub-index:
21
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑆𝐷𝑃𝑖𝑗′ ⋅ )
𝑎𝑠2 + 𝑚𝑠2
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗′ ⋅ )
[
] = [1
𝑎 𝑎 𝑟 + 𝑚𝑠 𝑚𝑜 𝑟𝑀
𝐶𝑜𝑣(𝑂𝑈𝑇𝑖𝑗𝑘 , 𝑆𝐷𝑃𝑖𝑗′ ⋅ ) 𝐶𝑜𝑣(𝑂𝑈𝑇𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗′ ⋅ )
2 𝑠 𝑜 𝐴
1 2
𝑎
4 𝑜
+ 𝑚𝑜2
1 2
𝑎
8 𝑜
+ 𝑚𝑜2
].
Between cousins where mothers are DZ twins or full siblings:
1 2
𝑎
2 𝑠
+ 𝑚𝑠2
[
] = [1
𝐶𝑜𝑣(𝑂𝑈𝑇𝑖𝑗𝑘 , 𝑆𝐷𝑃𝑖𝑗′ ⋅ ) 𝐶𝑜𝑣(𝑂𝑈𝑇𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗′ ⋅ )
𝑎𝑠 𝑎𝑜 𝑟𝐴 + 𝑚𝑠 𝑚𝑜 𝑟𝑀
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑆𝐷𝑃𝑖𝑗′ ⋅ )
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗′ ⋅ )
4
].
Between cousins where mothers are maternal half siblings:
1 2
𝑎
4 𝑠
+ 𝑚𝑠2
[
] = [1
𝐶𝑜𝑣(𝑂𝑈𝑇𝑖𝑗𝑘 , 𝑆𝐷𝑃𝑖𝑗′ ⋅ ) 𝐶𝑜𝑣(𝑂𝑈𝑇𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗′ ⋅ )
𝑎𝑠 𝑎𝑜 𝑟𝐴 + 𝑚𝑠 𝑚𝑜 𝑟𝑀
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑆𝐷𝑃𝑖𝑗′ ⋅ )
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗′ ⋅ )
8
1 2
𝑎
16 𝑜
+ 𝑚𝑜2
].
Between cousins where mothers are paternal half siblings:
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑆𝐷𝑃𝑖𝑗′ ⋅ )
1 2
𝑎
4 𝑠
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗′ ⋅ )
[
] = [1
𝐶𝑜𝑣(𝑂𝑈𝑇𝑖𝑗𝑘 , 𝑆𝐷𝑃𝑖𝑗′ ⋅ ) 𝐶𝑜𝑣(𝑂𝑈𝑇𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗′ ⋅ )
𝑎𝑠 𝑎𝑜 𝑟𝐴
8
1 2 ].
𝑎
16 𝑜
From this we may assemble any constellation of families included in the model. As an example, let
extended family 1 be a mother with one offspring, let extended family 2 be a mother with two full
sibling offspring, and let the mothers be maternal half siblings; the expected covariance matrix looks like
𝑆𝐷𝑃𝑖11
𝑂𝑈𝑇𝑖11
𝑆𝐷𝑃𝑖21
𝐶𝑜𝑣
𝑂𝑈𝑇𝑖21
𝑆𝐷𝑃𝑖22
([𝑂𝑈𝑇𝑖22 ])
𝑉𝑎𝑟(𝑆𝐷𝑃𝑖11 )
𝐶𝑜𝑣(𝑂𝑈𝑇𝑖11 , 𝑆𝐷𝑃𝑖11 ) 𝑉𝑎𝑟(𝑂𝑈𝑇𝑖11 )
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖21 , 𝑆𝐷𝑃𝑖11 ) 𝐶𝑜𝑣(𝑆𝐷𝑃𝑖21 , 𝑂𝑈𝑇𝑖11 )
=
𝐶𝑜𝑣(𝑂𝑈𝑇𝑖21 , 𝑆𝐷𝑃𝑖11 ) 𝐶𝑜𝑣(𝑂𝑈𝑇𝑖21 , 𝑂𝑈𝑇𝑖11 )
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖22 , 𝑆𝐷𝑃𝑖11 ) 𝐶𝑜𝑣(𝑆𝐷𝑃𝑖22 , 𝑂𝑈𝑇𝑖11 )
[𝐶𝑜𝑣(𝑂𝑈𝑇𝑖22 , 𝑆𝐷𝑃𝑖11 ) 𝐶𝑜𝑣(𝑂𝑈𝑇𝑖22 , 𝑂𝑈𝑇𝑖11 )
𝑉𝑎𝑟(𝑆𝐷𝑃𝑖21 )
𝐶𝑜𝑣(𝑂𝑈𝑇𝑖21 , 𝑆𝐷𝑃𝑖21 ) 𝑉𝑎𝑟(𝑂𝑈𝑇𝑖21 )
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖22 , 𝑆𝐷𝑃𝑖21 ) 𝐶𝑜𝑣(𝑆𝐷𝑃𝑖22 , 𝑂𝑈𝑇𝑖21 )
𝑉𝑎𝑟(𝑆𝐷𝑃𝑖22 )
𝐶𝑜𝑣(𝑂𝑈𝑇𝑖22 , 𝑆𝐷𝑃𝑖21 ) 𝐶𝑜𝑣(𝑂𝑈𝑇𝑖22 , 𝑂𝑈𝑇𝑖21 ) 𝐶𝑜𝑣(𝑂𝑈𝑇𝑖22 , 𝑆𝐷𝑃𝑖22 ) 𝑉𝑎𝑟(𝑂𝑈𝑇𝑖22 )]
22
𝑎𝑠2 + 𝑐𝑠2 + 𝑚𝑠2 + 𝑝𝑠2 + 𝑒𝑠2
1
𝑎 𝑎 𝑟 + 𝑐𝑠 𝑐𝑜 𝑟𝐶 + 𝑚𝑠 𝑚𝑜 𝑟𝑀 + 𝑝𝑠 𝑝𝑜 𝑟𝑃 + 𝑒𝑠 𝑒𝑜 𝑟𝐸
2 𝑠 𝑜𝐴
1 2
𝑎 + 𝑚𝑠2
4 𝑠
=
1
𝑎 𝑎 𝑟 + 𝑚𝑠 𝑚𝑜 𝑟𝑀
8 𝑠 𝑜𝐴
1 2
𝑎 + 𝑚𝑠2
4 𝑠
1
𝑎 𝑎 𝑟 + 𝑚𝑠 𝑚𝑜 𝑟𝑀
[
8 𝑠 𝑜𝐴
…
…
…
[
…
𝑎𝑜2 + 𝑐𝑜2 + 𝑚𝑜2 + 𝑝𝑜2 + 𝑒𝑜2
1
𝑎 𝑎 𝑟 + 𝑚𝑠 𝑚𝑜 𝑟𝑀
8 𝑠 𝑜𝐴
1 2
𝑎 + 𝑚𝑜2
16 𝑜
1
𝑎 𝑎 𝑟 + 𝑚𝑠 𝑚𝑜 𝑟𝑀
8 𝑠 𝑜𝐴
1 2
𝑎 + 𝑚𝑜2
16 𝑜
𝑎𝑠2 + 𝑐𝑠2 + 𝑚𝑠2 + 𝑝𝑠2 + 𝑒𝑠2
1
𝑎 𝑎 𝑟 + 𝑐𝑠 𝑐𝑜 𝑟𝐶 + 𝑚𝑠 𝑚𝑜 𝑟𝑀 + 𝑝𝑠 𝑝𝑜 𝑟𝑃 + 𝑒𝑠 𝑒𝑜 𝑟𝐸
2 𝑠 𝑜𝐴
𝑎𝑠2 + 𝑐𝑠2 + 𝑚𝑠2 + 𝑝𝑠2
…
1
𝑎 𝑎 𝑟 + 𝑐𝑠 𝑐𝑜 𝑟𝐶 + 𝑚𝑠 𝑚𝑜 𝑟𝑀 + 𝑝𝑠 𝑝𝑜 𝑟𝑃
2 𝑠 𝑜𝐴
]
𝑎𝑜2 + 𝑐𝑜2 + 𝑚𝑜2 + 𝑝𝑜2 + 𝑒𝑜2
1
𝑎 𝑎 𝑟 + 𝑐𝑠 𝑐𝑜 𝑟𝐶 + 𝑚𝑠 𝑚𝑜 𝑟𝑀 + 𝑝𝑠 𝑝𝑜 𝑟𝑃
2 𝑠 𝑜𝐴
1 2
𝑎 + 𝑐𝑜2 + 𝑚𝑜2 + 𝑝𝑜2
2 𝑜
𝑎𝑠2 + 𝑐𝑠2 + 𝑚𝑠2 + 𝑝𝑠2 + 𝑒𝑠2
1
𝑎 𝑎 𝑟 + 𝑐𝑠 𝑐𝑜 𝑟𝐶 + 𝑚𝑠 𝑚𝑜 𝑟𝑀 + 𝑝𝑠 𝑝𝑜 𝑟𝑃 + 𝑒𝑠 𝑒𝑜 𝑟𝐸
2 𝑠 𝑜𝐴
.
𝑎𝑜2
+
𝑐𝑜2
+
𝑚𝑜2
+ 𝑝𝑜2
In the ACMPE model there are a number of parameters which may be estimated:

The intercepts and covariate regression parameters; 𝜷𝑆𝐷𝑃 and 𝜷𝑂𝑈𝑇 .

The variance of random parameters A, C, M, P, and E for exposure and outcome;
𝑎𝑠2 , 𝑐𝑠2 , 𝑚𝑠2 , 𝑝𝑠2 , 𝑒𝑠2 , 𝑎𝑜2 , 𝑐𝑜2 , 𝑚𝑜2 , 𝑝𝑜2 , and 𝑒𝑜2 .

…
The cross-phenotype correlation parameters; 𝑟𝐴 , 𝑟𝐶 , 𝑟𝑀 , 𝑟𝑃 , and 𝑟𝐸 .
.
For each variable, both exposure and outcomes, we may use the above defined variance, e.g.
𝑉𝑎𝑟(𝑂𝑈𝑇𝑖𝑗𝑘 ) = 𝑎𝑜2 + 𝑐𝑜2 + 𝑚𝑜2 + 𝑝𝑜2 + 𝑒𝑜2 ,
to estimate the fraction of variance explained by each variance source. For example, the narrow sense
heritability for an outcome, i.e. the fraction of variance explained by additive genetic factors, may be
expressed as
narrow sense heritability =
𝑎𝑜2
.
𝑉𝑎𝑟(𝑂𝑈𝑇𝑖𝑗𝑘 )
Above we derived that the covariance between SDP and outcome within an individual is
1
𝐶𝑜𝑣(𝑆𝐷𝑃𝑖𝑗𝑘 , 𝑂𝑈𝑇𝑖𝑗𝑘 ) = 𝑎𝑠 𝑎𝑜 𝑟𝐴 + 𝑐𝑠 𝑐𝑜 𝑟𝐶 + 𝑚𝑠 𝑚𝑜 𝑟𝑀 + 𝑝𝑠 𝑝𝑜 𝑟𝑃 + 𝑒𝑠 𝑒𝑜 𝑟𝐸 .
2
The amount of explained covariance between phenotypes, within individual, per variance source is the
particular source divided by the total amount of covariance, e.g.
+
𝑒𝑜2
]
23
1
𝑎𝑠 𝑎𝑜 𝑟𝐴
2
explained covariance due to additive genetics = 𝐶𝑜𝑣(𝑆𝐷𝑃
𝑖𝑗𝑘 ,𝑂𝑈𝑇𝑖𝑗𝑘 )
.
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Appendix B: Generalizability of mothers who change smoking status
between pregnancies; carry-over and contagion effects
Within sibling comparison analyses may be regarded as having an estimated effect that is closer to a
causal effect compared to ordinary between individual analyses. Nevertheless, as all statistical models,
comparisons within siblings rely on a number of assumptions, discussed in detail in D’Onofrio et al.
(2013). We here address three assumptions which we believe are most important for our study.
Generalizability. Are women who change their smoking behavior between two
pregnancies different?
The within sibling comparisons utilize siblings discordant for exposure to smoking while in utero. If
mothers who change their smoking status between pregnancies are very different (i.e., in terms of how
smoking during pregnancy (SDP) affects the outcome) from those who do not, the results of our
analyses may not be generalizable to groups of women who do not change their smoking status
between pregnancies. Appendix Tables 6a-h present the proportions and means in the outcomes for
each possible combination of SDP in the offspring (where we used the first- and second-born of each
mother having her first child in 1983 or later, and having at least two children in exposure periods
defined as in the main article).
To investigate the generalizability of pairs discordant for SDP to pairs concordant, we calculate the
concordant proportions/means and an expected value for the discordant pairs (Appendix Table 7). We
realize that “expected value” is scale-dependent, so we consider additive scale and multiplicative scale
in our analyses. The expected value was calculated under the assumption that SDP had a linear effect
(either additive scale [unity link] or a multiplicative scale [logit link], where applicable) for both offspring
in the nuclear family, regardless if the mother smoked in the offspring’s pregnancy or his/her sibling’s.
As can be seen in the table, for all associations the observed prevalences and means in the outcomes for
SDP-discordant pairs were roughly halfway between that of SDP-concordant pairs. All values were closer
to the predicted values than to the observed values in any of the concordant pairs. This pattern is what
is expected if SDP is an expression of maternal characteristics (e.g., genes) and/or the association is
causal. Thus, the data suggest that the SDP discordant mothers carry a liability that is in between the
liabilities of the concordant mothers or that the association is causal, or a combination them between.
Further, if discordant siblings were very different from the general population we would not expect
within sibling results to be in agreement with results comparing cousins (Table 4 in the main paper).
Taken together, our analyses don’t provide any evidence for the hypothesis that SDP results from
discordant mothers should not be generalizable to other mothers.
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Carry-over and contagion effects. Does smoking behavior in first pregnancy
influence the next pregnancy?
Another issue is whether there are carry-over effects from child 1 to child 2, that is, when the exposure
status of sibling 1 (SDP1) affects the outcome of sibling 2 (OUT2) directly; for example, later born
offspring to mothers who had their first child born during adolescence were affected by the effect of the
adolescent child-bearing regardless of the mothers age at their own birth, maybe because environmental
factors specifically associated with early maternal age of first child (e.g., diminished financial and social
resources in families in which the mother had her first child at an early age (Coyne et al. 2013)). The
carry-over effects should be distinguished from the contagion effects, which occurs when the outcome
of sibling 1 (OUT1) affects the outcome of sibling 2 (OUT2). An example would be if criminal behavior of
an older sibling would influence criminality in the younger siblings. We note that both of these potential
effects would introduce an association between SDP1 and OUT2 through a pathway which is assumed to
be non-existing in the sibling analyses. Thus, if no carry-over or contagion effect exists we would expect
the association between the SDP1 and OUT2 to be of the same magnitude as the association between
SDP2 on OUT1 .On the other hand, if carry-over or contagion effects are important, the effect of SDP1 on
OUT2 should be stronger than the effect of SDP2 on OUT1.
To investigate carry-over and contagion effects we tested whether the SDP1-OUT2 association differed
from the SDP2-OUT1 association by including an interaction term between being first born and SDP in
one pregnancy on the outcome in the other pregnancy (after controlling for the effects of being firstborn; Appendix Table 8).
As evident in Appendix Table 8, in none of the associations where our analyses suggested that familial
confounding was responsible for the entire association (i.e., all the cognitive/behavioral outcomes)
there were no evidence for carry-over or contagion effects (note that for Low academic achievement,
the indication is that child 2 influence child 1 rather than the other way around). We only observe
significant interaction effects of the SDP1-OUT2 association being stronger than the SDP2-OUT1
association in pre-term birth and born small for gestational age. Thus, our main conclusion that smoking
during pregnancy seem to be associated to adolescent cognitive capacity and late adolescent
behavioral/conduct problems only due to genetic transmission of common susceptibility genes do not
seem to be affected by violation of carry-over or contagion effects.
References Appendix B
Coyne, C. A., Langstrom, N., Rickert, M. E., Lichtenstein, P., D'Onofrio, B. M. (2013). Maternal age at
first birth and offspring criminality: using the children of twins design to test causal hypotheses.
Development and Psychopathology 25(1): 17-35.
D'Onofrio, B. M., Lahey, B. B., Turkheimer, E. & Lichtenstein, P. (2013). Critical need for family-based,
quasi-experimental designs in integrating genetic and social science research. American Journal of Public
Health 103 Suppl 1, S46-55
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