Supplemental Digital Content eAppendix 1

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1 Supplemental Digital Content

eAppendix 1: Assessment of confounding

Confounding was assessed based on theoretical knowledge and statistical criteria (i.e. variables associated with both variables of each relationship without being mediators of the relationship).

The following variables were assessed as confounders of the exposure-outcome relationship (Asc-IQ), the mediator-outcome relationships (Mhb-IQ and Mhaz-IQ) and the exposure-mediator relationships (Asc-Mhb and Asc-Mhaz): socioeconomic status (i.e. residential district, urban/rural status, mother’s marital status, maternal education (completed secondary school), mother employed, father or mother’s partner employed, number of people living in the home, house material, cooks using gas, presence of electricity in the home, working radio ownership, working television ownership, water source, has a toilet with water and connection to public sewage in the home, and household income); sex; healthcare seeking behavior (i.e. number of healthy growth visits attended between birth and one year and vaccines up to date at baseline); hygiene (i.e. number of baths per day and use of soap for bathing); baseline nutrition (i.e. stunted, underweight, wasted, birth weight); baseline development scores (i.e. cognition raw score, receptive language raw score, expressive language raw score and, fine motor raw score);

breastfeeding (i.e. exclusively breastfed to six months and continued breastfeeding at one year);

and number of years in preschool by five years of age. Univariable linear and multinomial regression models were used to determine if each variable was associated with the outcome variable, mediator variables and exposure variable. Correlations and 2 x 2 tables were also examined to observe relationships between the confounding variables.

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2 eAppendix 2: Multiple Imputation models

A multinomial regression model was used as the imputation model for cumulative Ascaris infection and linear regression was used as the imputation models for birth weight, hemoglobin levels and height-for-age z-scores. All covariates included in the outcome models were also included in the imputation models as well as other relevant covariates, with complete data, that predicted the missing data, as appropriate.

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3 eAppendix 3: Development of priors for sensitivity and specificity

The clinical, optimistic and pessimistic priors were developed following a review and critical appraisal of the published literature. Only two studies were found that used appropriate

statistical methods to account for the lack of a gold standard.^{26, 39} One of these studies is a meta- analysis²⁶ that includes the data from the other study.³⁹ This meta-analysis, therefore, was considered to be the most informative publication available regarding the diagnostic parameters of the STH diagnostic techniques. The clinical priors for the sensitivities of the Kato-Katz and direct smear techniques were therefore centered at the sensitivity values reported in this meta- analysis with a probability range of ±10% (a larger range than the 95% CrIs reported in the meta- analysis, to be conservative). The optimistic priors assumed that the sensitivity values were at the high end of the reported 95% CrIs and the pessimistic priors assumed that the sensitivity values were at the low end of the reported 95% CrIs, with probability ranges of ±5%. All prior densities on the sensitivity and specificity parameters were assumed to follow a beta distribution.

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4 eAppendix 4: WinBUGS models

a) Variable definitions:

Variable Definition

f_totaliq Total IQ score from WPPSI-III

dNumAsc2T Dummy variable for being infected with Ascaris infection two times between one and five years of age (adjusted for Ascaris misclassification)

dNumAsc3T Dummy variable for being infected with Ascaris infection three times between one and five years of age (adjusted for Ascaris misclassification)

dNumAsc4T Dummy variable for being infected with Ascaris infection four or five times between one and five years of age (adjusted for Ascaris misclassification)

meanhb Mean hemoglobin level between three and five years of age Mated_sec Maternal education (completed secondary school)

Cocinar_gas Uses gas for cooking

Bano_tasa Has a toilet with water and connection to public sewage in the home stunting1 Stunted at one year of age

cog_raw Cognitive raw score at one year of age

CRED_12 Number of healthy growth visits attended from birth to one year of age f_yrsjardin Number of years of preschool attended by five years of age

RN_peso Birth weight (kg)

Peso_kg Weight at one year of age (kg) Mat_edad Mother’s age at recruitment

Ascprev60 Ascaris infection status at five years of age (unadjusted for Ascaris misclassification) Ascprev48 Ascaris infection status at four years of age (unadjusted for Ascaris misclassification) Ascprev36 Ascaris infection status at three years of age (unadjusted for Ascaris misclassification) Ascprev24 Ascaris infection status at two years of age (unadjusted for Ascaris misclassification) AscKKD12 Ascaris infection status at one year of age (unadjusted for Ascaris misclassification) Ascprev60_T Ascaris infection status at five years of age (adjusted for Ascaris misclassification) Ascprev48_T Ascaris infection status at four years of age (adjusted for Ascaris misclassification) Ascprev36_T Ascaris infection status at three years of age (adjusted for Ascaris misclassification) Ascprev24_T Ascaris infection status at two years of age (adjusted for Ascaris misclassification) AscKKD12_T Ascaris infection status at one year of age (adjusted for Ascaris misclassification) sensKK Sensitivity of Kato-Katz technique for detecting Ascaris infection

specKK Specificity of Kato-Katz technique for detecting Ascaris infection sensD Sensitivity of direct smear technique for detecting Ascaris infection specD Specificity of direct smear technique for detecting Ascaris infection

KK12 Use of Kato-Katz or direct smear technique to analyse stool specimen at one year visit fo_desp_SI Received deworming between three and four years of age visits

t_desp_SI Received deworming between two and three years of age visits nde2 Natural direct effect of two Ascaris infections

nie2 Natural indirect effect of two Ascaris infections te2 Total effect of two Ascaris infections

nde3 Natural direct effect of three Ascaris infections nie3 Natural indirect effect of three Ascaris infections te3 Total effect of three Ascaris infections

nde4 Natural direct effect of four or five Ascaris infections nie4 Natural indirect effect of four or five Ascaris infections te4 Total effect of four or five Ascaris infections

haz15 Mean height-for-age z-score between one and five years of age

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5 b) WinBUGS model 1 (analysis of hemoglobin alone as a mediator):

model {

for (i in 1:781) {

mu.f_totaliq[i] <- alpha1 + b1.asc2*dNumAsc2T[i] + b1.asc3*dNumAsc3T[i] + b1.asc4*dNumAsc4T[i] + b1.hb*meanhb[i] + b1.mated*Mated_sec[i] + b1.gas*Cocinar_gas[i] + b1.tasa*Bano_tasa[i] +

b1.stun*stunting1[i] + b1.cog*cog_raw[i] + b1.cred*CRED_12[i] + b1.jard*f_yrsjardin[i] + b1.birthw*RN_peso[i]

f_totaliq[i] ~ dnorm(mu.f_totaliq[i], tau1)

mu.meanhb[i] <- alpha2 + b2.asc2*dNumAsc2T[i] + b2.asc3*dNumAsc3T[i] + b2.asc4*dNumAsc4T[i] + b2.mated*Mated_sec[i] +

b2.gas*Cocinar_gas[i] + b2.tasa*Bano_tasa[i] + b2.stun*stunting1[i] + b2.cog*cog_raw[i]

+ b2.cred*CRED_12[i] + b2.jard*f_yrsjardin[i] + b2.birthw*RN_peso[i]

meanhb[i] ~ dnorm(mu.meanhb[i], tau2)

mu.birthw[i] <- alpha3 + b3.asc2*dNumAsc2T[i] +

b3.asc3*dNumAsc3T[i] + b3.asc4*dNumAsc4T[i] + b3.mated*Mated_sec[i] +

+ b3.cred*CRED_12[i] + b3.jard*f_yrsjardin[i] + b3.hb*meanhb[i] + b3.peso*Peso_kg[i] + b3.matage*Mat_edad[i]

RN_peso[i] ~ dnorm(mu.birthw[i], tau3)

Ascprev60[i]~dbern(pAsc60[i])

pAsc60[i]<- sensKK*Ascprev60_T[i] + (1-specKK)*(1- Ascprev60_T[i])

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6 AscKKD12[i]~dbern(pAsc12[i])

pAsc12[i]<- sensKK*AscKKD12_T[i]*KK12[i] + (1-specKK)*(1- AscKKD12_T[i])*KK12[i] + sensD*AscKKD12_T[i]*(1-KK12[i]) + (1- specD)*(1-AscKKD12_T[i])*(1-KK12[i])

Ascprev60_T[i]~dbern(pAscT60[i])

logit(pAscT60[i])<-alpha4 + b4.tasa*Bano_tasa[i] + b4.desp*f_desp[i]

logit(pAscT48[i])<-alpha5 + b5.jard*f_yrsjardin[i] + b5.desp*fo_desp_SI[i]

logit(pAscT36[i])<-alpha6 + b6.mated*Mated_sec[i] + b6.gas*Cocinar_gas[i] + b6.cred*CRED_12[i] +

b6.desp*t_desp_SI[i]

logit(pAscT24[i])<-alpha7 + b7.tasa*Bano_tasa[i]

AscKKD12_T[i]~dbern(pAscT12[i])

logit(pAscT12[i])<-alpha8 + b8.gas*Cocinar_gas[i]

}

for (i in 1:781) {

NumAsc_T[i] <- AscKKD12_T[i] + Ascprev24_T[i] + Ascprev36_T[i] + Ascprev48_T[i] + Ascprev60_T[i]

dNumAsc2T[i] <- equals(NumAsc_T[i], 2) dNumAsc3T[i] <- equals(NumAsc_T[i], 3) dNumAsc4T[i] <- step(NumAsc_T[i] - 4) }

nde2<- b1.asc2

nie2<- b1.hb * b2.asc2

te2<- b1.asc2 + (b1.hb * b2.asc2) nde3<- b1.asc3

te3<- b1.asc3 + (b1.hb * b2.asc3) nde4<- b1.asc4

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7 te4<- b1.asc4 + (b1.hb * b2.asc4)

}

c) WinBUGS model 2 (analysis of hemoglobin and height-for-age z-scores as mediators):

model {

for (i in 1:781) {

mu.f_totaliq[i] <- alpha1 + b1.asc2*dNumAsc2T[i] +

b1.asc3*dNumAsc3T[i] + b1.asc4*dNumAsc4T[i] + b1.hb*meanhb[i] + b1.haz*haz15[i] + b1.mated*Mated_sec[i] + b1.gas*Cocinar_gas[i] + b1.tasa*Bano_tasa[i] +

b1.stun*stunting1[i] + b1.cog*cog_raw[i] + b1.cred*CRED_12[i] + b1.jard*f_yrsjardin[i] + b1.birthw*RN_peso[i]

f_totaliq[i] ~ dnorm(mu.f_totaliq[i], tau1)

mu.meanhb[i] <- alpha2 + b2.asc2*dNumAsc2T[i] + b2.asc3*dNumAsc3T[i] + b2.asc4*dNumAsc4T[i] + b2.mated*Mated_sec[i] +

meanhb[i] ~ dnorm(mu.meanhb[i], tau2)

mu.haz15[i] <- alpha9 + b9.asc2*dNumAsc2T[i] +

haz15[i] ~ dnorm(mu.haz15[i], tau9)

mu.birthw[i] <- alpha3 + b3.asc2*dNumAsc2T[i] +

+ b3.cred*CRED_12[i] + b3.jard*f_yrsjardin[i] + b3.hb*meanhb[i] + b3.peso*Peso_kg[i] + b3.matage*Mat_edad[i]

RN_peso[i] ~ dnorm(mu.birthw[i], tau3)

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8 pAsc48[i]<- sensKK*Ascprev48_T[i] + (1-specKK)*(1-

Ascprev48_T[i])

AscKKD12[i]~dbern(pAsc12[i])

pAsc12[i]<- sensKK*AscKKD12_T[i]*KK12[i] + (1-specKK)*(1- AscKKD12_T[i])*KK12[i] + sensD*AscKKD12_T[i]*(1-KK12[i]) + (1- specD)*(1-AscKKD12_T[i])*(1-KK12[i])

logit(pAscT60[i])<-alpha4 + b4.tasa*Bano_tasa[i] + b4.desp*f_desp[i]

logit(pAscT48[i])<-alpha5 + b5.jard*f_yrsjardin[i] + b5.desp*fo_desp_SI[i]

logit(pAscT36[i])<-alpha6 + b6.mated*Mated_sec[i] + b6.gas*Cocinar_gas[i] + b6.cred*CRED_12[i] +

b6.desp*t_desp_SI[i]

logit(pAscT24[i])<-alpha7 + b7.tasa*Bano_tasa[i]

AscKKD12_T[i]~dbern(pAscT12[i])

logit(pAscT12[i])<-alpha8 + b8.gas*Cocinar_gas[i]

}

for (i in 1:781) {

NumAsc_T[i] <- AscKKD12_T[i] + Ascprev24_T[i] + Ascprev36_T[i] + Ascprev48_T[i] + Ascprev60_T[i]

dNumAsc2T[i] <- equals(NumAsc_T[i], 2) dNumAsc3T[i] <- equals(NumAsc_T[i], 3) dNumAsc4T[i] <- step(NumAsc_T[i] - 4) }

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9 nde2<- b1.asc2

nie2<- (b1.hb * b2.asc2) + (b1.haz * b9.asc2)

te2<- b1.asc2 + ((b1.hb * b2.asc2) + (b1.haz * b9.asc2))

nde3<- b1.asc3

te3<- b1.asc3 + ((b1.hb * b2.asc3) + (b1.haz * b9.asc3))

nde4<- b1.asc4

te4<- b1.asc4 + ((b1.hb * b2.asc4) + (b1.haz * b9.asc4)) }