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1.  Calculating statistical power in Mendelian randomization studies 
In Mendelian randomization (MR) studies, where genetic variants are used as proxy measures for an exposure trait of interest, obtaining adequate statistical power is frequently a concern due to the small amount of variation in a phenotypic trait that is typically explained by genetic variants. A range of power estimates based on simulations and specific parameters for two-stage least squares (2SLS) MR analyses based on continuous variables has previously been published. However there are presently no specific equations or software tools one can implement for calculating power of a given MR study. Using asymptotic theory, we show that in the case of continuous variables and a single instrument, for example a single-nucleotide polymorphism (SNP) or multiple SNP predictor, statistical power for a fixed sample size is a function of two parameters: the proportion of variation in the exposure variable explained by the genetic predictor and the true causal association between the exposure and outcome variable. We demonstrate that power for 2SLS MR can be derived using the non-centrality parameter (NCP) of the statistical test that is employed to test whether the 2SLS regression coefficient is zero. We show that the previously published power estimates from simulations can be represented theoretically using this NCP-based approach, with similar estimates observed when the simulation-based estimates are compared with our NCP-based approach. General equations for calculating statistical power for 2SLS MR using the NCP are provided in this note, and we implement the calculations in a web-based application.
PMCID: PMC3807619  PMID: 24159078
Power; Mendelian randomization; non-centrality parameter; instrumental variable
2.  Maternal smoking and child psychological problems: Disentangling causal and non-causal effects 
Pediatrics  2010;126(1):e57-e65.
To explore associations of maternal prenatal smoking and child psychological problems and determine the role of causal intrauterine mechanisms.
Patients and Methods
Maternal smoking and child psychological problems were explored in 2 birth cohorts in Pelotas, Brazil (n=509; random sub-sample) and Avon Longitudinal Study of Parents and Children (ALSPAC), Britain (n=6,735). Four approaches for exploring causal mechanisms were applied: 1) cross-population comparisons between a high-income and a middle-income country, 2) multiple adjustment for socioeconomic and parental psychological factors, 3) maternal-paternal comparisons as a test of putative intrauterine effects; and 4) search for specific effects on different behavioural subscales.
Socioeconomic patterning of maternal prenatal smoking was stronger in the ALSPAC compared with the Pelotas cohort. Despite this difference in a key confounder, consistency in observed associations was found between these cohorts. In both cohorts, unadjusted, maternal smoking was associated with greater offspring hyperactivity, conduct/externalizing problems, and peer problems, but not with emotional/internalizing problems. After adjusting for confounders and paternal prenatal smoking, only the association with conduct/externalizing problems persisted in both cohorts (conduct problems in the ALSPAC cohort, odds ratio OR: 1.24 [95% confidence interval (CI): 1.07–1.46], p= .005; externalizing problems in the Pelotas cohort, OR:1.82 [95% CI:1.19–2.78], p=.005; ORs reflect ordinal ORs of maternal smokers having offspring with higher scores). Maternal smoking associations were stronger than paternal smoking associations, although statistical evidence for differences was weak in 1 cohort.
Evidence from 4 approaches suggests a possible intrauterine effect of maternal smoking on offspring conduct/externalizing problems.
PMCID: PMC3605780  PMID: 20587678
ALSPAC; Pelotas; prenatal smoking; child; behavioral problems; developmental origins
3.  Maternal Pre-pregnancy Overweight and Child Cognition and Behavior: Exploring Intrauterine Effects in Two Pregnancy Cohorts 
Pediatrics  2010;127(1):e202-e211.
Maternal greater pre-pregnancy adiposity has been associated with behavioral problems, such as ADHD, and lower intellectual function in offspring. However, few human studies have explored this and it is unclear if intrauterine mechanisms or confounding factors drive these associations.
Patients and Methods
Parental BMI and offspring verbal skills, non-verbal skills and behavioral problems were assessed in the British ALSPAC (N~5000) and Dutch Generation R (N~ 2500) cohorts. We aimed to determine the plausibility of intrauterine effects by (i) adjusting for multiple confounders, (ii) comparing associations between maternal and paternal BMI with offspring cognition/ behaviors, and (iii) searching for cross-cohort consistency.
Maternal pre-pregnancy overweight was associated with reduced child verbal skills (unadjusted). However, after adjusting for confounders, this was not consistently observed in both cohorts. Maternal overweight was also associated with child total behavior problems and externalising problems, even after adjusting for confounders. However, this was observed in Generation R only and was not replicated in ALSPAC. No associations of maternal overweight with child attention problems, emotional/internalising problems, or non-verbal skills were observed in either cohort. Paternal overweight was not associated with any of the child outcomes, but was also less strongly related to potential confounding factors than was maternal overweight.
Overall, we find little consistent evidence of intrauterine effects of maternal pre-pregnancy overweight on child cognition and behavior. Some associations initially observed were not consistently replicated across cohorts or robust to adjustment for confounding factors and are thus likely to reflect confounding by socioeconomic or postnatal factors.
PMCID: PMC3605781  PMID: 21187310
ALSPAC; behavioral problems; cognitive function; cohort; Generation R; intrauterine exposure; obesity; pregnancy
4.  What are the causal effects of breastfeeding on IQ, obesity and blood pressure? Evidence from comparing high-income with middle-income cohorts 
Background A novel approach is explored for improving causal inference in observational studies by comparing cohorts from high-income with low- or middle-income countries (LMIC), where confounding structures differ. This is applied to assessing causal effects of breastfeeding on child blood pressure (BP), body mass index (BMI) and intelligence quotient (IQ).
Methods Standardized approaches for assessing the confounding structure of breastfeeding by socio-economic position were applied to the British Avon Longitudinal Study of Parents and Children (ALSPAC) (N ≃ 5000) and Brazilian Pelotas 1993 cohorts (N ≃ 1000). This was used to improve causal inference regarding associations of breastfeeding with child BP, BMI and IQ. Analyses were extended to include results from a meta-analysis of five LMICs (N ≃ 10 000) and compared with a randomized trial of breastfeeding promotion.
Findings Although higher socio-economic position was strongly associated with breastfeeding in ALSPAC, there was little such patterning in Pelotas. In ALSPAC, breastfeeding was associated with lower BP, lower BMI and higher IQ, adjusted for confounders, but in the directions expected if due to socioeconomic patterning. In contrast, in Pelotas, breastfeeding was not strongly associated with BP or BMI but was associated with higher IQ. Differences in associations observed between ALSPAC and the LMIC meta-analysis were in line with those observed between ALSPAC and Pelotas, but with robust evidence of heterogeneity detected between ALSPAC and the LMIC meta-analysis associations. Trial data supported the conclusions inferred by the cross-cohort comparisons, which provided evidence for causal effects on IQ but not for BP or BMI.
Conclusion While reported associations of breastfeeding with child BP and BMI are likely to reflect residual confounding, breastfeeding may have causal effects on IQ. Comparing associations between populations with differing confounding structures can be used to improve causal inference in observational studies.
PMCID: PMC3147072  PMID: 21349903
ALSPAC; breastfeeding; causation; cognition; cohort; Pelotas
5.  Maternal macronutrient and energy intakes in pregnancy and offspring intake at 10 y: exploring parental comparisons and prenatal effects1234 
Background: High maternal dietary intakes in pregnancy may lead to increased fetal growth and program neuroendocrine pathways that result in greater appetite, energy intake, and adiposity in offspring later in life. Few prospective dietary studies have explored this relation.
Objective: The objective was to assess associations of maternal dietary intake in pregnancy and maternal and paternal dietary intake postnatally with child dietary intake and adiposity.
Design: Dietary intakes of energy, protein, total fat, and carbohydrate were assessed prospectively in mothers during pregnancy, in mothers and their partners at 47 mo postnatally, and in children at 10 y (n = 5717 mother-child pairs prenatally, 5593 mother-child pairs postnatally, and 3009 father-child pairs). Child body composition was assessed at 9 and 11 y (n = 5725).
Results: Maternal dietary intakes of protein, fat (when adjusted for energy intake), and carbohydrate in pregnancy were positively associated with child dietary intakes of the same nutrients, and these associations were greater than those observed for paternal dietary intake, which was not strongly associated with offspring diet. Associations of maternal prenatal-offspring intakes were stronger than those of maternal postnatal-offspring intakes for protein and fat. Greater child energy and macronutrient intakes were only associated with greater adiposity in children when adjusted for potential energy underreporting. Maternal diet during pregnancy was not associated with offspring adiposity or lean mass.
Conclusion: The stronger prenatal maternal associations with child dietary intake, particularly protein and fat, compared with both paternal intake associations and maternal postnatal intake associations provide some evidence for in utero programming of offspring appetite by maternal intake during pregnancy.
PMCID: PMC2822901  PMID: 20053880
6.  Mining the Human Phenome Using Allelic Scores That Index Biological Intermediates 
PLoS Genetics  2013;9(10):e1003919.
It is common practice in genome-wide association studies (GWAS) to focus on the relationship between disease risk and genetic variants one marker at a time. When relevant genes are identified it is often possible to implicate biological intermediates and pathways likely to be involved in disease aetiology. However, single genetic variants typically explain small amounts of disease risk. Our idea is to construct allelic scores that explain greater proportions of the variance in biological intermediates, and subsequently use these scores to data mine GWAS. To investigate the approach's properties, we indexed three biological intermediates where the results of large GWAS meta-analyses were available: body mass index, C-reactive protein and low density lipoprotein levels. We generated allelic scores in the Avon Longitudinal Study of Parents and Children, and in publicly available data from the first Wellcome Trust Case Control Consortium. We compared the explanatory ability of allelic scores in terms of their capacity to proxy for the intermediate of interest, and the extent to which they associated with disease. We found that allelic scores derived from known variants and allelic scores derived from hundreds of thousands of genetic markers explained significant portions of the variance in biological intermediates of interest, and many of these scores showed expected correlations with disease. Genome-wide allelic scores however tended to lack specificity suggesting that they should be used with caution and perhaps only to proxy biological intermediates for which there are no known individual variants. Power calculations confirm the feasibility of extending our strategy to the analysis of tens of thousands of molecular phenotypes in large genome-wide meta-analyses. We conclude that our method represents a simple way in which potentially tens of thousands of molecular phenotypes could be screened for causal relationships with disease without having to expensively measure these variables in individual disease collections.
Author Summary
The standard approach in genome-wide association studies is to analyse the relationship between genetic variants and disease one marker at a time. Significant associations between markers and disease are then used as evidence to implicate biological intermediates and pathways likely to be involved in disease aetiology. However, single genetic variants typically only explain small amounts of disease risk. Our idea is to construct allelic scores that explain greater proportions of the variance in biological intermediates than single markers, and then use these scores to data mine genome-wide association studies. We show how allelic scores derived from known variants as well as allelic scores derived from hundreds of thousands of genetic markers across the genome explain significant portions of the variance in body mass index, levels of C-reactive protein, and LDLc cholesterol, and many of these scores show expected correlations with disease. Power calculations confirm the feasibility of scaling our strategy to the analysis of tens of thousands of molecular phenotypes in large genome-wide meta-analyses. Our method represents a simple way in which tens of thousands of molecular phenotypes could be screened for potential causal relationships with disease.
PMCID: PMC3814299  PMID: 24204319
7.  Genetic variation at the SLC23A1 locus is associated with circulating levels of L-ascorbic acid (Vitamin C). Evidence from 5 independent studies with over 15000 participants 
L-ascorbic acid is an essential part of the human diet and has been associated with a wide-range of chronic complex diseases including cardiovascular outcomes. To date, there are no confirmed genetic correlates of circulating levels of L-ascorbic acid.
We aimed to confirm the existence of association between common variation at the SLC23A1 gene locus and circulating levels of L-ascorbic acid.
We employed a two-stage design which used a discovery cohort (the British Women’s Heart and Health Study) and a series of follow-up cohorts and meta-analysis (totalling 15087 participants) to assess the relationship between variation at SLC23A1 and circulating levels of L-ascorbic acid.
In the discovery cohort, variation at rs33972313 was associated with a reduction in circulating levels of L-ascorbic acid (−4.15μmol/L (95%CI −0.49, −7.81), p=0.03 reduction per minor allele). Pooled analysis of the relationship between rs33972313 and circulating L-ascorbic acid across all studies confirmed this, showing that each additional rare allele was associated with a reduction in circulating levels of L-ascorbic acid of −5.98μmol/L (95%CI −8.23, −3.73), p=2.0×10−7 per minor allele.
Work here has identified a genetic variant (rs33972313) in the SLC23A1 vitamin C active transporter locus that is reliably associated with circulating levels of L-ascorbic acid in the general population. This finding has implications more generally for the epidemiological investigation of relationships between circulating L-ascorbic acid and health outcomes.
PMCID: PMC3605792  PMID: 20519558
Vitamin C; genotype; L-ascorbic acid
8.  Vitamin B-12 Status during Pregnancy and Child’s IQ at Age 8: A Mendelian Randomization Study in the Avon Longitudinal Study of Parents and Children 
PLoS ONE  2012;7(12):e51084.
Vitamin B-12 is essential for the development and maintenance of a healthy nervous system. Brain development occurs primarily in utero and early infancy, but the role of maternal vitamin B-12 status during pregnancy on offspring cognitive function is unclear. In this study we assessed the effect of vitamin B-12 status in well-nourished pregnant women on the cognitive ability of their offspring in a UK birth cohort (ALSPAC). We then examined the association of SNPs in maternal genes FUT2 (rs492602) and TCN2 (rs1801198, rs9606756) that are related to plasma vitamin B-12, with offspring IQ. Observationally, there was a positive association between maternal vitamin B-12 intake and child’s IQ that was markedly attenuated after adjustment for potential confounders (mean difference in offspring IQ score per doubling of maternal B-12 intake, before adjustment: 2.0 (95% CI 1.3, 2.8); after adjustment: 0.7 (95% CI −0.04, 1.4)). Maternal FUT2 was weakly associated with offspring IQ: mean difference in IQ per allele was 0.9 (95% CI 0.1, 1.6). The expected effect of maternal vitamin B-12 on offspring IQ, given the relationships between SNPs and vitamin B-12, and SNPs and IQ was consistent with the observational result. Our findings suggest that maternal vitamin B-12 may not have an important effect on offspring cognitive ability. However, further examination of this issue is warranted.
PMCID: PMC3515553  PMID: 23227234
9.  Association of maternal weight gain in pregnancy with offspring obesity and metabolic and vascular traits in childhood 
Circulation  2010;121(23):2557-2564.
We aimed to examine the association of gestational weight gain (GWG) and pre-pregnancy weight with offspring adiposity and cardiovascular risk factors.
Methods and results
Data from 5,154 (for adiposity and blood pressure) and 3,457 (for blood assays) mother-offspring pairs from a UK prospective pregnancy cohort were used. Random effects multilevel models were used to assess incremental GWG (median and range of repeat weight measures per woman: 10 (1, 17)). Women who exceeded the 2009 Institute of Medicine recommended GWG were more likely to have offspring with greater body mass index, waist, fat mass, leptin, systolic blood pressure, CRP and IL-6 levels, and lower HDLc and Apolipoprotein A1 levels. Children of women who gained less than the recommended amounts had lower levels of adiposity, but other cardiovascular risk factor tended to be similar in this group to offspring of women gaining recommended amounts. When examined in more detail greater pre-pregnancy weight was associated with greater offspring adiposity and more adverse cardiovascular risk factors at age 9. GWG in early pregnancy (0 to 14 weeks) was positively associated with offspring adiposity across the entire distribution, but strengthened in women gaining more than 500g/week. By contrast, between 14 and 36 weeks GWG was only associated with offspring adiposity in women gaining at least 500g/week. GWG between 14-36 weeks was positively and linearly associated with adverse lipid and inflammatory profiles with these associations largely mediated by the associations with offspring adiposity.
Greater maternal pre-pregnancy weight and GWG up to 36 weeks gestation are associated with greater offspring adiposity and adverse cardiovascular risk factors. Before implementing any GWG recommendations, the balance of risks and benefits of attempts to control GWG for short- and long-term outcomes in mother and child should be ascertained.
PMCID: PMC3505019  PMID: 20516377
Pregnancy; Gestational Weight Gain; Offspring cardiovascular risk factors; ALSPAC
10.  Genetic variation in the 15q25 nicotinic acetylcholine receptor gene cluster (CHRNA5–CHRNA3–CHRNB4) interacts with maternal self-reported smoking status during pregnancy to influence birth weight 
Human Molecular Genetics  2012;21(24):5344-5358.
Maternal smoking during pregnancy is associated with low birth weight. Common variation at rs1051730 is robustly associated with smoking quantity and was recently shown to influence smoking cessation during pregnancy, but its influence on birth weight is not clear. We aimed to investigate the association between this variant and birth weight of term, singleton offspring in a well-powered meta-analysis. We stratified 26 241 European origin study participants by smoking status (women who smoked during pregnancy versus women who did not smoke during pregnancy) and, in each stratum, analysed the association between maternal rs1051730 genotype and offspring birth weight. There was evidence of interaction between genotype and smoking (P = 0.007). In women who smoked during pregnancy, each additional smoking-related T-allele was associated with a 20 g [95% confidence interval (95% CI): 4–36 g] lower birth weight (P = 0.014). However, in women who did not smoke during pregnancy, the effect size estimate was 5 g per T-allele (95% CI: −4 to 14 g; P = 0.268). To conclude, smoking status during pregnancy modifies the association between maternal rs1051730 genotype and offspring birth weight. This strengthens the evidence that smoking during pregnancy is causally related to lower offspring birth weight and suggests that population interventions that effectively reduce smoking in pregnant women would result in a reduced prevalence of low birth weight.
PMCID: PMC3516066  PMID: 22956269
11.  Maternal smoking during pregnancy and offspring trajectories of height and adiposity: comparing maternal and paternal associations 
Background Maternal smoking during pregnancy is associated with reduced offspring birth length and has been postulated as a risk factor for obesity. Causality for obesity is not established. Causality is well-supported for birth length, but evidence on persistence of height deficits is inconsistent.
Methods We examined the association between maternal smoking during pregnancy and trajectories of offspring height (0–10 years, N = 9424), ponderal index (PI) (0–2 years, N = 9321) and body mass index (BMI) (2–10 years, N = 8887) in the Avon Longitudinal Study of Parents and Children. To strengthen inference, measured confounders were controlled for, maternal and partner smoking associations were compared, dose–response and associations with post-natal smoking were examined.
Results Maternal smoking during pregnancy was associated with shorter birth length, faster height growth in infancy and slower growth in later childhood. By 10 years, daughters of women who smoke during pregnancy are on average 1.11 cm (SE = 0.27) shorter after adjustment for confounders and partner smoking; the difference is 0.22 cm (SE = 0.22) for partner's smoking. Maternal smoking was associated with lower PI at birth, faster PI increase in infancy, but not with BMI changes 2–10 years. Associations were stronger for maternal than partner smoking for PI at birth and PI changes in infancy, but not for BMI changes after 2 years. A similar dose–response in both maternal and partner smoking was seen for BMI change 2–10 years.
Conclusion Maternal smoking during pregnancy has an intrauterine effect on birth length, and possibly on adiposity at birth and changes in height and adiposity in infancy. We do not find evidence of a specific intrauterine effect on height or adiposity changes after the age of 2 years.
PMCID: PMC3396309  PMID: 22407859
Smoking; growth; obesity; pregnancy; child; ALSPAC
12.  Maternal smoking during pregnancy and offspring growth in childhood: 1993 and 2004 Pelotas cohort studies 
Archives of Disease in Childhood  2011;96(6):519-525.
To explore the effects of maternal smoking during pregnancy on offspring growth using three approaches: (1) multiple adjustments for socioeconomic and parental factors, (2) maternal–paternal comparisons as a test of putative intrauterine effects and (3) comparisons between two birth cohort studies.
Population-based birth cohort studies were carried out in Pelotas, Brazil, in 1993 and 2004. Cohort members were followed up at 3, 12, 24 and 48 months. Multiple linear regression analysis was used to examine the relationships between maternal and paternal prenatal smoking and offspring anthropometric indices. In the 2004 cohort, the association of smoking with trunk length, leg length and leg-to-sitting-height ratio at 48 months was also explored.
Maternal smoking during pregnancy was associated with reduced z scores of length/height-for-age at each follow-up in both cohorts and reduced leg length at 48 months in the 2004 cohort. Children older than 3 months born to smoking women showed a higher body mass index-for-age z score than children of non-smoking women.
The results of this study strongly support the hypothesis that maternal smoking during pregnancy impairs linear growth and promotes overweight in childhood.
PMCID: PMC3093240  PMID: 21377989

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