Multiple imputation using auxiliary imputation variables that only predict missingness can increase bias due to data missing not at random.

BACKGROUND: Epidemiological and clinical studies often have missing data, frequently analysed using multiple imputation (MI). In general, MI estimates will be biased if data are missing not at random (MNAR). Bias due to data MNAR can be reduced by including other variables ("auxiliary variables") in imputation models, in addition to those required for the substantive analysis. Common advice is to take an inclusive approach to auxiliary variable selection (i.e. include all variables thought to be predictive of missingness and/or the missing values). There are no clear guidelines about the impact of this strategy when data may be MNAR. METHODS: We explore the impact of including an auxiliary variable predictive of missingness but, in truth, unrelated to the partially observed variable, when data are MNAR. We quantify, algebraically and by simulation, the magnitude of the additional bias of the MI estimator for the exposure coefficient (fitting either a linear or logistic regression model), when the (continuous or binary) partially observed variable is either the analysis outcome or the exposure. Here, "additional bias" refers to the difference in magnitude of the MI estimator when the imputation model includes (i) the auxiliary variable and the other analysis model variables; (ii) just the other analysis model variables, noting that both will be biased due to data MNAR. We illustrate the extent of this additional bias by re-analysing data from a birth cohort study. RESULTS: The additional bias can be relatively large when the outcome is partially observed and missingness is caused by the outcome itself, and even larger if missingness is caused by both the outcome and the exposure (when either the outcome or exposure is partially observed). CONCLUSIONS: When using MI, the naïve and commonly used strategy of including all available auxiliary variables should be avoided. We recommend including the variables most predictive of the partially observed variable as auxiliary variables, where these can be identified through consideration of the plausible casual diagrams and missingness mechanisms, as well as data exploration (noting that associations with the partially observed variable in the complete records may be distorted due to selection bias).

Age-specific effects of weight-based body size on fracture risk in later life: a lifecourse Mendelian randomisation study.

Musculoskeletal conditions, including fractures, can have severe and long-lasting consequences. Higher body mass index in adulthood is widely acknowledged to be protective for most fracture sites. However, sources of bias induced by confounding factors may have distorted previous findings. Employing a lifecourse Mendelian randomisation (MR) approach by using genetic instruments to separate effects at different life stages, this investigation aims to explore how prepubertal and adult body size independently influence fracture risk in later life.Using data from a large prospective cohort, univariable and multivariable MR were conducted to simultaneously estimate the effects of age-specific genetic proxies for body size (n = 453,169) on fracture risk (n = 416,795). A two-step MR framework was additionally applied to elucidate potential mediators. Univariable and multivariable MR indicated strong evidence that higher body size in childhood reduced fracture risk (OR, 95% CI: 0.89, 0.82 to 0.96, P = 0.005 and 0.76, 0.69 to 0.85, P = 1 × 10- 6, respectively). Conversely, higher body size in adulthood increased fracture risk (OR, 95% CI: 1.08, 1.01 to 1.16, P = 0.023 and 1.26, 1.14 to 1.38, P = 2 × 10- 6, respectively). Two-step MR analyses suggested that the effect of higher body size in childhood on reduced fracture risk was mediated by its influence on higher estimated bone mineral density (eBMD) in adulthood.This investigation provides novel evidence that higher body size in childhood reduces fracture risk in later life through its influence on increased eBMD. From a public health perspective, this relationship is complex since obesity in adulthood remains a major risk factor for co-morbidities. Results additionally indicate that higher body size in adulthood is a risk factor for fractures. Protective effect estimates previously observed are likely attributed to childhood effects.

Parental depressive symptoms across the first three years of a child's life and emotional and behavioural problem trajectories in children and adolescents.

BACKGROUND: The risk associated with parental perinatal depressive symptoms and the continuum of emotional and behavioural problems in offspring is unclear. This study aimed to investigate the association between maternal and paternal perinatal depressive symptoms and behavioural problem trajectories in offspring aged 3-16 years. METHODS: We used data from the Avon Longitudinal Study of Parents and Children (ALSPAC) in Bristol, Avon, United Kingdom (UK). Parental perinatal depressive symptoms in the first three years of a child's life were measured using the Edinburgh Postnatal Depression Scale (EPDS). Offspring emotional- and behavioural problems were measured using the Strengths and Difficulties Questionnaire (SDQ) when the child was 3.5, 7, 9, 11, and 16 years. A group-based trajectory modelling was used to identify the distinct trajectories of emotional and behavioural problems. Multinomial logistic regression analyses were used to examine associations, and z-scores were calculated to compare maternal and paternal associations. RESULTS: We identified three trajectories of emotional and behavioural problems in offspring between the ages of 3.5 and 16: low, moderate and high symptom trajectories. We found that maternal and paternal antenatal and postnatal depressive symptoms were associated with high levels of emotional and behavioural problem trajectories in offspring. We also found that children exposed to maternal (adjusted RR = 8.11; 95% CI: 5.26-12.48) and paternal (adjusted RR = 2.32; 1.05-5.14) persistent depressive symptoms were more likely to be in high levels of total behavioural problem trajectory group than in the normal trajectory group. The maternal-effect was stronger (p < 0.001). CONCLUSION: Our findings suggest that exposure to parental depressive symptoms were associated with high levels of emotional and behavioural problem trajectories in offspring, with the maternal effect being stronger than the paternal effect.

Multiple imputation of missing data under missing at random: including a collider as an auxiliary variable in the imputation model can induce bias.

Epidemiological studies often have missing data, which are commonly handled by multiple imputation (MI). In MI, in addition to those required for the substantive analysis, imputation models often include other variables ("auxiliary variables"). Auxiliary variables that predict the partially observed variables can reduce the standard error (SE) of the MI estimator and, if they also predict the probability that data are missing, reduce bias due to data being missing not at random. However, guidance for choosing auxiliary variables is lacking. We examine the consequences of a poorly chosen auxiliary variable: if it shares a common cause with the partially observed variable and the probability that it is missing (i.e., it is a "collider"), its inclusion can induce bias in the MI estimator and may increase the SE. We quantify, both algebraically and by simulation, the magnitude of bias and SE when either the exposure or outcome is incomplete. When the substantive analysis outcome is partially observed, the bias can be substantial, relative to the magnitude of the exposure coefficient. In settings in which a complete records analysis is valid, the bias is smaller when the exposure is partially observed. However, bias can be larger if the outcome also causes missingness in the exposure. When using MI, it is important to examine, through a combination of data exploration and considering plausible casual diagrams and missingness mechanisms, whether potential auxiliary variables are colliders.

Multiple imputation of missing data under missing at random: compatible imputation models are not sufficient to avoid bias if they are mis-specified.

OBJECTIVES: Epidemiological studies often have missing data, which are commonly handled by multiple imputation (MI). Standard (default) MI procedures use simple linear covariate functions in the imputation model. We examine the bias that may be caused by acceptance of this default option and evaluate methods to identify problematic imputation models, providing practical guidance for researchers. STUDY DESIGN AND SETTING: Using simulation and real data analysis, we investigated how imputation model mis-specification affected MI performance, comparing results with complete records analysis (CRA). We considered scenarios in which imputation model mis-specification occurred because (i) the analysis model was mis-specified or (ii) the relationship between exposure and confounder was mis-specified. RESULTS: Mis-specification of the relationship between outcome and exposure, or between exposure and confounder, can cause biased CRA and MI estimates (in addition to any bias in the full-data estimate due to analysis model mis-specification). MI by predictive mean matching can mitigate model mis-specification. Methods for examining model mis-specification were effective in identifying mis-specified relationships. CONCLUSION: When using MI methods that assume data are MAR, compatibility between the analysis and imputation models is necessary, but not sufficient to avoid bias. We propose a step-by-step procedure for identifying and correcting mis-specification of imputation models.

Association of Maternal Depressive Symptoms During the Perinatal Period With Oppositional Defiant Disorder in Children and Adolescents.

Importance: An association between perinatal maternal depression and risk of oppositional defiant disorder (ODD) in offspring has not been established. Identifying early determinants of ODD can help inform preventative intervention efforts. Objective: To investigate the association between maternal perinatal depressive symptoms and the risk of ODD in offspring aged 7 to 15 years. Design, Setting, and Participants: This population-based longitudinal birth cohort study used data from the Avon Longitudinal Study of Parents and Children (ALSPAC), in Bristol, UK. All pregnant women residents in Avon, UK, with expected delivery dates from April 1, 1991, to December 31, 1992, were invited to participate in the study. The study cohort ranged from approximately 8000 (at 7 years of age) to 4000 (at 15 years of age) mother-offspring pairs. Data were analyzed from November 2020 to July 2021. Main Outcomes and Measures: Maternal depressive symptoms were measured using the Edinburgh Postnatal Depression Scale (EPDS) antenatally at 18 and 32 weeks of gestation and postnatally at 8 weeks and 8 months. This study primarily used a cutoff score of 12 or more on the EPDS to identify mothers with symptoms of depression, and the continuous EPDS scores were used to confirm the results of the main analyses. Offspring ODD at 7, 10, 13, and 15 years of age were diagnosed using the parent-reported Development and Well-Being Assessment. Results: Of 7994 mother-offspring pairs for whom data were available on offspring ODD at 7 years, 4102 offspring (51.3%) were boys. The mean (SD) age of mothers was 28.6 (4.6) years. Maternal antenatal depressive symptoms (measured at 32 weeks of gestation) were associated with offspring ODD (adjusted odds ratio [AOR], 1.75; 95% CI, 1.33-2.31). Offspring of mothers with postpartum depressive symptoms at 8 weeks and 8 months were more than 2 times more likely to have a diagnosis of ODD over time (AOR at 8 weeks, 2.24 [95% CI, 1.74-2.90]; AOR at 8 months, 2.04 [95% CI, 1.55-2.68]), and maternal persistent depressive symptoms were associated with a 4-fold increased risk of offspring ODD (AOR, 3.59; 95% CI, 1.98-6.52). Conclusions and Relevance: These findings suggest that perinatal depressive symptoms are associated with ODD in offspring and further support the need for early identification and management of prenatal and postnatal depression in women of childbearing age.

State anxiety and alcohol choice: Evidence from experimental and online observational studies.

BACKGROUND: Experimental studies have investigated the effects of physical, psychological and pharmacological stressors (that induce state anxiety) on alcohol outcomes. However, no study has investigated the effects of state anxiety on alcohol outcomes, and the moderating role of drinking to cope (DTC) motives, using the 7.5% carbon dioxide (CO2) challenge. AIMS: We aimed to investigate the relationships between state anxiety and alcohol-related outcomes (primarily alcohol choice). We also explored whether DTC motives moderated these relationships. METHODS: We conducted two experiments using the 7.5% CO2 challenge (Studies 1 and 2) and an observational study (Study 3) (ns = 42, 60 and 219, respectively), to triangulate findings. RESULTS: In Study 1, experimentally induced state anxiety increased alcohol choice (p < .001, ηp2 = .29). This finding was replicated in Study 2, but the effect was weaker (p = .076, ηp2 = .06). Furthermore, DTC moderated the effect (p = .013, ηp2= .11). However, in Study 3 there was no clear evidence of an association between naturally occurring state anxiety and alcohol choice (b = 0.05, p = .655), or a moderating role of DTC (b = 0.01, p = .852). CONCLUSIONS: Experimentally induced, but not naturally occurring, state anxiety increases alcohol choice, although state anxiety levels were lower in the non-manipulated sample.

The effect of foraging parameters on the probability that a dive is successful.

In this paper, we investigate the foraging decisions of an animal that dives to obtain its food. It might seem reasonable to use the probability that the diver is successful in any dive as an indicator of habitat quality. We use a dynamic model of optimal prey choice to show that this interpretation of diving success is not generally valid. In particular, we show that diving success is not directly proportional to the overall rate of gain that can be achieved in an environment. Furthermore, some environmental factors can have a non-monotonic effect on the probability of success. For example, as the travel time to the foraging area increases, the probability of success may first increase and then decrease. We point out that the same conclusions are likely to apply in the context of mate choice, i.e. the probability of getting a mate may not be an indicator of the quality of the environment in terms of reproductive success.

Maternal smoking during pregnancy and offspring smoking initiation: assessing the role of intrauterine exposure.

AIMS: To assess whether associations between maternal smoking during pregnancy and offspring smoking initiation are due to intrauterine mechanisms. DESIGN: Comparison of associations of maternal and partner smoking behaviour during pregnancy with offspring smoking initiation using partner smoking as a negative control (n = 6484) and a Mendelian randomization analysis (n = 1020), using a genetic variant in the mothers as a proxy for smoking cessation during pregnancy. SETTING: A longitudinal birth cohort in South West England. PARTICIPANTS: Participants of the Avon Longitudinal Study of Parents and Children (ALSPAC). MEASUREMENTS: Smoking status during pregnancy was self-reported by mother and partner in questionnaires administered at pregnancy. Latent classes of offspring smoking initiation (non-smokers, experimenters, late-onset regular smokers and early-onset regular smokers) were previously developed from questionnaires administered at 14-16 years. A genetic variant, rs1051730, was genotyped in the mothers. FINDINGS: Both mother and partner smoking were similarly positively associated with offspring smoking initiation classes, even after adjustment for confounders. Odds ratios (OR) [95% confidence interval (CI)] for class membership compared with non-smokers were: experimenters: mother OR = 1.33 (95% CI = 1.06, 1.67), partner OR = 1.28 (95% CI = 1.06, 1.55), late-onset regular smokers: mother OR = 1.80 (95% CI = 1.43, 2.26), partner OR = 1.86 (95% CI = 1.52, 2.28) and early-onset regular smokers: mother OR = 2.89 (95% CI = 2.12, 3.94), partner OR = 2.50 (95% CI = 1.85, 3.37). There was no clear evidence for a dose-response effect of either mother or partner smoking heaviness on class membership. Maternal rs1051730 genotype was not clearly associated with offspring smoking initiation class in pre-pregnancy smokers (P = 0.35). CONCLUSION: The association between smoking during pregnancy and offspring smoking initiation does not appear to operate through intrauterine mechanisms.