Long-term Exposure to Neighborhood Deprivation and Intimate Partner Violence Among Women: A UK Birth Cohort Study

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Association (analysis)
Benson et al. 1 USA is United States of America. B is unstandardised regression coefficient. SE is standard error. OR is odds ratio. CI is confidence interval. SES is socioeconomic status. RR is risk ratio. GEE is generalised estimating equation. Studies were identified through a systematic review of longitudinal studies of all risk and protective factors for IPV victimisation among adult women (search completed June 2016), 6 automated alerts on relevant literature via GoogleScholar (since June 2016), and additional focused searches (March 2019). Prospective-longitudinal studies were defined as studies with at least two time-points of data where exposure was measured prior to outcome or an analysis of change was conducted -note: this included studies that only had one time point of exposure data and one time point of outcome data, as was the case for most of the above studies. Studies were only included if majority of women were at least 18 years old at time of outcome assessment. a A series of studies were conducted using data from the same cohort but either using one time point of cross-sectional neighbourhood exposure and IPV outcome data 7-9 or using two time points of data but analysing any IPV at both time points as the outcome. 10 As the study by Benson et al. provided the strongest longitudinal design, only this study is summarised above. The association between concentrated disadvantage and IPV against women was positive in all of these studies. b Studies included in previous meta-analysis of the longitudinal association between neighbourhood disadvantage and IPV against women. 6 c Identified in updated searches (published in 2018). d Unclear if adjusted covariate was measured contemporaneously/after exposure (as opposed to prior). eFigure 1: Simplified directed acyclic graph (DAG) for the effect of exposure to neighbourhood disadvantage on IPV against women over time. This DAG was drawn based on the most up-to-date synthesis of the longitudinal IPV literature 6 and, where gaps exist in this literature, hypotheses based on available cross-sectional evidence 11 and prior longitudinal studies of neighbourhood deprivation. [12][13][14] For simplicity, concurrent paths between confounders are not shown. Likewise, only variables that are hypothesised to confound the relationship between exposure to neighbourhood deprivation and IPV are included. We used DAGitty to create the figure. 15

Marginal structural models estimated by inverse probability weighting
The current study sought to estimate the effect of exposure to neighbourhood deprivation from birth until age 18 on the risk of experiencing intimate partner violence (IPV) in early adulthood (ages [18][19][20][21]. However, as depicted in the directed acyclic graph above (eFigure 1), socioeconomic and psychosocial characteristics of the family environment affect the neighbourhoods that families live in and are in turn affected by neighbourhood environments; these family characteristics may additionally affect the risk of experiencing IPV in early adulthood. 6,11,14 This is a classic case of time-varying confounding affected by past exposure, the simplest example of which is depicted below, where A is the exposure variable measured at T0 and T1, L is a vector of time-varying covariates at T0 and T1 and Y is the final study outcome: Formally, time-varying or time-dependent confounding affected by past exposure occurs when a timevarying exposure is both affected by the level of prior time-varying covariates and affects future values of those time-varying covariates -all of which then cause the outcome of interest. 16 The result is that, when estimating the effect of exposure on the outcome, controlling for the values of time-varying covariates using conventional regression methods would lead to 'over-adjustment' (partialling out part of the effect of the exposure on the outcome) and potentially induce collider-stratification bias, yet not controlling for these covariates would result in bias due to confounding. 17,18 Marginal structural models allow for the estimation of a causal effect of a time-varying exposure in the presence of both time-varying confounders and mediators using observational data (under the assumptions of exchangeability, consistency, positivity, and correct model specification -as described in the main text). 18 Of note, these assumptions are the same as those required by conventional regression methods when estimating causal associations. In fact, the latter require the additional assumption that measured time-varying covariates are not affected by prior exposure -which is not required of marginal structural models. 14 The model is referred to as marginal because it estimates the average effect of exposure based on the marginal distribution of the counterfactual variables or potential outcomes (e.g., if the entire sample was exposed versus unexposed at time t) and structural because the estimate is of a causal effect. 19 Marginal structural models can be estimated using inverse probability weighting. This essentially involves a two-step process, where (1) each participant's cumulative probability of experiencing the exposure history she actually experienced conditional on her covariate history and (2) running a crude analysis (i.e., without time-varying covariates) in a sample where each participant is weighted by the inverse of this probability. This means that participants whose exposure histories are more common given their covariate histories will be proportionally under-weighted in the analytic sample whereas participants whose exposure histories are less common given their covariate histories will be proportionally overweighted. Intuitively, this creates a pseudo-population, where the probability of exposure is made comparable across levels of the confounders at each time point as though exposure had occurred at random (assuming no unmeasured confounders). As a result, marginal structural models estimated by inverse probability weighting can account for nonrandom selection of participants into neighbourhoods (e.g., due to socioeconomic variables) that may otherwise confound effect estimates but do not partial out the indirect effects of neighbourhood exposures via these variables at later time points. 14 They also are easy to interpret for researchers used to more conventional methods (e.g., generalized linear regression) as they are simply an extension of these models to weighted samples. 19 Of further benefit for use with cohort data, inverse probability weights can also be constructed for censoring or attrition, whereby, in addition to the exposure weights, participants in the analytic sample are also weighted by the inverse probability of remaining in the sample given their prior covariate and exposure histories -thus accounting for nonrandom attrition conditional on observed covariates. See 'Computing the stabilised inverse probability weights and estimating marginal structural models' (eAppendix 2) for further details on the use of marginal structural models estimated by inverse probability weighting in practice and application in the current study.

Indices of Multiple Deprivation
As described in the main manuscript, the Indices of Multiple Deprivation are an official measure of arealevel deprivation in England, which considers deprivation beyond economic poverty alone, using indicators across seven domains: income, employment, education, health, crime, housing, and living environment. 20-22 eTable 2 describes the indicators used to construct each domain of deprivation and the domain's weight in the final index. Based on these indicators, each lower-layer super output area (~1500 residents or 650 households designed to approximate residential neighbourhoods) is assigned a domainspecific and total deprivation rank score relative to all other neighbourhoods. A neighbourhood is thus defined as more or less deprived based on the extent of inequality in its living conditions compared to other neighbourhoods in England (i.e., relative deprivation) as opposed to whether it falls above or below an objective standard of conditions (i.e., absolute deprivation). The Indices of Multiple Deprivation is constructed using an exponential transformation of neighbourhoods' rank scores; this standardises the scores for different indicators, allowing them to be combined, and makes the most deprived neighbourhoods easier to identify: the 10% most deprived neighbourhoods make up 50% of the score distribution (i.e., have a transformed-rank score between 50-100). See Figure

Time-invariant covariates
All covariates were measured by mother-report, with time-invariant covariates measured at baseline, unless otherwise noted. Parental education was coded as 1=at least the mother or her partner had higher than O-level (A-level or degree), 0=otherwise. Maternal marital status was coded as 1=married, 0=otherwise (including widowed, divorced, separated, or never married). Parental social class was coded using the standard occupational classification 2000, where 1=at least mother or partner were part of lower social class (partly or unskilled occupations), 0=otherwise (professional, managerial, or skilled occupations). Mothers reported on their own, their partners', and their parents' race/ethnicities at baseline and on the young person's race/ethnicity when the child was age 11.5. To use all available data, participants coded as 'non-white' at age 11.5 were coded as 'non-white' on the final ethnicity variable and, in addition, those who were missing at the age 11.5 assessment but whose mothers, fathers, grandmothers, or grandfathers were reported as 'non-white' were also coded as such. Race/ethnicity was dichotomised as 1=non-white, 0=white because of the lower proportion of non-white race/ethnicities (e.g., Asian, Black) in the sample. We also used the mother's number of children at baseline as a time-invariant covariate.

Time-varying covariates
Maternal depressive symptoms were measured using the Edinburgh Post-Natal Depression Scale, a 10item scale which asks about positive and negative behaviours/emotions in the last seven days (e.g., 'I have been anxious or worried for no good reason'). 24 Response categories were 0 'Never' to 3 'Often'. Items were all coded in the negative direction and summed so that higher scores indicate more depressive symptoms (a=.85). Residential mobility was measured based on mothers' reports of whether they had moved house between questionnaire assessments. Maternal social support was measured using a Social Network Index developed for ALSPAC, where mothers reported on 10 social situations (e.g., 'How many of your relatives or your partner's relatives do you see at least twice a year?'). Response categories were 0 'None' to 3 'More than 4' and items were summed so that higher scores indicated a stronger social network (a=.79). Parental employment was typically indicated by mother-report of whether her partner was currently employed, except at baseline, when mothers reported on whether they themselves were currently employed. Family structure was coded as 1=both biological parents live with child, 0=only one or neither biological parent lives with child. Mothers reported on their difficulty in affording each of five items -food, clothing, heating, accommodation, or items for their child(ren) -on a 4-point scale from 0=not difficult to 3=very difficult. Responses were summed to create a composite for financial difficulties. Mothers reported on the take-home family income as a weekly average, apart from when children were age 18 when the monthly average was reported. Response categories varied over time, as expected with inflation, from baseline (weekly average, 1=<£100 to 5=>£400) to age 18 (monthly average, 1=<£899 to 10=>£4000).

Computing the stabilised inverse probability weights and estimating marginal structural models
Constructing inverse probability weights involves estimating a denominator that is the product of the probabilities that each participant received the exposure she actually did at time t conditional on prior exposure up until time t-1, time-varying covariates up until time t or time t-1 (depending on the study), and baseline covariates (including time-invariant covariates). 16,18,25,26 In practice, inverse probability weights tend to be very variable; thus stabilised weights are typically used for more efficient effect estimates. 16,18 Stabilised weights involve estimating a numerator as well, which is typically a function of prior exposure and baseline covariates (i.e., excluding time-varying covariate history beyond baseline). The analysis in the weighted sample (i.e., marginal structural model) is then conducted conditioning on the baseline covariates.
In the current study, to compute the denominator of the stabilised weights, we regressed the level of neighbourhood deprivation at time k (A k ) onto the level of previous exposure (A k-1 ) and time-varying covariates (L k-1 ) at time k-1 and baseline covariates (X and L 0 ) using a pooled binary logistic regression in a long-form dataset (i.e., with participant-observations as the unit of analysis). 18,26 The only exception was for the weights constructed for T 9 , which used time-varying covariates measured at T 9 because none were measured at T 8 . We then estimated the predicted probabilities of exposure from the corresponding regression and derived participants' probabilities of their observed exposure status. The denominator for the final exposure weight at each time t is then the product of probabilities up until time t (i.e., the estimated probability of participants' observed exposure histories up until time t conditional on prior exposure and covariate history up until time t-1). In a wide-form dataset, where the unit of analysis is participants, this final weight would equate to the product of probabilities over all time points. We computed the numerator in the same way as the denominator but excluding the time-varying covariates beyond baseline (L k-1 ) from the regression. The final form for the stabilised weights for the ith participant was thus: We estimated censoring (i.e., permanent attrition) weights (and where relevant weights for intermittent missingness) in the same way as the exposure weights, but instead predicting the probability of being censored (or missing). The final weights were the product of the stabilised exposure and censoring weights (and, where relevant, intermittent missingness weights).
As in any longitudinal analysis of an exposure-outcome association, estimating marginal structural models further requires defining the exposure trajectories (and potential outcomes) of interest. In simple settings (e.g., two time points of binary exposure), marginal structural models can be estimated nonparametrically, where the expected outcomes are compared for each possible exposure trajectory (e.g., E(Y 0,0 ), E(Y 0,1 ), E(Y 1,0 ), and E(Y 1,1 )). 16,18 However, in more complex settings, for instance due to many more time points, parametric models are required. In the current study, with 10 time points of binary exposure data, there were 2 10 or 1,024 potential exposure trajectories. We thus estimated parametric marginal structural models. Based on prior marginal structural model studies of neighbourhood disadvantage, we used a cumulative or duration-weighted exposure, defined as the average exposure over the study period ( 7 ( 8 (61 /10). 12,14 As noted by these studies and the broader neighbourhood effects literature, this specification is of theoretical interest because it allows for estimation of the effects of sustained exposure to neighbourhood deprivation: for instance, in the current study, differences in IPV risk between women who spent more of their childhood in the most deprived neighbourhoods in England versus the least.
We estimated two primary marginal structural models in our weighted sample. One was a negative binomial regression, where the discrete IPV frequency score (Y) was modelled as a function of durationweighted exposure to more severe neighbourhood deprivation ()) and (time-invariant and time-varying) covariates measured at baseline (X and L 0 ): The second was a log-binomial model, where the risk of experiencing any IPV (Y) was modelled as a function of duration-weighted exposure to more severe neighbourhood deprivation ()) and timeinvariant/baseline factors (X and L 0 ): Typically, when the outcome is an end-of-study outcome as opposed to repeated measures, researchers will conduct their marginal structural models in a wide-form dataset, where each participant is weighted by the product of the time-specific weights. 13,14,16,27,28 This is analogous to the practice used in repeatedmeasures marginal structural models, where researchers weight each participant-observation at time k by the product of the time-specific weights up until time k. 12,19,26,28 However, in a wide-form dataset, this means that participants without complete data at all time points are listwise deleted. In the current study, this would have resulted in an analytic sample of n<200 participants. Therefore, to make the most of the available data, we conducted our analyses at the time-point level (i.e., in a long-form dataset), where each participant-observation was weighted by the appropriate time-varying weight (i.e., the cumulative probability of observed exposure and censoring history until time t) with cluster-robust (conservative) standard errors. This allowed us to include participants who did not have complete exposure and covariate data at all time points, but did have at least 50% exposure data, IPV data, and time points with complete covariate data (see eFigure 2 for further details). Participant observations are resultantly included in the analysis up until the time point with missing data (i.e., when the time-specific weight is missing). We explore alternative strategies in our sensitivity analyses. eFigures 4-6 demonstrate the longitudinal variation in exposure to neighbourhood-level deprivation within participants. eFigure 4 compares participants' IMD quintiles at gestation (baseline) and age 18. It shows that within each IMD quintile at baseline, 31-51% of participants were in a different IMD quintile by age 18. eFigure 5 shows the absolute sum of changes in the level of exposure to neighbourhood-level deprivation (IMD quintile) experienced by participants over the study period: 46% of participants experienced any change in their IMD quintile over the study period. Finally, eFigure 6 summarises the net or directional change in participants IMD quintile over the study period: 26% of participants experienced a net decrease and 16% a net increase in the severity of their neighbourhood deprivation exposure.

Sensitivity and secondary analyses for the effect of neighbourhood deprivation on IPV among women
In addition to the secondary analyses to explore alternative hypotheses described in the main manuscript, we ran three types of sensitivity analyses (n=38 analyses) to test the robustness of our findings from our main analyses: (1) Outcome operationalisation: We tested the robustness of our findings to several stricter definitions of IPV. These included: (a) 1=any IPV with at least one of the eight self-reported negative impacts versus 0=otherwise; (b) both (i) the average frequency and (ii) any experience of IPV, excluding emotional abuse (i.e., made fun of, insulted, shouted); and (c) based on a recent measurement study, 29 any physical, sexual, or (i) moderate-intensity (i.e., at least one item occurring at least a few times since age 18) or (ii) severe-intensity (i.e., at least one item occurring many times) psychological IPV. (2) Additional missing data strategies, including: (a) creating stabilised weights for intermittent missingness (so that final weights were the product of cumulative probabilities of exposure, censoring, and intermittent missingness histories); 28 (b) based on prior marginal structural model studies, 26 imputing missing covariate data with the last available observation (if t-1 missing, data set to missing), and (c) setting missing weights to 1, so that all complete participant-observation cases would be included (even when t-1 was missing), in both (i) long and (ii) wide data format to demonstrate consistency. (3) Alternative model specifications. This included (a) re-running analyses using time-varying, pointin-time exposure, similar to a prior marginal structural model study. 12 In the current study, this estimated the average effect of living in more versus less deprived neighbourhoods at each time point up until age 18 on IPV risk between ages 18-21. We also (b) used covariate and exposure data from the last available time period (T 6 ) to estimate the T 9 weights, to test the influence of using cross-sectional data in the main analyses, and (c) re-ran analyses using the availablecovariate weights but excluding T 8 , to test the influence of this time period (which was not included in analyses using consistent-covariate weights). Additionally, (d) we conducted conventional analyses in the un-weighted sample (i.e., not accounting for time-varying confounding) to compare methods. That is, in a crude model, we regressed each primary outcome onto exposure and all time-invariant and time-varying covariates measured at baseline and in an adjusted model we added the average value of time-varying covariates over the remaining time period.

Validity checks
The weight distributions for each relevant sensitivity and secondary analysis are shown in eTable 6. Unless otherwise noted, analysis is negative binomial regression (for count outcome) or log-binomial generalised linear model (for binary outcome), weighted as indicated, conducted in a long-form data set (with participant-time as the unit of analysis) with clustering accounted for with robust (conservative) standard errors and adjusting for baseline time-invariant and time-varying covariates. Relative risk in the log negative binomial regression is the incidence rate ratio and in the log-binomial model is the risk ratio. a Conventional generalised linear model adjusting for all available covariates at baseline in unweighted sample in wide format. b Conventional generalised linear model adjusting for all available covariates at baseline and the average value of all available time-varying covariates in unweighted sample in wide format. eTable 8 shows the effect estimates from all secondary analyses exploring alternative hypotheses. As we expected given the exponential distribution of the deprivation scores, we did not find a meaningful association between the ordinal exposure variable and risk of IPV. To confirm the robustness of these findings, we also re-ran our analyses using exposure weights constructed by multinomial rather than ordinal logistic regression (in case of violations of the proportional odds assumption). However, results did not differ and are thus not shown.  18 1.10 0.76, 1.60 N is number. CI is confidence interval. MSM is marginal structural model. Unless otherwise noted, analysis is negative binomial regression (for count outcome) or log-binomial generalised linear model (for binary outcome), weighted as indicated, conducted in a long-form data set (with participant-time as the unit of analysis) with clustering accounted for with robust (conservative) standard errors and adjusting for baseline time-invariant and time-varying covariates. Relative risk in the negative binomial regression is the incidence rate ratio and in the log-binomial model is the risk ratio. a Referent is never lived in most deprived neighbourhoods. Only n=2 participants were living in a deprived neighbourhood at age 18 without ever previously living in a deprived neighbourhood. As such, these participants were analysed in the same category as all other participants living in a deprived neighbourhood at age 18.