Do childhood socioeconomic circumstances moderate the association between childhood cognitive ability and all-cause mortality across the life course? Prospective observational study of the 36-day sample of the Scottish Mental Survey 1947

Background There is growing evidence that higher childhood cognitive ability predicts lower all-cause mortality risk across the life course. Whereas this association does not appear to be mediated by childhood socioeconomic circumstances, it is unclear whether socioeconomic circumstances moderate this association. Methods The moderating role of childhood socioeconomic circumstances was assessed in 5318 members of the 36-day sample of the Scottish Mental Survey 1947. Univariate, sex-adjusted and age-adjusted, and mutually adjusted Cox models predicting all-cause mortality risk up to age 79 years were created using childhood IQ scores and childhood social class as predictors. Moderation was assessed by adding an interaction term between IQ scores and social class and comparing model fit. Results An SD advantage in childhood IQ scores (HR=0.83, 95% CI 0.79 to 0.86, p<0.001) and a single-class advantage in childhood social class (HR=0.92, 95% CI 0.88 to 0.97, p<0.001) independently predicted lower mortality risk. Adding the IQ–social class interaction effect did not improve model fit (χ2Δ=1.36, p=0.24), and the interaction effect did not predict mortality risk (HR=1.03, 95% CI 0.98 to 1.07, p=0.25). Conclusions The present study demonstrated that the association between higher childhood cognitive ability and lower all-cause mortality risk is not conditional on childhood social class. Whereas other measures of socioeconomic circumstances may play a moderating role, these findings suggest that the benefits of higher childhood cognitive ability for longevity apply regardless of the material socioeconomic circumstances experienced in childhood.


Bias analyses
Although the analyses presented in the main text incorporates sex and age as covariates, there is the potential for unmeasured factors to confound the observed associations with mortality risk. To account for this, we calculated E-values to estimate the minimum strength of association that an unmeasured confounder would need to have with each predictor (age-11 IQ or father's social class) and mortality risk, on the hazard ratio (HR) scale, to fully explain the observed associations. Large E-values indicate that strong confounding would be required to fully account for a given association. Notably, it is recommended that E-values are reported both for a given point estimate HR and for its 95% CI boundary closest to the null (1 on the HR scale) (1).
Based on the univariate association between age-11 IQ and mortality risk (Main Text, Table 2), we estimated an E-value of 1.58 (E-value for upper limit of 95% CI = 1.51). Based on the sexand age-adjusted association between age-11 IQ and mortality risk (Main Text, Table 2), we estimated an E-value of 1.58 (E-value for upper limit of 95% CI = 1.48). Finally, based on the point estimate of the mutually-adjusted (sex, age and father's social class) association between age-11 IQ and mortality risk (Main Text, Table 2), we estimated an E-value of 1.56 (E-value for upper limit of 95% CI = 1.46).
Based on the univariate association between father's social class and mortality risk (Main Text, Table 2), we estimated an E-value of 1.39 (E-value for upper limit of 95% CI = 1.28). Based on the sex-and age-adjusted association between father's social class and mortality risk (Main Text, Table 2), we estimated an E-value of 1.39 (E-value for upper limit of 95% CI = 1.28). Finally, based on the point estimate of the mutually-adjusted (sex, age and father's social class) association between father's social class and mortality risk (Main Text, Table 2), we estimated an E-value of 1.28 (E-value for upper limit of 95% CI = 1.17).
In the context of the associations observed in the present study, this analysis suggests that a potential confounder would need to have a relatively strong association with the predictors and mortality risk to fully explain their association, particularly the association between age-11 IQ and mortality risk.

Unadjusted interaction analyses
The interaction analyses reported in the main text are adjusted for sex and age in days at Scottish Mental Survey 1947. In the analyses presented below (Table A1) we re-estimate the mutually-adjusted model (including IQ score and father's social class) and the interaction model (including the IQ X social class interaction) without adjusting for these potential confounders, and with adjusting for only one confounder (sex or age). Adding the IQ-social class interaction term did not significantly improve model fit versus the corresponding main effects model (Unadjusted: AIC = 35357.72, X 2 Δ = 0.95, p = 0.33; Sexadjusted: AIC = 35270.27, X 2 Δ = 1.36, p = 0.24; Age-adjusted: AIC = 35356.28, X 2 Δ = 0.96, p = 0.33). Furthermore, the interaction did not significantly predict all-cause mortality in any of the models (see Table A1).
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3-way Interaction
At the request of a reviewer, we additionally performed an exploratory analysis of a three-way interaction between IQ z-scores, father's occupational social class (reversed, continuous) and sex. In particular, the aim was to test whether the moderating role of childhood socioeconomic circumstances itself depended on sex.
This was done by constructing a Cox regression model that included main effects of IQ zscores, father's social class (reversed, continuous), sex and age in days at the Scottish Mental Survey 1947, two-way interactions between IQ z-scores X father's social class, IQ z-scores X sex and father's social class X sex, as well as the three-way interaction between IQ z-scores X father's social class X sex.
Including these additional interaction effects resulted in multicollinearity issues (all interaction VIFs > 8.50). Furthermore, it did not significantly improve model fit versus the IQ z-score X father's social class model included in the main text (AIC = 35275.82; X 2 Δ = 0.26, p = 0.97; Interaction R 2 = 0.04). None of the included interactions significantly predicted all-cause mortality risk (Table A2).

Additive hazards model
At the request of a reviewer, we performed Additive Hazards regression using Aalen's additive regression models equivalent to the Cox Proportional Hazards models used in the main text. Additive models have the advantage of allowing the effects of covariatesincluding interaction effectsto vary over time (2). For example, advantage in childhood cognitive ability may benefit survival in particular socioeconomic groups but only in specific periods of life. Additive models help to provide information about the effect in the context of the underlying hazarda small hazard ratio for the interaction may still be important if the underlying hazard is large (2). We estimated the number of additional deaths per 10,000 person years predicted by each covariate of interest -IQ z-scores, father's occupational social class and the IQ-social class interaction. As in the main text, univariate, sex and age-adjusted, mutually-adjusted, and interaction models were constructed.
As with mortality risk in the main text, a 1SD advantage in IQ and a 1 class advantage in father's social class were both significantly associated with a small reduction in the number of deaths, even when adjusted for sex and age at time of the Scottish Mental Survey 1947 (Table  A3). These associations remained significant when mutually-adjusting, supporting the suggestion that childhood cognitive ability and childhood socioeconomic circumstances independently predict mortality risk.
We then tested the moderating effect of father's social class. The IQ-social class interaction predicted a small increase of 0.13 deaths per 10,000 person years, though this was only marginally-significant and 95% CIs included 0 (95% CI [0.00-0.25], p = 0.05). That is, a 1SD advantage in childhood cognitive ability predicted 0.13 more deaths per increase in father's social class. Note that this association was much smaller in magnitude than the decreases in additional deaths associated with the main effects.
Additive models were constructed to examine the IQ-mortality association within each social class, including those whose father's occupational social class was missing, as in the main text (Table A4). The direction and pattern of associations was consistent with the Cox Proportional Hazards models used in the main text: a 1SD advantage in IQ was significantly associated with fewer deaths per person year among those from unskilled, semi-skilled and skilled social class backgrounds. The benefit of advantage in IQ appeared to diminish slightly as class increased, suggesting that high IQ may benefit those from lower social classes most. Note again, however, that the interaction effect in the whole-sample model above was not significant. There was no significant association between IQ and mortality in those from intermediate, professional or missing occupational social classes, and confidence intervals in these groups were wide.
We conclude that the additive hazards approach presented here is in keeping with the proportional hazards approach used in the main text. In the context of the underlying mortality hazard for this sample, advantage in IQ and childhood social class predict modest reductions in the number of deaths per 10,000 person years. In contrast, the interaction effect was relatively weak, with no consistent trend across classes.