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Association of Wealth With Longevity in US Adults at Midlife

This cohort study examines the shared environmental and genetic characteristics as well as the mortality risk of adult individuals, siblings, and twins participating in a longitudinal study.

that had complete data on analysis variables utilizing robust SEs to account for dependence among family members (Model 1).
Next, we estimated survival models only within the sub-sample of twins and non-twin siblings. In Model 2, siblings and twins were treated "as individuals" but a shared frailty was included to model dependence among family members. In Model 3, we estimated the withinfamily association between wealth and longevity by calculating the family-level average net worth (among families that had >=2 members with complete data) and subsequently calculating the difference between each individual's net worth and their family average. When included alongside the family-level mean, the hazard ratio (HR) for these mean-deviation scores estimate the within-family association between net worth and longevity. This "between-within" (BW) method is a common approach to fixed-effects modeling 4,5 . When applied in this way, it allows us to compare siblings/twins in the same family to one another, and thus to control for all unmeasured shared family-level variables, consistent with the discordant sibling/twin design [6][7][8] . In survival analysis, the BW method has been shown to provide similar estimates to more common approaches for co-twin/sibling control with survival data (e.g. conditional likelihood methods like stratified Cox regression) and has been observed to be optimal statistically 5 .
To further disambiguate environmental versus genetic influences, we tested whether within-family associations between net worth and longevity varied across non-twin sibling, MZ, and DZ subsamples. We did this by including a pair of two-way interaction terms crossing the mean-deviation scores of net worth with dummy codes for DZs or MZs; non-twin full siblings modeled as reference group). A Wald test tested the equality of the within-family net worth models for non-twin siblings, DZ pairs, and MZ pairs (Models 4-6). A significant within-family association (p < 0.05) observed among non-twin siblings -but not among DZ or MZ pairs -would suggest some residual confounding by early life factors since twins share a closer pre-and postnatal environment than non-twin siblings who may be born years apart. A within-family association observed both among siblings and DZ pairs but not among MZ pairs would suggest genetic confounding. Sensitivity analyses were undertaken to test the robustness of findings.
These analyses addressed the skewed distribution of the net worth variable and tested the possibility of non-linear associations between net worth and longevity. They also clarified the role of pre-existing health problems and considered other model specifications. Primary models were also re-estimated as stratified Cox regressions using STATA 3 (see eMethods 2) and as multilevel Cox regressions using Mplus 9 (see eMethods 3).

eMethods 2. Supplementary Sensitivity Analyses
Sensitivity analyses were undertaken in the combined sibling and twin subsample to test the robustness of the findings to different model specifications. First, to assess the potential for a non-linear association between net worth and longevity, we estimated a spline model (eTable 1) including two knots: one at the 75 th percentile of net worth ($125,000) and one at the 90 th percentile ($382,500). As shown in eTable 1, HRs for net worth for those below the 75 th percentile (HR=.86, CI=.76-.97, p=.01) and between the 75 th -90 th percentiles (HR=.90, CI=.82-.98, p=.01) were similar, and a subsequent test of the estimates confirmed that their difference was no greater than chance (p=.66). The HR for net worth for those above the 90 th percentile (individuals with >=$680,000; n=182, 45 decedents) was not statistically significant (HR=1.02, 95%CI=.97-1.08, p=.31) and a test of the estimates indicated that the difference between this HR and the HR for those between the 75 th -90 th percentiles was statistically significant (p=.03).
This indicates a possible diminished return on net worth at the very high end of the net worth distribution, though this reflects only approximately 7% of the sample. Collectively, the spline model indicates that among the large majority (93%) of siblings and twins (i.e. those whose net worth was <= $382,000), the association between net worth and survival was approximately linear.
We subsequently reran Model 3 in a subsample of siblings and twins who were in family groups where all members had <= $382,500 in net worth (n=2,110; 321 deaths). As shown in eTable 2 of this supplement, the HR for net worth in this restricted sample (HR=0.89, CI=0.82-0.96, p=0.004) suggested a larger association between net worth and longevity among those with lower family-level wealth. However, these results should be interpreted with a high level of caution due to the restricted sample size.
In another sensitivity analysis, we recoded net worth into ordinal decile groups, given the large positive skew of the net worth distribution. In the combined sibling and twin subsample, between-family (HR = 0.90, 95% CI = 0.85-0.94, p < .001) and within-family (HR = 0.92, 95% CI = 0.87-0.96, p = .001) net worth estimates remained significant predictors of mortality.
Next, to account for the possibility of residual confounding by health status (having a medical problem may both reduce one's ability to accumulate wealth and increase mortality risk), analyses were re-estimated among sibling/twin pairs who were free of previous cancer or heart disease. Among sibling groups with >2 members, only those siblings without heart disease and cancer were compared to one another. Results were largely similar in this restricted sample We also tested the possibility of a nonlinear age trend by including an age 2 term (HR =1.00, 95% CI = 0.99-1.00, p = .65) and also an age*sex interaction term (HR = 1.01, 95% CI = 0.99-1.03, p = 0.14), neither of which was associated with mortality risk nor changed the interpretations of other model estimates. We also tested an interaction between the withinfamily net worth estimate and participant age at MIDUS 1. The rationale being that the withinfamily association between net worth and longevity may vary as a function of age. The interaction term was not statistically significant, HR = 1.00, 95% CI =0.99-1.00, p=0.37, suggesting that the within-family association between net worth and longevity did not vary by age at MIDUS 1.
Lastly, as a more conservative test of possible confounding by early experience, we

eMethods 3. Deviations From Original Preregistered Analysis Plan
The analyses presented in the main text are consistent with the study rationale, hypotheses, and overall analytic plan outlined in our preregistration (https://osf.io/zyedp). We did, however, deviate from the original analytic plan in some minor ways-these deviations are outlined below.
First, in the original analysis plan, we specified that survival analyses would be estimated as multi-level Cox regression models. Instead, each survival model was estimated as a Cox model with shared frailty term to account for clustering. Both analytic approaches gave very similar results for all models-compare coefficients in Model 1 and Model 3 of Table 2  Instead, in the main text, we present results from three separate survival models: one among non-twin siblings, one among DZ twins, and one among MZ twins. With either analytic strategy, coefficients were very similar and provided the same interpretations-compare coefficients from Models 4, 5, and 6 in main text Table 2 to coefficients in eTable 5, which display results from the multilevel mixture model using Cox regression with KNOWNCLASS option in Mplus version 8).
Third, as described in the main text, we undertook a conservative test of whether the within-family net worth effect varied across full sibling, MZ twin, and DZ twin subsamples by including two-way interaction terms between the within-family net worth variable and dummy codes for cluster type and conducting a Wald test to test the equality of the within-family estimates. This test of the equality of within-family net worth effects across sibling subsamples was not described in the original analysis plan.
We also originally proposed an exploratory test of the two-way interaction between parent education and the within-family net worth twin/sibling difference score. We decided to omit this test from the main text because we felt that the rationale for this test was tangential to our primary analyses, which were already many in number. It is also not an optimal test for answering questions related to social mobility, its stated purpose in the preregistration. In any case, we report results from this test here. Among the combined sample of non-twin siblings, DZ twins, and MZ twins (n =2,490) there was no interaction between parents' highest level of education and sibling/twin net worth difference score (HR = .99, 95% CI .98-1.00, p = .30).
We also specified that full-information maximum likelihood estimation (FIML) would be used to handle missing data. In the preregistration, we specified the criteria by which siblings and twin pairs would be excluded from our analysis sample-resulting in an analytic sample of n=7,017.