Does positive affect mediate the association of multimorbidity on depressive symptoms?

Data

We used data from the German Ageing Survey (DEAS), which is a cross-sectional and longitudinal nationally representative study of people aged 40 and older (Klaus et al., Citation2017). Funded by the German Federal Ministry of Family Affairs, Senior Citizens, Women and Youth (BMFSFJ), the DEAS is an ongoing survey, started in 1996. Overall the DEAS consists of six survey time-points (1996, 2002, 2008, 2011, 2014, 2017), each with different samples. For the survey waves in 1996, 2002, 2008 and 2014, nationally representative samples (cross-sections) were drawn. The survey method consists of computer-assisted personal interviews (CAPIs) and self-completed questionnaires (drop-off). The main research areas of the survey are employment and retirement; health and health behaviour; quality of life; and subjective wellbeing. The longitudinal design and the main research areas make the dataset well suited for the aim of analysis.

To maximise the number of cases and time-points, we used data from panel participants within four time-points, spanning nearly a decade (2008, 2011, 2014, 2017). We excluded the earlier waves (1996 and 2002) from analysis due to the longer gaps between surveys (6 years) and the high number of drop-outs. Additionally, in 2008 a new starting cohort joined the panel. The panel participation rate of the starting sample in 2008 (N = 6,205) is about 46% in 2011 (N = 2,858), about 41% (N = 2,569) in 2014 and about 34% (N = 2,109) between 2014 and 2017. The eligible birth cohorts were 1923 to 1968. Furthermore, the drop-off questionnaire had lower participation than the CAPI.

Figure 2 illustrates the sample selection process. The data restriction criteria were continuous observation since 2008 and uninterrupted participation in the CAPI and the drop-off questionnaire. As we wanted to inspect changes of multimorbidity, positive affect and depressive symptoms within individuals over four points in time, we required valid values for the primary analysis variables. In total, 125 respondents were removed from the analysis due to missing or incomplete values for the analysis variables (case-wise deletion). From the initial 6,089 respondents in 2008, only 1,558 remained in the final analysis sample in 2017. Missing panel-participation consent caused the highest amount of respondent loss.

Longitudinal mediation analyses

Our investigation focuses on the mediation of the effect of multimorbidity $(X)$ on depressive symptoms $(Y)$ by positive affect $(M).$ Although empirical studies of mediation have a long tradition (Baron & Kenny, Citation1986; Hayes, Citation2009), the conditions under which these analyses can identify direct and indirect effects have been detailed only recently. These are often captured under the term ‘sequential ignorability’ (Imai, Keele, & Tingley, Citation2010) or ‘unconfoundedness assumptions’ (Pearl, Citation2014; Shpitser & VanderWeele, Citation2011) and require the researcher to measure and adjust for common causes of the exposure, the mediator and the outcome. The first three assumptions (A to C) all address the confounding between exposure, mediator and outcome. The last assumption (D) states that there must be no mediator-outcome confounder that is affected by the exposure, regardless of the observability of such confounders, which means that even adjusting for this type of confounding is insufficient. In longitudinal mediational settings, however, this type of confounding (D-confounding) is very likely to occur (VanderWeele, Vansteelandt, & Robins, Citation2014).

Especially in the setting of multimorbidity, positive affect and depressive symptoms, D-confounding is inherent due to the reciprocal process. Figure 1 illustrates D-confounding. Depressive symptoms at t0 (DS-t0) confound the path between positive affect at t1 (PA-t1) and depressive symptoms at t1 (DS-t1) while also being influenced by multimorbidity at t0 (MM-t0), which renders the depressive symptoms at t0 as a D-confounder. Our analysis, therefore, requires sophisticated methods that specifically account for D-confounding.

Figure 1. Simplified DAG.

Note: MM = Multimorbidity; PA = Positive affect; DS = Depressive symptoms. Depicted time-points t0 and t1. Confounding factors and time-points t2 and t3 omitted for illustration purposes.

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Mediational g-formula

As a solution to D-confounding, VanderWeele and Tchetgen Tchetgen (Citation2017) proposed the mediational g-formula. This formula cancels the exposure-induced mediator outcome confounding by simultaneously intervening on the mediator and fixing its distribution (for a detailed proof, see: VanderWeele & Tchetgen Tchetgen, Citation2017, pp. 921–922).

The practical application of this method follows three steps: (1) adjustment for D- confounding by inverse probability weighting (IPW); (2) the estimation of two marginal structural models (MSM), an outcome model and a mediator model, each weighted by its IPW of step 1; and (3) multiplication and bootstrapping of the coefficients derived from step 2.

For the calculation of the IPWs in step 1, we used logistic regressions to estimate the probability of being multimorbid at each time-period. We used least-square regressions for the estimated probability of the level of positive affect at each time-point, using the previous values of multimorbidity, positive affect and depressive symptoms as time-varying confounders. The addition of these previous values adjusts the weights for the reciprocity. We further stabilised the weights as suggested by Robins, Hernán, and Brumback (Citation2000). Additionally, we truncated the 1^st and the 99^th percentiles to improve stability. In settings where the occurrences of certain combinations of $X,$ $M,$ $Y$ are implausible to occur, truncation has become a standard practice for applying IPWs (Cole & Hernán, Citation2008). This especially holds for multimorbidity, as multiple changes are unlikely during the observation period.

We used these weights for the MSMs of step 2 and applied generalised linear models with maximum likelihood optimisation and clustered standard errors at the individual level. The first MSM is the outcome model (EquationEq. (1)(1) $$E\left(Y_{\stackrel{\to }{xm}}\right)={\Delta }_0+{\Delta }_{1}cum\left(\stackrel{\to }{x\mathrm{ }}\right)+{\Delta }_{2}cum\left(\stackrel{\to }{m\mathrm{ }}\right)$$(1) ). This model estimates the cumulative effect of the multimorbidity $\stackrel{\to }{X\mathrm{ }}$ and positive affect $\stackrel{\to }{M\mathrm{ }}$ trajectories on depressive symptoms; where $\stackrel{\to }{X\mathrm{ }}$ is the sum of multimorbidity exposures after t0 and $\stackrel{\to }{M\mathrm{ }}$ is the sum of the positive affect scores after t0. EquationEquation (1)(1) $$E\left(Y_{\stackrel{\to }{xm}}\right)={\Delta }_0+{\Delta }_{1}cum\left(\stackrel{\to }{x\mathrm{ }}\right)+{\Delta }_{2}cum\left(\stackrel{\to }{m\mathrm{ }}\right)$$(1) tests for H1, the direct effect of multimorbidity on depressive symptoms.(1) $$E\left(Y_{\stackrel{\to }{xm}}\right)={\Delta }_0+{\Delta }_{1}cum\left(\stackrel{\to }{x\mathrm{ }}\right)+{\Delta }_{2}cum\left(\stackrel{\to }{m\mathrm{ }}\right)$$(1)

The second MSM is the mediator model, which evaluates the effect of the average multimorbidity trajectory on positive affect. EquationEquation (2)(2) $$g^{-1}\left[E\left\{M_{\stackrel{\to }{x\mathrm{ }}}\left(t\right)\right\}\right]={\beta }_0\left(t\right)+{\beta }_1\left(t\right)avg\left\{\stackrel{\to }{x\mathrm{ }}\left(t\right)\right\}$$(2) tests the assumption that multimorbidity decreases positive affect. We use the identity link function because positive affect is continuously measured.(2) $$g^{-1}\left[E\left\{M_{\stackrel{\to }{x\mathrm{ }}}\left(t\right)\right\}\right]={\beta }_0\left(t\right)+{\beta }_1\left(t\right)avg\left\{\stackrel{\to }{x\mathrm{ }}\left(t\right)\right\}$$(2)

In step 3, as shown by VanderWeele and Tchetgen Tchetgen (Citation2017, pp. 927–928), the interventional direct effect (IDE) and interventional indirect effect (IIE) can be calculated using EquationEq. (3)(3) $$\mathit{IDE}={\Delta }_{1}T; \mathit{IIE}={\beta }_1{\Delta }_{2}T$$(3) .(3) $$\mathit{IDE}={\Delta }_{1}T; \mathit{IIE}={\beta }_1{\Delta }_{2}T$$(3)

The IDE equals the coefficient for multimorbidity ( ${\Delta }_{1}cum(\stackrel{\to }{x\mathrm{ }})$) of EquationEq. (1)(1) $$E\left(Y_{\stackrel{\to }{xm}}\right)={\Delta }_0+{\Delta }_{1}cum\left(\stackrel{\to }{x\mathrm{ }}\right)+{\Delta }_{2}cum\left(\stackrel{\to }{m\mathrm{ }}\right)$$(1) multiplied over all time-points $\mathrm{ }T,$ which is the cumulative direct effect of multimorbidity on depressive symptoms. The IIE is the product of multimorbidity’s effect on positive affect $({\beta }_1)$ and positive affect effect on depressive symptoms ( ${\Delta }_2)$ on all time-periods ( $T).$ Therefore, the IIE captures the quantity of multimorbidity’s effect on depressive symptoms that proceeds through positive affect.

H3 assumed that longer durations of multimorbidity would deplete positive affect more strongly; thus, the mediation would be different. The mediational g-formula is flexible towards XM-interactions, which allows for testing moderated mediation. EquationEquation (4)(4) $$E\left(Y_{\stackrel{\to }{xm}}\right)={\Delta }_0+{\Delta }_{1}cum\left(\stackrel{\to }{x}\right)+{\Delta }_{2}cum\left(\stackrel{\to }{m}\right)+{\Delta }_{3}cum\left(\stackrel{\to }{x}\right)cum\left(\stackrel{\to }{m}\right)$$(4) extends EquationEq. (1)(1) $$E\left(Y_{\stackrel{\to }{xm}}\right)={\Delta }_0+{\Delta }_{1}cum\left(\stackrel{\to }{x\mathrm{ }}\right)+{\Delta }_{2}cum\left(\stackrel{\to }{m\mathrm{ }}\right)$$(1) with an interaction term, allowing the mediation by positive affect to be different for the duration of multimorbidity.(4) $$E\left(Y_{\stackrel{\to }{xm}}\right)={\Delta }_0+{\Delta }_{1}cum\left(\stackrel{\to }{x}\right)+{\Delta }_{2}cum\left(\stackrel{\to }{m}\right)+{\Delta }_{3}cum\left(\stackrel{\to }{x}\right)cum\left(\stackrel{\to }{m}\right)$$(4)

The interventional effects can be calculated through Eq. (5), as demonstrated by VanderWeele and Tchetgen Tchetgen (Citation2017, pp. 934–936).

$\mathit{IDE}={\Delta }_{1}T+{\beta }_0{\Delta }_{3}T2;\mathrm{ }\mathit{IIE}={\beta }_{1}T({\Delta }_2+{\Delta }_{3}T)$ (5)

Generally, the interventional effects (EquationEqs. (3)(3) $$\mathit{IDE}={\Delta }_{1}T; \mathit{IIE}={\beta }_1{\Delta }_{2}T$$(3) and (5)) provide an intuitive interpretation. They express the difference in depressive symptoms if positive affect’s distribution would have been the same (intervened), irrespective of multimorbidity status. In some cases, interventional effects are even of primary interest. This especially holds in the context of multimorbidity, as positive affect is more tangible than multimorbidity. In this setting, interventional effects are of practical relevance, because they could potentially be realised through interventions on positive affect (VanderWeele & Tchetgen Tchetgen, Citation2017, p. 921). In the online supplementary material, we provide step-by-step Stata code for the estimation of the IPWs and the interventional effects. The Appendix includes the formulas used to obtain the set of IPWs (EquationEqs. (6)(6) $$\begin{array}{c}\stackrel{̂}{P}\left\{M\left(t\right)\right|\mathrm{ }\stackrel{\to }{X\mathrm{ }}\left(t\right),\stackrel{\to }{M\mathrm{ }}\left(t-1\right)\left\}\mathrm{ }\stackrel{̂}{P}\right\{X\left(t\right)\left|\mathrm{ }\stackrel{\to }{X\mathrm{ }}\right(t-1),\stackrel{\to }{M\mathrm{ }}(t-1\left)\right\}/\\ \left[\stackrel{̂}{P}\right\{M\left(t\right)\mathrm{ }\left|\mathrm{ }\stackrel{\to }{X\mathrm{ }}\right(t),\stackrel{\to }{M\mathrm{ }}(t-1),\stackrel{\to }{D\mathrm{ }}(t-1),V\}\mathrm{ }\stackrel{̂}{P}\left\{X\right(t\left)\mathrm{ }\right|\mathrm{ }\stackrel{\to }{X\mathrm{ }}\left(t-1\right),\stackrel{\to }{M\mathrm{ }}\left(t-1\right),\stackrel{\to }{D\mathrm{ }}\left(t-1\right),\mathrm{ }V\left\}\right]\end{array}$$(6) and Equation(7)(7) $$\stackrel{̂}{P}\left\{X\left(t\right)\right|\mathrm{ }\stackrel{\to }{X\mathrm{ }}\left(t-1\right)\}/\stackrel{̂}{P}\{X\left(t\right)\left|\mathrm{ }\stackrel{\to }{X\mathrm{ }}\right(t-1),\stackrel{\to }{M\mathrm{ }}(t-1),\mathrm{ }\stackrel{\to }{D\mathrm{ }}(t-1),\mathrm{ }V\}$$(7) ).

Descriptive statistics

Table 2 displays the distribution of the main variables and age between different nested samples. The starting sample of Figure 2 is the parent sample, which consists of all individuals who participated in 2008 (t0). The remained at t3 sample consists of all individuals who were observable in 2008 and in 2017 (t3). The final analysis sample consists of all the individuals who were consistently observed between 2008 and 2017 with valid entries at each measurement occasion. We calculated selectivity effects according to Lindenberger, Singer, and Baltes (Citation2002). The total selectivity (TS) compares the parent sample with the analysis sample. The TS decomposes into mortality-associated selectivity (MAS), which is the selectivity between the remain at t3 sample and the parent sample, and the experimental selectivity (ES), which is the selectivity between the remain at t3 sample and the analysis sample. The selectivity effect sizes can be interpreted according to Cohen (Citation1977).

Figure 2. Flow chart for the analysis data selection of the German Ageing Survey (DEAS). Note: Survey time-points are: t0 = 2008, t1 = 2011, t2 = 2014, t3 = 2017.

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In total, multimorbidity increased in the parent sample from 37.5% in t0 to 47.5% in t3. The total selectivity at t0 is −0.110, indicating a low selectivity effect towards less morbid individuals. Similarly, there is a low selectivity of age at t0 (TS = −0.199). The TS of depressive symptoms is < −0.1, indicating only a weak selection towards less depressed individuals. The TS for positive affect is slightly higher (0.128 at t0), showing a low selectivity towards individuals with higher positive affect. In summary, we found a low selectivity caused by the MAS towards younger, less morbid individuals with higher positive affect.

Table 3 lists the reliability measure Cronbach’s alpha for the sum scores of positive affect and depressive symptoms for all measurement occasions. Overall, the reliabilities of the sum scores were similar and acceptable, with a Cronbach’s alpha ranging from 0.830 to 0.850.

To illustrate the difference in mean changes between the multimorbidity exposure durations, we Z-standardised the measures of positive affect and depressive symptoms to a mean of 0 and a SD of 1.

Figure 3 indicates coherent changes for positive affect and depressive symptoms. Increased exposure duration to multimorbidity results in decreased positive affect and increased depressive symptoms over time. The comparison of the mean differences between those ‘never’ observed as multimorbid and ‘always’ observed as multimorbid after t0 indicate larger differences in depressive symptoms. Together both groups represent the majority (63.41%) of observations in the analysis sample. The differences in mean at t3 between these groups are 0.7 (0.4 to −0.3) for depressive symptoms and 0.4 (0.2 to −0.2) for positive affect.

Figure 3. Mean changes of Z-standardised positive affect and depressive symptoms over time and multimorbidity exposure duration.

Note: Changes in Z-standardised positive affect (left side) and depressive symptoms (right side) for the different multimorbidity exposure durations (MM(ED)) over the observation periods (t). MM(ED) = multimorbidity exposure duration after t0. Bold-black lines represent individuals continuously observed as multimorbid after t0 (#MM(ED) = 3). Dotted lines represent individuals never observed as multimorbid after t0 (#MM(ED) = 0).

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Main results

Table 4 displays the distributional properties of the stabilised weights before and after truncation. A high SD and mean value much larger than 1 indicates an unstable weight. Unstable weights are often present when the underlying models are not correctly specified (Cole & Hernán, Citation2008). In Table 4, all weights have mean values around 1.1, which indicates sufficient stability. Truncation increased stability further by reducing the SD. No case received a weight below 0.330 or above 5.26.

All models used the truncated weights. Table 5 shows the respective coefficients. The estimated coefficients of the mediator and outcome model are highly significant (p < 0.001). The outcome model with interaction (M2) has a significant interaction (p < 0.01) with an appropriate effect size. The correlation of error terms $\rho$ between the mediator and outcome model provides information on the violation of confounding assumptions and ranges between −1 and 1 (Imai et al., Citation2010). Values of $\rho \ne 0$ can indicate the presence of unobserved confounding. Table 5 shows that $\rho =-0.096.$

Table 6 contains the cumulative interventional effects with and without XM-interaction. In the model without XM-interaction (M1), all interventional effects are highly significant with an overall effect of 2.934, an indirect effect of 0.537 and a direct effect of 2.397. Thus, the share mediated amounts to 18.3%. After adding the interaction term in M2, the indirect effect becomes 0.759 and is highly significant, but the direct and overall effects are insignificant.

To gain clearer insights into the effects changed by the XM-interaction we inserted the mean value of cumulative positive affect ( $\mathit{mean}\mathrm{ }\stackrel{\to }{m\mathrm{ }}=5.765$) into Eq. (5) for the different multimorbidity exposure durations. Practically, this would equal an intervention on positive affect to the mean value. We then calculated the share mediated relative to the effect sizes. The results reveal that the indirect and direct effects increase as exposure durations to multimorbidity increase (MM(ED) ≥ 2). At two exposure durations (MM(ED) = 2), the indirect effect is 4.365 (p < 0.01) with a share of the overall effect of 45.4%. At three exposure durations to multimorbidity (MM(ED) = 3), the indirect effect doubles in size to 8.732 (p < 0.01). The overall effect is 21.643 (p < 0.001), and the share mediated by positive affect is about 40.3%. For the ‘once’ or ‘never’ multimorbidity exposure durations, we omitted the percentage mediated due to the missing direct and total effects. The comparison of M1 and M2 in Table 6 reveals that the mediation differs vastly after the addition of an interaction.

Figure 4 illustrates the difference in the level of mediation between the multimorbidity exposure durations (MM(ED) ≤ 1 vs. MM(ED) ≥ 2); see also, Fritz and MacKinnon (Citation2008). It contrasts the linear predictions of the outcome models from Table 5 (M1 and M2) for the multimorbidity exposure duration groups MM(ED) ≤ 1 and MM(ED) ≥ 2.

Figure 4. Difference in mediation between M1 and M2 for different multimorbidity exposure durations.

Note: Presented differences are between the multimorbidity exposure duration groups: MM(ED) ≤ 1 & MM(ED) ≥ 2. M1: mediation model without interaction; M2: mediation model with interaction. Predictions obtained from Table 5.

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Figure 4 also illustrates that equality of mediation for all exposure durations of multimorbidity is not true. M1, however, assumes equal mediation for the exposure durations of multimorbidity, as shown by the parallel linear predictions (dashed lines) at different levels. After inclusion of the XM-interaction (M2), the predictions are not parallel, as shown by the difference between the bold lines. In comparison to M1, M2 shows a much steeper prediction for individuals with prolonged exposure to multimorbidity (bold black line vs. dashed black line). The prediction is less steep for individuals with short or recent exposure to multimorbidity (bold grey line vs. dashed grey line).