Since 1996 the German Ageing Survey (DEAS) comprises several representative data collections from the German population 40 + years (Klaus et al., 2017; Vogel et al., 2021). A cohort-sequential study design is applied, i.e., similar samples of the population are drawn from population registration offices at equidistant time intervals using a multistage random procedure. The DEAS started in 1996 with recruitment of the first sample; in 2002, 2008, and 2014 further samples were drawn. Respective cross-sections of the general population are then repeatedly interviewed at predetermined intervals but only in those study participants who consented in follow-up examinations (Fig. 1). The data are collected in face-to-face interviews (usually in participants’ homes) and via paper-pencil questionnaires, which are to be completed by the participants either immediately or within a few days after the interview. The data collection comprises, among other topics, socio-demographic and health information. An overview over all DEAS samples is provided by Klaus et al. (Klaus et al., 2017) and detailed information can be obtained from the corresponding Research Data Center (https://www.dza.de/en/research/fdz/german-ageing-survey). Funding for the German Ageing Survey is provided by the Federal Ministry for Family Affairs, Senior Citizens, Women and Youth (BMFSFJ).

Self-perceptions of aging (SPA) were measured by established multidimensional scales (AgeCog scales) that differentiate between three SPA dimensions related to (1) physical losses, (2) social losses, and (3) ongoing development (Steverink et al., 2001; Wurm et al., 2007). The latter dimension consists of four items, all starting with: Aging means to me that: (i) … I continue to make plans, (ii) … I can still learn new things, (iii) … I can still put my ideas into practice, and (iv) … my capabilities are increasing. These statements are answered each on a 4-point Likert scale ranging from 1 = “strongly agree” to 4 = “strongly disagree”.

In this study, SPA ongoing development (SPA-OD) will be considered and operationalized similarly to previous studies based on DEAS (Diehl et al., 2021; Wurm & Schäfer, 2022), i.e. item coding (1 to 4) is reversed so that higher scores correspond to more positive SPA (range of sum scores: 4–16).

For continuous covariates descriptive statistics of mean, median, standard deviations, minimum and maximum are presented. Discrete covariates are described using absolute numbers and percentages. The number of missing data is presented for each covariate in compliance with STROBE (von Elm et al., 2007). For some descriptive analyses dichotomization of SPA-OD according to a median split is conducted in line with previous studies that used this approach to illustrate mortality differences between individuals with more or less positive SPA (Levy et al., 2002; Wurm & Schäfer, 2022). Different to previous studies, in our descriptive analysis of raw data (without imputations) a separate stratum is created for observations with missing SPA-OD.

According to the TRIPOD statement for multivariable prediction models (Collins et al., 2015), our approach represents a Type 2a modelling approach, i.e. data are randomly and repeatedly split into internal learning data (used for model fit) and internal validation data (used for prediction of the mortality risk). The bootstrap approach is used for resampling (Hastie et al., 2009).

To examine the (additive) predictive value of SPA-OD, five different Cox PH models are fitted to internal learning data (in-bag) and the fitted models are then used to predict the risk of death in internal validation data (out-of-bag). The first Cox-PH model comprised only the SPA-OD sum score, the second only age and sex, and the third model included age, sex, and SPA-OD. This specification was applied to determine the predictive value of SPA-OD alone, to compare it with the predictive value of a model adjusted only for age and sex, and to obtain an estimate of improvement if SPA-OD is added to age and sex as an additional covariate. The fourth model comprised all covariates but not SPA-OD that was included in the fifth model.

Harrels’ c-index was computed from the predicted vs. the observed risk (Rahman et al., 2017). The c-index can be considered the fraction of pairs in the data, in which model-based predictions, e.g. survival times or probabilities, correspond to observed values. The index is calculated by:

Here, corresponds to observed survival time or probability and corresponds to the model-based prediction of individual i^th observation time (or probability) (Pencina & D'Agostino, 2004). A models’ c-index of 0.5 is equivalent to the accuracy of flipping a coin; a c-index close to 1 indicates very good predictive performance.

In addition, the integrated discrimination index (IDI; (Pencina et al., 2008) was calculated to provide information on the improvement in sensitivity and specificity in terms of discriminating those who survived and those deceased (Pencina et al., 2010; Yates, 1982). The IDI is calculated as follows:

Here, represents the average over model-based predictions , “new” refers to the new or updated model in either “events” (e.g., deceased participants) or “non-events” (e.g., survivors) (Pencina et al., 2008). The IDI is positive, if discrimination between deceased and survivors is better for the new model compared to the old model.

This procedures was applied to each of the 20 imputed data sets separately (100 replications per imputation and 2000 repetitions in total); aggregates of percent change in c-index/IDI and corresponding confidence intervals were calculated using Rubins’ rule (Rubin, 1987).

To evaluate the effect of a sum score of comorbidities on all-cause mortality, data preparation (incl. multiple imputation) was repeated while individual comorbidities were replaced by a sum score of (physical) comorbidities. Similarly, in adjusted Cox PH models’ diabetes, cardiovascular disorders, and cancer were replaced by the sum score.

All analyses of this study were conducted using R software (R Development Core Team, 2023) version 4.3.3. Table 1 of participant characteristics is created using R package Table1 (Rich, 2023) and rendered with flextable (Gohel & Skintzos, 2023). Graphical illustrations were generated using R packages ggplot (Wickham, 2016) and ggsci (Xiao, 2023). For adjusted survival plots the R package adjustedCurves was used (Denz et al., 2023). Parallelized computations were conducted using R packages foreach and doParallel (Weston & Microsoft Corporation, 2022). All R code is stored in a public repository to enable for reproducibility (Richter, 2024).

Participant characteristics of the DEAS 1996 sample are shown in Table 1 using stratification according to a median split of the sum score of SPA ongoing development (SPA-OD) as this has been done in previous studies (see Table 1 Supplementary Materials). Participants not completing the paper-pencil questionnaire or with missing information on SPA are presented as a separate stratum. With respect to all characteristics, participants with SPA-OD sum score below the median are considerably different from those with SPA-OD above the median (except for cancer disease (p = 0.007), all t-test or Chi² test p-values < 0.001). The differences were particularly notable regarding age, the frequency of male sex, and number of comorbidities. Similar results are found for all other DEAS samples (Supplementary Table 1 to 3). Figure 2 illustrates the inverse association of chronological age and SPA-OD if the sum score is split by the median.

The amount of missing information is low to moderate, being highest for SPA-OD with 15.8% and for the comorbidities (only DEAS 1996 and 2002 sample). In the remaining DEAS samples, there is no missing information on comorbidities as this information was collected as part of the face-to-face interviews.

Multivariable Cox PH models showed very consistent findings across all samples of the DEAS for most of the covariates (see Table 2). The risk to decease increased nonlinear with age and was lower for females. Similarly, the risk was higher with the presence of cancer disease and diabetes. Participants in the lowest household income group, compared to a household income of 2000 € (reference), had an increased risk to decease. The risk was attenuated with household incomes > 2000 €. Results were less consistent for education; in the DEAS 1996 and 2008 sample, the risk to decease was lower for higher educational level but not in DEAS 2002 and 2014. In the DEAS samples 2002, 2008, and 2014, current smoking was consistently associated with higher risk to decease. For the association of BMI and all-cause mortality a non-linear association was found but likely due to limited power in the tails of the distribution, confidence intervals include the null value. Lastly, higher scores of SPA-OD were consistently associated with lower risk to decease across all samples of the DEAS. But compared to the effect of chronological age, changes in the probability of death obtained from adjusted models vary only slightly with SPA-OD (Supplementary Fig. 6).

Figure 2 compares unadjusted (left panel) vs. adjusted (right panel) survival estimates in the DEAS 1996 sample. The unadjusted model comprised only SPA-OD (median split) as a stratification variable and shows a considerable discriminatory effect of SPA-OD (Fig. 2, left panel). Comparing the difference in observation time at a survival probability of 0.75 (similar to Wurm & Schäfer (Wurm & Schäfer, 2022)), the median difference over all imputations between lower and higher SPA-OD is 115.5 months (min = 109; max = 123). After adjustment for covariates as shown in Table 2, the median difference over all imputations between lower and higher SPA-OD is 14 months (min = 7; max = 22). Similar results were found for all other DEAS samples (Supplementary Fig. 7 to 9).

Regarding prediction of survival outcomes in internal validation data, Harrels’ c-index is shown for 2000 bootstrap replications in Fig. 3. Compared to a Cox PH model adjusted for age and sex only (Model 2), the predictive accuracy was reduced by SPA-OD (Model 1 in Fig. 4) on average by -17.3% [-18.4%; -16.3%] (percent change in c-index, Model 1 vs. Model 2 in Fig. 3) in the DEAS 1996 sample (DEAS 2002: -19.9 [-21.2%; -18.6%], DEAS 2008: -14.9% [-16.6%; -13.2%], DEAS 2014: -14.8% [-17.0%; -12.7%]).

Modeling SPA-OD in addition to age and sex (Model 3 vs. Model 2), improved prediction accuracy on average by 0.11% [-0.04%; 0.26%] in the DEAS 1996 sample. Improvements did not exceed 1.1% in other samples of the DEAS (2002, 2008, and 2014): 0.27% [0.10%; 0.45%], 1.06% [0.68%; 1.44%], and 0.96% [0.36%; 1.57%] respectively. The completely specified Cox PH model as shown in Table 2 vs. a model without SPA-OD (Model 5 vs. Model 4, Fig. 3), improved prediction accuracy on average for DEAS 1996 by 0.18% [0.09%; 0.29%], DEAS 2002 by 0.32% [0.15%; 0.48%], DEAS 2008 by 0.50% [0.27%; 0.73%], and for the DEAS 2014 by 0.29% [-0.06%; 0.65%]. Results regarding the integrated discrimination index (IDI) were similar (Supplementary Table 4). Largest improvement in discrimination of those who survived from those deceased was obtained when modeling age and sex alone; adding SPA-OD to the model led to marginal improvement being highest with 0.76% [0.53%; 0.99%] in the DEAS 2008 when comparing Model 3 vs. Model 1.

Our findings need to be interpreted in the light of some limitations. Our study also uses observational data that might be subject to residual confounding. In line with all previous studies on subjective aging and mortality, this analysis did not consider time-varying covariates. Situations of participants, particularly regarding comorbidities, can change over time, which is not taken into account in this study. Due to high panel attrition (e.g., 68.5% in the DEAS 1996 sample at 1st follow-up (Klaus et al., 2017)), we were unable to model time-varying covariates appropriately. Effects of covariates were not fully consistent across waves, with higher levels of education being associated with greater risks of mortality for the 2002 DEAS wave, which is inconsistent with the remaining samples and previous findings (Balaj et al., 2024). Similar inconsistencies emerged for birth region. Moreover, the definition of comorbidities might be criticized, especially for cardiovascular diseases as the definition applied here likely overestimates the prevalence of this disease type (Busch & Kuhnert, 2017). In addition, there were also between-wave differences in the assessment of comorbidities. These factors may result in mixed findings for cardiovascular risk factors. Continuous covariates such as chronological age, BMI, and household income were modelled using natural splines with an arbitrary default of three degrees of freedom (Gauthier et al., 2020; Harrell, 2015). Indeed, non-linear associations are often more plausible. In addition, non-linear modeling compared to linear modelling of covariates means slight overfitting in the case of linear associations, while linear modelling as the default can lead to the conclusion of a non-existent association (Nakatochi et al., 2023). Based on previous findings (Wurm & Schäfer, 2022), we focused on a single indicator of subjective aging, that is SPA-OD. Moreover, the analysis sample is biased as a substantial number of participants did not agree to participate in follow-up assessments which is a prerequisite for assessing their survival status. Wurm and Schäfer (2022) found that those participants included in follow-ups were on average younger, healthier, more educated, more likely to be male and live in Western Germany, and reported more positive SPA. Similar biases, however, existed in other previous studies.

It is plausible to assume that other health-benefitting factors, that were found to be associated with mortality such as optimism (Kim et al., 2017) or self-efficacy (Assari, 2017), are subject to similar patterns of confounding. To illustrate, in a study on optimism (Kim et al., 2017), the results consistently moved towards a null effect when more confounders were included, supporting their critical role. Research in these areas will benefit from application of more robust methods and more “causal thinking” (Rohrer, 2024).

Moreover, there are implications for the analysis of comorbidities. So far, most studies use non-validated sum scores to measure comorbid diseases, neglecting differential associations of specific diseases with mortality and carrying at risk for confounding by mental health (Østergaard & Foldager, 2011). The selection and consideration of comorbidities should be based on the research question at hand. For some outcomes such as mortality validated sum scores can be used (Austin et al., 2015). For other research questions, specific comorbidities might be preferable.

In many psychological fields, the common explanatory research that generates effects of association should be extended by a subsequent step of causal thinking. In particular, it is recommended to include methods permitting the analysis of evidence pertaining to causal relationships (Stuart, 2010). Models should also be evaluated in independent data or using internal validation (Collins et al., 2015). Such a holistic approach has recently been described as integrative modelling (Hofman et al., 2021).

This research did not receive any external funding. The German Ageing Survey was funded under Grant No. 301-6083-05/003*2 by the German Federal Ministry of Family Affairs, Senior Citizens, Women and Youth. The content is the sole responsibility of the authors.