In this article, we demonstrate the application of Rule-Based Modeling as a tool to improve our understanding about the influence of social support and specific late-life events on depression among the elderly. The application and approach at hand may be used as a template for studying the epidemiology of other chronic conditions.
As we can see from the results, the fit between the simulated curves and the empirical data are not always optimal. This is often the case in simulation models used to study social phenomena. This link between the simulated and the empirical data remains a delicate topic that feeds the debate on the empirical validity of simulation models 
However, two modeling traits need to be kept in mind while analyzing any kind of model. On the one hand, a model is a simplified representation of reality. We therefore assumed in our conceptual framework that the only drivers of elderly depression are socially related. If the patterns reproduced by the model do not correspond fully to observed patterns, this may indicate that “socially related rules” may not suffice, thereby establishing a need for further studies integrating additional drivers. On the other hand, a model is also a purposeful representation of reality. Hence the major aim of this model is not to produce a perfect representation of reality but to improve the conceptual understanding of the role of social factors related to late-life depression.
Taking this into consideration, a number of interesting insights emerge from our modeling exercise. Each individual scenario and their combinations provided useful lessons.
The first scenario assesses the experts' answers, independently of other effects. The simulated curves from this scenario indicate that a peak in the prevalence of depression is observed after the spouse's death. This could suggest that the experts attribute a large influence of the spouse on the Depressive Status. While this may appear as an intuitive truism, different answers from Types A and B experts indicate that this influence may be perceived differently. These two types of responses illustrate two facets of the perception of losing a spouse. For Type A experts, there was no further impact of spouses after their death, and this absence is not compensated by other sources of social support. For Type B experts, the spouse had a “ghost” contact influence after dying, though that influence was smaller than the influence of a living spouse.
The unique peak of depression in the simulated curve after the spouse's death does not fit the two apparent rises and falls in the empirical prevalence patterns. Changing the ages of widowhood actually allowed the simulated data to better fit with either one of these peaks. If the reason of these empirical peaks is only related to widowhood, this could possibly suggest that two waves of depression resulting from widowhood occur in the population at two different ages. For example, depressive people could die at younger ages, as already reported in some literature 
. None of the scenarios included such a rule.
The second scenario includes a gender distinction and a widowhood effect. The results indicate a smooth increasing linear pattern through all typologies of experts. This is the result of the spread of the year of widowhood depression through the late-life span. Furthermore, this year of depression induces the use of the depressive Contact Table, two years after the death of the spouse. Thus, the widow is not only depressed during one year, but this year of bereavement can also modify the social landscape, resulting in a possible longer-term depressive vicious cycle. This effect has been observed before and already encouraged the modification of urban structures of widow neighborhoods together with initiatives for new social engagements for widows 
In these two first scenarios, the levels of depression prevalence in the simulations appear higher than the levels obtained from empirical data. On the one hand, this could indicate that respondents had a tendency to quantify social parameters overestimating the prevalence of depression in the elderly. It is difficult to determine whether this could be due to an unconscious perception (“stereotype”) of the experts that “old age is depressing” or whether our conceptual framework does not optimally reflect the experts' internal representations of late-life depression. However, the overestimation of elderly depression itself has already been debated 
and may explain a possible overprescription of antidepressants to the elderly 
. On the other hand, this higher level of simulated prevalences could as well be explained by an underestimation of elderly depression by the empirical data. Indeed, symptoms of depression may be atypical and stay unnoticed 
. Moreover, denial and the stigma of diagnosis can further hamper the accurate assessment of depression in the elderly 
In the third scenario, the effect of a treatment by psychotherapy, as modeled, decreases the overall level of prevalences of depression compared to the second scenario. While the indicator of depression used did not rely on treatment or diagnostic information, the reported empirical prevalences include inherently people under treatment. However no treatment effect was mentioned in the questionnaire. Hence, this result could suggest that experts evaluated correctly the natural prevalence evolution of depression (second scenario), independently of the positive effect of a treatment (induced in the third scenario). Considering the statistical tests, this scenario provides the best fit with the empirical patterns.
In the fourth scenario, the conception of one simple rule structured our inquiries about the correlation between the socio-economic status of elderly people and their depressive status. When investigated independently, the curves of each SES categories are parallel, at different levels. This is due to the fact that each individual is assigned an SES permanently, and the negative effect is then permanent, as modeled. In fact, each individual could also perceive a personal dynamical change (worsening) of SES through the late-life time. In fact, the “relative” evolution can also have an impact on the depressive status at all ages 
. To some extent, a relative change in the social status is already embedded within our initial conceptual framework, as the different life events modify the social landscape. Regarding the economic status, the income level was chosen naively as a simple criterion to classify groups. However this distinction might not be appropriate as health disparities by income are reported to be reduced at older ages 
. In fact, people surviving into old age might be skewed towards economic advantage 
Finally, in the three last scenarios, the good correlation between the trends of simulated curves and the slope of the empirical regression line is remarkable. This result could suggest that, through our conceptual framework, experts may have a good internal representation of the factors dynamics influencing the depression through the late-life time. Further, the indices in suggests that the results of the simulation based on the answers of Type 2 experts provide the best fit, through all scenarios. Type 2 experts are health care professionals and have frequent contact with elderly persons. Hence, it appears consistent with common sense that their better-informed knowledge enables them to adapt their opinions within our abstract analogy. This may suggest that our conceptual framework, combined with rules mimicking real population evolution, together with the opinions of well-selected experts, can reproduce a realistic evolution of the prevalences of depression. Further interviews with experts of all types could help to explain the sources of discrepancies and similarities between expert types. In addition, this exploration could raise additional questions and encourage other possible conceptual frameworks.
Several choices made in the development of our model may show some shortcomings. For example, we used data from repeated cross-sectional studies. This may introduce several biases (e.g. possible confusion between age, period, and cohort effects) that could be avoided in longitudinal studies. The use of such classical longitudinal data in future work may improve our model. However, currently available cohort studies (e.g. the Share cohort study and the Annual Belgian Household Panel Survey) do not cover social and life-course mechanisms that are important to this study.
Moreover, the design of the rules related to the widowhood effect, the treatment effect and the socio-economic distinction can be criticized. However, the purpose was to prove the experimental capacity of RBM. This simple model can actually be used to structure these criticisms and further refine the model.
In addition, our model is purposefully simplistic when using the concept of depression. Indeed, our focus was not on describing precisely the pathology, but to study its social aspects and the experts' perceptions. Using the word “depression” in our questionnaire may have biased the answers, suggesting a self-evident association between elderly people and depression 
. In place of depression, using the concepts of mood, such as happiness or sadness might have been more neutral and would not have conflicted with our illustrative purposes.
In conclusion, this paper indicates that RBM provides a possible balance between the technical thoroughness of quantitative studies, and the exploratory power of qualitative studies. The qualitative aspects can help to reveal complex mechanisms and abstract analogies
The simulation model presented here should be seen primarily as a tool for thinking and learning 
. Indeed, the comparison between the simulated and the empirical data enlightens different facets of our personal internal representation of the topic at hand. In addition, it helps to identify and properly formulate new context-specific questions 
submitted to new assumptions. However, causal explanations and the predictive power of the simulation model should be limited and interpreted in the light of these same contexts and assumptions, as this is the case in statistical analysis.
Hence, the designed analogies or conceptual framework can be investigated and tested as in an experimental lab 
, without long and costly longitudinal studies. In fact, this process can assist in the design of new models, which may better guide the collection of new data 
Another advantage of RBM lies in its flexibility. Virtually all scenarios can be simulated, with as many interactions and variables as needed, allowing additional rules to be included. However, the abstraction and the rules should always be kept simple enough to be understood, and logical enough to allow the learning process to continue 
This flexibility and the formalism of RBM make it a powerful tool of communication and negotiation between experts, providing an interactive medium for social exploration 
. As the simulation program requires a formal language with simple rules, it forces experts to build theories following an architecture that reduces ambiguity. The informative interactions between modelers and experts allow for improving and learning from the elicitation in the absence of empirical data. Simulated data can fuel further discussion among experts, and new abstractions can be considered, forming a dynamic learning cycle of trial-error-rework.
RBM does not require high-level skill in mathematics, and may attract researchers from quantitative and qualitative backgrounds alike. Combining wisely both insights can only increase our understanding of complex phenomena.