Additional Commentary on the Mathematical Model of Recovery

Mr. Coon had an excellent post on the recent paper offering statistical modeling of recovery utilizing a non-parametric model. Mr. Coon does a great job explaining the paper and highlighting the contexts, so I would like to offer a broader overview of the concept of measuring recovery and why this paper is kind of a big deal.

At the personal level

Defining and measuring pathology has been the main focus of addiction research. In recent years, the concept of recovery as a distinct phenomenon (and not just a form of outcome) has come into its own concepts, definitions, and metrics. Obviously, with socialized pathologies like addiction (pathology that requires an external social or cultural component to become problematic), the measure of illness and the concept of wellness constitute the validity of the experiential. This means that often (especially when illness alters one’s capacity for self-judgment and reality testing), the adverse social effects are the most acute. It is an interesting scientific quandary because both illness and wellness have an individual subjective and collective social component, which must, at some point, align for the individual to thoroughly realize the reality of their situation. For example, in the Big Book of A.A., it is noted that the recovering individual is often the last to realize certain truths – not just about their own behavior, but also the last to recognize their own progress. This latency is referred to (in the pathological sense) in various ways, like “denial and minimalization,” among many other labels. However, there is no accurate concrete term for such latency in recovery progress. Often, those of us in recovery are our own harshest critics, which is one reason why recovery’s therapeutic and spiritual articulations are so helpful. They offer clear signifiers that one is, in fact, actually better. How to operationalize the concept of recovery variables is one part of the challenge, but this paper highlights another possible way to consider the problem.

At the scientific level

At the scientific level, measurement becomes more rigid. There are often transparent and predictable courses of addiction pathology and rich commonalities historically labeled everything from “sin” to “disease.” Whatever ways these commonalities have been labeled through the ages is less important than their shared consistency (often due to the social effects in Western society). With the advent of modern psychology and medicine, these fields have made it possible to construct fairly consistent instruments for gauging these common signs and symptoms of pathology. These instruments can measure both the subjective and the observable, and while not without weaknesses; it has become relatively easy to diagnose and predict pathology in some ways using the commonality of related pathologies like genetic propensity, co-occurring illnesses, family histories, concepts like anxiety or depression, and behaviors like an inability to control how much one consumes, coupled with the desire, but subjectively-defined inability, to stop. Social indicators are related to modern relationships, labor, and social function.

Nevertheless, this relatively accurate understanding of pathological course and related co-occurrence has yet to really be equivocated across the recovery threshold. Until recently, most recovery was measured merely by the absence of the pathological, which, as many recovery scientists have asserted, is wholly insufficient for gauging recovery. The absence of pathological indices is not, in fact, a sign of health or well-being. It is merely the absence of observable pre-determined signals.

Theories of measures

The question then, as Mr. Coon is rightly excited to note, becomes how the addition rather than negation can be mathematically operationalized that, in turn, provides linkages that can be drawn between the experiential negative and the experiential positive, along with the social indices thereof? In other words, how can science build the statistical and empirical bridge between illness and wellness in ways that meaningfully link each? In my own work and that of my colleagues, we have tried to define and find ways to measure recovery. However, this article offers something new in that by linking positive changes over time to negative experiences, the interplay between illness and wellness can be understood. Furthermore, if it can be understood, it can be affected therapeutically and changed. What this article offers is something new to consider in my work, and I want to illustrate what I mean.

I have been trying to produce a theoretical understanding of how recovery occurs over time. Processes are the occurrence of change, which can only be measured through time. One sort of structural equation I have come up with considers the intrapersonal plus the interpersonal (i.e., dual aspects of relational health with self and others), set against or compared to the stability of the recovery identity as it moves across a second component consisting of a measure of stability in daily roles and settings.

This second component comes from Bronfenbrenner’s development model across ecologies (e.g., student identity stability at school, among friends, and at home). Bronfenbrenner (and others) have theorized that when positive aspects of one’s own identity and development become stable across multiple life spheres, one has achieved a degree of psychosocial stability. So, for example, I am a person in long-term recovery, whether I am celebrating a wedding, consoling a friend in a bar, watching re-runs at home on the couch, or at work typing on my computer. At no time in any of these environments do I consider myself to not be in recovery, and if any such environments or roles threaten that identity, I will prioritize it over other concerns, no matter the context. Alternatively, consider one’s identity as a parent – a lifelong role and one in which “good” parents prioritize over all other concerns and roles, even when such settings, roles, and concerns might conflict with the act of parenting. The reason why one’s role or identity as a father or mother is so enduring, applying this theory, is because of the stability and priority of that role and identity.

For me, this paper brings to mind an idea- that there is a direct and establishable link between that which threatens the stability of one’s recovery identity and that which is used to overcome or positively adapt while maintaining the identity as a priority.

The final component in my own model is time. How and in what ways do the identity and roles that define a person in recovery evolve? How does it become evident through one’s relations to the self and society, and what are the temporal and conditional parameters for such changes to not only occur but to become stable in ways that provide some degree of long-term permanency in one’s life?

Those of you working in the clinical trenches no doubt have your ideas about any number of variables such a model might require, how long they should be measured, and in what ways. When a person finishes treatment, what indicators do you use to evaluate their chances? When you discuss clients, what terms or signifiers do you highlight that describe or predict their recovery course?

This understanding and measuring of recovery is an essential incremental step in recovery science; though not yet fully realized, scientists like myself and my coauthors have been working on this very idea. However, what is evident in the article cited by Mr. Coon is that perhaps we can do an even more granular, reflective, and perhaps more statistically sound analysis that bridges the gap between pathological metrics and recovery metrics.

The Novelty Here

What is novel in this paper is the mathematical approach. I am more of a theorist than a statistician, so my understanding is relatively weak in terms of how useful certain models may be. Still, at least half a dozen ways exist to measure longitudinal and multivariate clusters of feelings, thoughts, actions, and behaviors (including TVEM). Even in a single measure, one might be able to better select the appropriate tool of prediction if the proper variables are linked with the temporal component. (For example, what do you look for in someone with say, a year on medication-assisted treatment [or any other mode] to gauge their progress?)

One of the first statistical procedures I do with data is to see how it behaves on its own over time before I start testing hypotheses. I do this because I find it interesting and because commonalities are easy to overlook when the rigidity of statistics meets the “squishiness” of human behavior, affect, and reason. Isolating phenomena to provable cause and effect is the last stage of any inquiry. More broadly, my curiosity is about what aspects of illness and wellness interact over time and which ones cluster together in ways that do not fit well within parametric tests. This paper is unique because it offers a statistical roadmap for this and some early variables of interest and prompts recovery scientists to consider the possibilities for future research.

For example, anyone who has ever gone through cravings knows what a miserable monomania it is. Cravings crowd out everything, demand to be satisfied, and essentially ruin everything they touch until satisfaction is rendered. It is a ruthless state of being. Nevertheless, for me personally, when I consider how much cravings used to dictate virtually all of my daily behaviors, I am overcome with a sense of liberation that recovery has offered me. Thus, there is a relation between the abject suffering of craving and my sense of liberation – not just in early recovery but throughout all the years of my recovery. Each day, I feel a sense of gratitude that my consciousness upon waking is not unceasingly driven by a singular obsession that must be satisfied before any and all things can be considered. This enduring sense of liberation becomes a part of my identity as someone in recovery and as someone who sees themselves as “free.”

Regarding variables in this example, my recovery would be mainly centered on a concept of freedom if I measured it. Thus, freedom is a significant primary variable that requires the misery of craving during my pathology to manifest the magnitude in which I experience freedom at a daily level in recovery. The depth of the variable of freedom (i.e., its measurability) takes its cue from the inverse pathological deprivation thereof and in ways distinct from the experience of an individual without substance use disorder. With models such as TVEM, I can build out a whole set of variables on both the cravings polarity and freedom polarity and then observe them interacting over time, all under the recovery variable, which is absent but implicit, but that becomes apparent if I compare it to a non-recovery sample longitudinally. And this can be done (in whole or in part) in several other statistical ways as well.

Think about the impact of this – there are thousands of such relations between pathological states and the inverse states of wellness. We can now consider how we might understand these inverse variable combinations or clusters statistically and longitudinally. Finally, if I leave you with nothing else in this post, such a relationship between variables is exciting because it can finally synthesize a link between the pathological course of addiction and the version of that course into health and recovery.

Further Reading


Shelton, L. (2018). The Bronfenbrenner primer: A guide to develecology. Routledge.

Shiyko, M. P., Lanza, S. T., Tan, X., Li, R., & Shiffman, S. (2012). Using the time-varying effect model (TVEM) to examine dynamic associations between negative affect and self confidence on smoking urges: Differences between successful quitters and relapsers. Prevention science13, 288-299.

Lanza, S. T., & Linden-Carmichael, A. N. (2021). Further applications and future directions. In Time-Varying Effect Modeling for the Behavioral, Social, and Health Sciences (pp. 133-147). Cham: Springer International Publishing.

Flannery, K. M., Vannucci, A., & Ohannessian, C. M. (2018). Using time-varying effect modeling to examine age-varying gender differences in coping throughout adolescence and emerging adulthood. Journal of Adolescent Health62(3), S27-S34.

One thought on “Additional Commentary on the Mathematical Model of Recovery

  1. This does a great job of capturing one of the essential elements of addiction that differentiates it from other AOD problems and explains why recovery is much more than a category or concept for people who have experienced addiction with its loss of freedom and the liberation that recovery represents.

    “anyone who has ever gone through cravings knows what a miserable monomania it is. Cravings crowd out everything, demand to be satisfied, and essentially ruin everything they touch until satisfaction is rendered. It is a ruthless state of being. Nevertheless, for me personally, when I consider how much cravings used to dictate virtually all of my daily behaviors, I am overcome with a sense of liberation that recovery has offered me. Thus, there is a relation between the abject suffering of craving and my sense of liberation – not just in early recovery but throughout all the years of my recovery. Each day, I feel a sense of gratitude that my consciousness upon waking is not unceasingly driven by a singular obsession that must be satisfied before any and all things can be considered. This enduring sense of liberation becomes a part of my identity as someone in recovery and as someone who sees themselves as “free.”

    Regarding variables in this example, my recovery is mainly about freedom if I measure it. Thus, freedom is a significant primary variable that requires the misery of craving to manifest the magnitude in which I experience freedom at a daily level. The depth of the variable of freedom (i.e., its measurability) takes its cue from the pathological deprivation thereof and in ways distinct from the experience of an individual without substance use disorder.”

    I’d go further. SUD is such a broad category that most people with an SUD do NOT experience that loss of freedom, making addiction and other SUDs categorically distinct and, therefore, “recovery” from each categorically distinct.

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