Introduction
Most studies in medical and behavioral science use statistics with the assumption that the conclusions derived from calculated mean-level results apply at least probabilistically to most members of the sample. Said in another way, it is assumed that measurement of central tendencies and variability between people can be used to model central tendencies and variability within persons.
Measurement theorists have long understood that this assumption could be wrong (Cattell,
1952) and it has sometimes been challenged in areas such as developmental psychology (Wohlwill,
1973), epigenetics (Gottlieb,
1992), or behavior analysis (Peters & Sidman,
1961). In the main, these intellectual objections have made little impact and most of the modern medical and behavioral science is based on normative statistical approaches.
Peter Molenaar (
2004) appears to be the first to have linked this issue to a well-established concept in the physical sciences: ergodicity (Birkhoff,
1931; Boltzmann,
1885; von Neumann,
1932). Although its focus is on modeling the distribution of elements in space and time, in a more abstract sense the ergodic theorem describes the conditions under which data applying to a collective also applies to components of that collective. The theorem reveals that such an extension is only proper if the elements are ergodic. A simple way to think of ergodicity in a fashion that relates to medical and behavioral science is that for ergodic events the means and standard deviations of all individuals across time and for all cross-sectional samples of collections of individuals at any given point in time will be the same (Gates et al., in press). That is sometimes true and sometimes not in the physical sciences (Cherstvy et al.,
2019; Galenko & Jou,
2019; Kuehn & Abrahamson,
2020), but it is rare to the point of being absent in the human and life sciences (Horst,
2008; Kelderman & Molenaar,
2007).
A small number of empirical studies have shown that nomothetic and idiographic analyses can lead to different conclusions (Fisher et al.,
2018; Miller & van Horn,
2007; Molenaar & Campbell,
2009) but these ideas have not been widely adopted in intervention research. One reason may be that these studies have generally been based on complex methods or with data requirements that are far from typical research practices in the medical and behavioral sciences. For example, while complex network analyses, p factor analyses, replicated multivariate time series analyses, and other methods can be applied to longitudinal data sets when scores of within person observations are available, such data are usually not available from most randomized controlled trials, which typically have only a few measurement points. The net effect has been that theoretical alarms about the applicability of normative analyses have seemed empirically remote, and empirical tests of the need for idiographic data are both uncommon and readily set aside.
This issue has recently taken on special urgency in psychological intervention and the health sciences writ large because research attention is increasingly being focused on identifying processes of change that meaningfully and reliably apply to those presenting for treatment, in such areas as process-based therapy or personalized medicine. Focusing on processes of change creates a conundrum. On the one hand, a change process cannot be ergodic because stationarity is a key feature of ergodic events (Molenaar,
2013); on the other hand, knowledge drawn from a truly idiographic approach cut off from nomothetic conclusions cannot be applied to others. One possible solution would be for analyses to initially be based on idiographic conclusions, examined in the context of within person variability. These individual analyses could then be gathered into nomothetic generalizations that are ultimately shown to improve idiographic fit—what has been called an “idionomic” rather than normative approach (Hayes & Hofmann,
2021).
The absence of ergodicity does not invalidate nomothetic generalizations provided that generalizations are derived from intra-individual variation. It is important to examine ways to begin analysis entirely idiographically using commonly available data before gathering individuals into similar subpopulations and examining whether doing so improves the fit between individual behavior and subpopulation average behavior. Applied researchers may believe that they are doing something similar with moderation analysis, cluster analysis, growth curve modeling, longitudinal mixed regression models, and so on but these standard methods interpret individuals in the context of inter-individual variability first—precisely the step that may not be justified if the ergodicity assumption is violated (Molenaar,
2013). In contrast, if analyses that begin with intra-individual variability were routinely successful, intervention scientists might be able to select targeted interventions tailored to a more homogenous group or subgroup of similar patients. It remains empirically untested, however, whether such an approach would render more accurate and useful predictions in clinical trials.
Theoretically, subgroups can be based on any observable, treatment-relevant variable ranging from scores on a questionnaire, to genetic polymorphisms, to nurse observations. The growing evidence in support of a focus on processes of change, however, suggests that the treatment relevance of building subgroups will be increased to the degree that the grouping variable a) stipulates a hypothesized mechanism of action that can be assessed and manipulated, and b) predicts a clinically relevant outcome; e.g., visual acuity, white blood cell count, mortality, depression symptoms, well-being, and so on (Gloster & Karekla,
2020; Hofmann & Hayes,
2019).
The present study implemented this process-based strategy with a sample of patients who were assessed on hypothesized mechanisms of action consistent with state-of-the-art theories of change during psychotherapy (Gloster et al.,
2017; Hayes et al.,
2019; Kashdan & Rottenberg,
2010) in addition to the measurement of typical syndromal features. We included variables previously shown to be active mechanisms of change in psychotherapy using nomothetic methods, such as mindfulness, relating differently to one’s thinking, and acting on one’s values (Hayes et al.,
2020).
Different patients will respond differently to exercises designed to change such processes: e.g., some will improve their mindfulness skills, others may not change at all or even worsen in their ability to be mindful. Because change occurs over time, it is necessary to collect longitudinal data to model change trajectories (Gloster et al.,
2014) and to assess it in terms of intra-individual variability. In the long run, daily diary apps or wearable automated data collection may allow the routine use of longitudinal models that are based on a series of several dozen longitudinal data points (Gates & Molenaar,
2012; Gates et al.,
2017), but at the moment, data of that kind is rarely part of existing research designs. In the present study, we examined the application of a relatively simple idiographic approach built upon a limited number of data points of the kind routinely collected in clinical practice. In this approach, each individual was characterized in a bottom-up way that involved estimating individual effects that were uninfluenced by other individual effects. These were then clustered in a fashion that never treated the individual as “error”.
In the present study, this idionomic strategy was used to examine three key aims: (1) test whether assumptions of ergodicity are met or violated in clinical data; (2) test whether building subgroups using a bottom-up idiographic procedure before nomothetic analysis leads to different conclusions about underlying change than traditional nomothetic approaches; and (3) test whether idiographically identified bottom-up subgroups predicted a clinically meaningful distal outcome (namely, well-being), suggesting possible advantages for a more idionomic approach. These questions were examined using longitudinal data from a real clinical sample with time series data. Examining these questions under real world conditions was designed to maximize the chance that the results are clinically relevant.
Discussion
The efficacy of psychotherapy for mental disorders is well documented. The vast majority of studies show that on average patients improve to a statistically significant degree and that this change is clinically meaningful (Butler et al.,
2006; Gloster et al.,
2020a; Gloster et al.,
2020b; S. Hofmann et al.,
2010). Although it is an oversimplification to assume that results from randomized trials apply to a given individual, this interpretation is common and individual patient trajectories are extended from such studies into clinical care. The present study presented a method for identifying different patterns of change and illustrated that meaningful subgroups can be found even when the intervention has been shown to be effective at the group level. The present study also points towards one possible way to methodologically and empirically explore such sub-groups.
Ergodicity requires both stationarity and that the same dynamic model applies to all constituent elements. In the present study, the data did not meet the ergodic assumption. We found that, for example, defusion was related with either more symptoms, less symptoms, or not related at all—depending on the individual. Furthermore, very different trajectories were present over a treatment of eight weeks. Cluster analysis based on idiographic data identified distinguishable patterns of deterioration, no change, or improvement. When looking at week-by-week patterns, a group of sudden gains was visible. When results were examined idiographically relevant to intra-individual variability, the relationship of a given process to outcome could vary from significantly positive to significantly negative. Thus, both of the key requirements for ergodicity (stationarity and common dynamic models) were violated. Because the ergodic assumption was demonstrably violated in these clinical data, relying exclusively on nomothetic results would misrepresent some individuals. It is not hard to see why from the present data: at the purely nomothetic level these idiographic differences largely cancelled each other out, and process to outcome relationships were no longer evident.
Recent studies on ergodicity have reached the same conclusion, though the percentage of a sample that belongs to a sub-group that is not characterized by the nomothetic finding differs (Fisher et al.,
2018; Sahdra et al.,
2023). The present results also suggest one possible way forward. In the present approach, analyses began by examining entirely idiographic data linked to intra-individual variability. Nomothetic clustering procedures that avoided inter-participant averaging as input then identified multiple sub-groups of patients with varied patterns of change. These bottom-up analyses allowed for the identification of differentiated patterns person by person that predicted a clinically useful distal outcome, well-being, for at least some of the key processes (acceptance, defusion, and own values) that were targeted in the underlying psychotherapy trial. Conversely, the three other targeted processes (being present, steady self, and being engaged) and idionomically identified patterns of symptom change, were not related to distally assessed well-being. Said simply, bottom-up idionomic analyses lead to different conclusions than top-down nomothetic analyses. It is not widely appreciated that purely nomothetic conclusions and those based on idiographic data within the same population can be virtual opposites. This is known as
Simpson’s paradox and it is quite common in behavioral and medical areas (Kievit et al.,
2013). As a simple example, in all large groups of people better typists will both type fast and make fewer errors per typed word, resulting in a negative correlation between speed and errors; nevertheless, as individuals, every single typist regardless of expertise will make more errors the faster they type, reversing that relation. Keivit et al. (
2013) suggest several steps to avoid falling prey to Simpson’s paradox, including several of the steps taken here: intervene; study change over time idiographically; conduct cluster analysis; and visualize the data.
In order to make progress towards personalized interventions, it is important to understand multiple patterns of change in their own right. By extension, this will help advance our understanding of the underlying processes of change initiated by an intervention. The exact number of subgroups and trajectories is likely a function of the subject matter, intervention, and clinical presentation of patients. Although these patterns shown here are largely consistent across the variables examined in this study and with patterns hypothesized in the literature (Lutz et al.,
2013), we do not claim that these are the only patterns that exist. Indeed, much more research is needed to help identify the nature of change itself. We do argue, however, that the idionomic results from the present study can be extended to individuals if idiographic patterns are the basis for such an extension.
In the present study with patients suffering from mental disorders, the idionomically derived clusters of change based on accepting and defusing from one’s thoughts as well as engaging in values were most predictive of the distal outcome of well-being. Clusters of change patterns based on other variables were less differentially predictive of the distal outcome. Importantly, across all process variables and symptoms, the trajectory of the cluster of patients that declined the most by the end of treatment was already visually discernible from the other cluster of patients by the fourth or fifth week in the graphs depicting week-by-week change per cluster. In a fully idionomic approach, the implications of such nomothetic extensions would be formally tested. For example, when treating patients suffering from mental health issues a clinician might pay particular attention to the weekly development of acceptance, defusion and values after a month or so of treatment. If the patterns observed here are replicated in other studies, it would enable clinicians to begin to pinpoint the timepoint within an ongoing psychotherapy at which their current patients’ outcome is most predictive of an outcome similar to the bottom-up derived empirical clusters. If one’s current patient’s course is most identified with a cluster associated with high levels on the desired distal outcome, then the therapist can hold the course. If, however, the patient’s course is most similar to a cluster associated with poor prognosis, changes can be introduced. Such individualization of the treatment would save resources and hopefully improve the lives of patients via more efficient care.
It is noteworthy that these results were obtained in a real-world clinical sample that was relatively small in terms of participants and time points. The bottom-up idionomic approach thus appears to be reasonably sensitive, perhaps in part because the building of homogeneous subgroups partitions the variance in ways that increase statistical power. This could be an advantage for clinical research aimed at understanding processes of change.
Other lines of research on the science of change suggest that there is fertile ground for idionomic approaches. Personalized medicine, for instance, aims to tailor interventions by grouping patients into categories based on indicators that are predictive of outcome. Within the field of psychotherapy, efforts are underway to systematically organize the understanding of processes of therapeutic change as something separate from the techniques or therapies that give rise to change. Examining the processes of change using idionomic bottom-up approach may help realize this goal.
This study has multiple limitations. First, our sample size was relatively small. Larger sample sizes will allow us to detect more complex patterns of change and will be more representative of the clusters we are likely to identify in the population. Second, the iterative process used in this study of calculating the clusters separately for each variable does not allow for the real possibility that the variables dynamically influence each other’s development. We did not have sufficient power to conduct such dynamic analysis. To our knowledge, such multivariate approaches are currently missing and statistical work in this area is needed. Third, although this approach allowed for clustering of shorter time series than the currently most used models, a good approach to model individual cluster time-series analysis for shorter time-series is also needed. Likewise, the idionomic approach used here relied on distance between observations to derive clusters. Approaches are needed that can also use time as a weighted parameter. Fourth, for clarity and simplicity we included participants with complete data sets. Future research may examine what effect missing values have on the results. Finally, these real-world data were derived using one intervention (i.e., Acceptance and Commitment Therapy) and the variables targeted the hypothesized processes of change. It is necessary to test whether these or other clusters of change emerge with different therapies and targeted processes of change.
To rectify these limitations, future studies should focus on systematically investigating how to translate results from this approach into clinical practice, comparing them to other emerging idionomic approaches (Gloster & Karekla,
2020; Snijders & Bosker,
2012). This could include further tests of what distal outcomes the idionomically identified clusters predict and which they do not. Studies could also explicitly test whether tailoring treatment based on clusters improves outcomes for individual patients.
In conclusion, as clinical change applies to particular people, average is not enough. Whereas nomothetic approaches inform about the efficacy of an intervention in general, ergodicity is seldom present and the nomothetic statistics are incomplete and may at times lead to faulty conclusions. Additional, bottom-up idionomic approaches are needed to augment traditional knowledge from clinical trials to better understand the process of change and to use this knowledge to provide better treatments for all subgroups of patients.
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