Blogs

Scenario Planning with Causal Queries

This technique supports health care organizations’ planning. Emerging recently in healthcare, scenario planning is not new in the business and scientific worlds and gives a deep experience to draw from. As a planning tool, causal queries differ from simple predictions by framing the future as truly new and unique and not fully described by past events. Support for a future orientation includes more than quantitative data analytics of known data, but a qualitative suite of potentialities generated from domain experts. This blog will suggest how to develop a formal mathematical interaction that blends the past and the future.

Causality & Counterfactuals

The first dive into quantitative support for the future briefly explains what a causal approach offers. The causal approach has foundational principles; first the direction of influence from cause to effect, and next the context of the cause and effect relationship which allows elevating counterfactuals to where causal queries include data from the past and potential future data. This is a complex concept essential for causal queries that are not limited to known, observable data. The technology discussed here derives from Judea Pearl’s decades long work in cognitive science and statistics. An excellent introduction is “The Book of Why” (Basic Books 2018), which complements his mathematically oriented Book “Causality” (Cambridge University Press 2009). An excellent lead into the mathematics and philosophy of Causality is Dr. Pearl’s “Ladder of Causation” which will be the basis of the discussions to follow. The above foundations provide the basis for the distinction of cause and correlation, and with help from the hierarchy of the Ladder of Causation, real world and pragmatic queries become possible. For those unfamiliar with causal methods, which in the professional and technical worlds of healthcare, includes most of us, the Ladder will be grounding and locates data in a framework that explicitly supports causation. The Ladder will be radical, for the simple reason that in the confusing world of the healthcare ecosystem, all suffer from data overload, mandates, nonsensical requirements for compliance, and lack of flexibility and interoperability in the technical fields that interferes with the basic mission of providing person centered healthcare. The power of the Ladder elevates causal methods to addressing these concerns by blending the past and the future to understand how actions today will change the course of history for tomorrow.

The Ladder of Causation

 

It is clear a basic understanding of how causal methods differ from prediction (via statistical methods) arises from accepting that cause and correlation can be distinguished mathematically using graphical methods. The Ladder elucidates a hierarchical relationship of information; the first rung as observable; the next action based on broader classes of information than just observables; the third counterfactual. The features of these rungs include all the methods of information analysis and data architecture in common use in healthcare, but does not include counterfactuals. More is required than standard methods to achieve causal explanatory value. Before touching on the details to make sense of the utility of the Ladder, modelling mathematical relationships to support the goal of determining causal effects, framed by scenarios, creates the payoff of using the causal ordering of information in building a model query. To go from the Ladder to Models requires several steps. The two forms of causal models described in this blog include Structural and Graphical. The first is symbolic and the second is visual. Each supports crafting variables that capture the fundamentals of causality, which is direction of influence from cause to effect, and context. The steps apply the fundamentals of causality by how variables are named as observed or unobserved, and ordered by relations to each other.

 

Structural Equation Model

The ecosystem however has an infinite number of past, present, and future decisions and outcomes, based on correlations that do not nor could not achieve statistical significance. The ability to infer causality statistically, requires randomized control trials, infeasible for most actions. As stated above, and what cannot be over emphasized; any action for actors at any scale in the ecosystem requires context, which can be organized in a mathematically structured way, as graphs, to support decisions acted on in an empirical or presumptive basis. These need not be significant, in the statistical sense. Well-designed graphical causal models can account for confounders and biases, and most importantly link an action X to an effect Y with a defined likelihood the relationship is causal. To briefly introduce the causal equation that shows this (the Structural Equation Model or SEM) is as follows:

M=(U,V,F)

M is the Model, which includes endogenous V variables, exogenous U variables with their relationship by functions, F. In this blog structural models can also be visual as graphs following the lead of the ladder of causation. To be discussed below graphical representations of variables is key in distinguishing cause from correlation.

U is a exogenous variable outside the world of actions, observed, unobserved, or latent sourced from any relevant place in the ecosystem of many worlds.

V is the set of variables, most simply X and Y, that are observed and available for agents of one world to select actions. These endogenous variables, causes and effects, are influenced by exogenous U variables that serve the role of context; in other words, as influence from many worlds of the ecosystem. These actions can be causal if they meet criteria to be discussed below. Pragmatically this one world is limited because causes and effects are multiple and complex, mathematical formulations are needed to describe them. Another blog will dive into this.

Recent work in Causality has extended the power of causal methods beyond idealized relationships of few variables (Antonucci, 2022). To follow is a section on multiple causation, average causal effects determined by sets of inequality relations, graphical methods to determine bias and confounding. Not to give the game away these new methods when applied to the ecosystem above will allow quantitative measurement of the infinite number of relationships demonstrated graphically when statistical significance is not possible nor needed.

The other model is Graphical, representations showing vertices and edges of U and V linked by F that define explanatory, causal or spurious relationships. However, only part of the ecosystem in a given scenario lends itself, or is necessary for causal interpretation. This is the purpose of the Model, to show what belongs in a particular realization of a causal query.

Causal Ordering

The graphic places causal ordering in the context of the ecosystem with observables from the past and the actions signified by Cubes. The ladder is contained in one moment (the Cube), the next cube by the terminology of causal ordering is “augmented”, meaning changed by the action (intervention) of the first Cube (the Moment). What a graph needs to convey is the geometric increase in data as the causal chain proceeds, which is shown by the red, yelow and green span at the end of the path of causal ordering on the right. The counterfactual potential endpoints of the Ladder extends beyond the moment of action (the cube), and is the summation of multiple actions changing the world of the agent as the explainer of the past and creator of a desired future. The future counterfactually is problematic because it could be infinite with many possible outcomes. There are tools to limit this high dimensionality which will be introduced below (Complex world of future potentialities). Limiting information in successive cubes allows cause and effect to be accessible to “human understanding”. This is where counterfactual “bounding” creates ranges of data, rather than point estimates from statistical parameters. Can this be done in a query tree? There is a technology called credal networks that does this, which is a topic for a future blog.

The HealthCare Ecosystem

The Master Graphic clarifies the hierarchical ordering of the Ladder of Causation.

In reviewing the Ladder’s detail, some general comments about why context derived from the ecosystem supports causal ordering, as shown in the sequence of information laden cubes in the above graph. Cause and correlation, never far from mind at any place in the ecosystem; from provider networks to plans, to evidence-based medicine, to cost containment, has become a mantra of statistical methods to show the hazard of decisions based on information of insufficient scale. These decisions demand statistical significance coming from the appropriate size of a population which puts a demand on decision-making agents that do not always have a world at their disposal that is free of unobservables. However, at the action level of the ladder, to expect decisions to meet the test of statistical significance, overlooks the importance of unobserved variables in the realm of low dimensions of most worlds.

The Master Graphic is basically an illustration of comprehensively organized information. Because causal methods account for context from many sources that impact causal ordering (with a privileged place of intrinsic information of the agent of the action step of the Ladder of Causation), the collection of ecosystem entities spans many scales. Actions are encoded based on the role of the agents, not their scale. Thus the Master Graphic has a place for any agent that creates of receives information that flows through the ecosystem. From a causal standpoint, small scale agents have an outsized role in changing the course of history, largely because it is possible to measure counterfactuals in small domains. Large domains, the space of statistical methods, miss the granularity of small scale, and thus miss a large swath of potentialities for the future. The Master Graphic is a tool to show actual, and counterfactual information, of all entities regardless of scale. From a pragmatic standpoint this comprehensiveness of information empowers the agents of the scenario planning process to be complete in their assessment of their success in a complex ecosystem.

The HealthCare Ecosystem

Differing Lenses for Causal Queries

The illustration below orients the ecosystem scale to a single agent, in this case a provider. Imagine a scenario where the objective is to meliorate the effects of healthcare complexity on physician burnout, a massive problem easy to identify but hard to solve. The solution requires a deterministic lens that accounts for the granularity of a provider’s interaction with a single patient. This lens prioritizes engagement. But when this granularity is lost, or more correctly the possibility of engagement on the providers terms is lost, estrangement results. The above pyramids from the ecosystem show how release from estrangement requires a balance of lens. The top down pyramid on the left denotes the hierarchy of transactions which uses the lens of probabilities; the inverted pyramid on the right shows a deterministic lens, heavily weighted with counterfactuals. Measurement tools are different for these lenses, but these lenses interact in quantitative ways. Physician engagement likewise is heavily weighted with hypotheticals, or counterfactuals. Accounting for this is how physicians do their job. Given a platform where methods link determinism and probabilities in the common language of graphical causal models, the tricky problem of burnout can be addressed. Causal methods highlight interventions in the spirit of the ladder of causation that target interventions that change the world as we know it, in this case the outcome of a new world is physician engagement.

The cycle of engagement is very abstract, and concrete examples will follow with the details of a scenario plan to follow. Before the details make sense, more insight into the details and causal terminology need more depth. Understanding the deterministic lens is the key to deriving causation from correlations, moving from; “correlation is not causation” to “there is no causation without correlation”. In the causal world of the single actor, variables that define the moment of action are:

• V (intrinsic/endogenous to the single moment)
• U (extrinsic/exogenous that may affect the causal mechanisms F and V variables)

This separation of V as endogenous from U as exogenous, creates the context from the ecosystem that impacts endogenous causes and effects. This lens works in the single actor scale, the “You and Me” with features as variables V in the structural causal equations. These features are not washed out as averages in statistical distributions but exist as unique values in causal equations. Subscribing to this lens of determinism allows mathematical relationships to include counterfactuals along with observables and derived abstract parameters to be presented in a visible set of vertices (nodes) and edges (links as in network) that moves correlations into the causal realm. To reiterate, the single agent in the ecosystem, acting as “you and me”, with actions supported by unique deterministic data, allows causation to move up the ladder to actions “that change the world”, then to the complex world of counterfactuals as potentialities for the future.

Complex World of Future Potentialities

Though it may seem the deterministic lens makes data architecture simpler, counterintuitively this lens creates a complexity vastly larger than the scales of networks and populations. To better understand what this statement means, one can consider a causal query framed by a government plan compared to a patient centered query. This amounts to relating value-based purchasing and accountability to actions by and for “you and me”. A government plan would query what policy gives the desired effect such as cost containment and quality. Implementation relies on probabilities to create mandates such as benchmarks and compliance metrics, applied to populations with no deterministic patient centered granularity. The result is blanket application of a large swath of interventions that may have the desired effect on a few with unnecessary effects on the many. This mandate therefore creates inefficiency with the potential to raise costs for the many even though benchmarks lower costs for the few (Berkson’s paradox). A policy level query may account for administrative costs, or it may not. In a similar vein, a granular patient centered query would not likely focus on global costs, but can account for point of care costs, presumed under the control of you and me.

In the aforementioned government plan, a likely scenario generating a patient centered query would be forced to focus on the global effect of factors originating from the ecosystem. In causal terms, U exogenous variables, expressed as a maze originating as financial and clinical mandates and guidelines. The query would be: can a scenario be developed that narrows the complexity of the maze by a focus on a subset of V variables (in causal terms V endogenous variables)? Preauthorization mandates give a clear example of estrangement; where engagement prevails when the objective of preauthorization is met with an alternative causal pathway visualized by a linked structure of V variables. Here the contrast between policy and you and me is striking. Policy has few variables that can be controlled; you and me has far more V variables that retain the uniqueness of the patient deterministically, not generated by probabilities. The method for teasing out the V variables is not statistical, but graphic and relies on subject matter experts qualitatively narrowing the scope of V variables that are candidates for cost containment from a deterministic lens. These experts can span the Ladder of Causation with insight into what is possible matched to what is observable.

Complex World of Future Potentialities

Point Estimates vs. Bounds

Potentialities for the future framed as outcomes of any pathway through the ecosystem exist as combinations of:

• Known outcomes from prior experience (quasi counterfactual).
• Presumptive outcomes from inductive reasoning by subject matter experts (“white swan”).
• Unexpected unobserved causal effects (“black swan”).

In the formal, narrow view of counterfactuals, these are the obligatory absent outcomes of an action not taken. Causal ordering, links series of causes and effects temporally. An effect of one cause at a point in time is a cause of the next action. Pathways are successive, leading to cumulative outcomes, the result, a series of potential outcomes.

Potential outcomes techniques, a branch of causality (Pearl ref 2012), blends the past and the future by linking the known and experienced prior outcomes to the breadth of future potential outcomes. The ladder of causation describes this interplay of observables to actions, to counterfactuals relevant both to an event, and to cumulative effects of events on future outcomes. Causal ordering comes into play in the structural equation framework by adjusting U exogenous and V endogenous variables within each successive event on the path. For example, an outcome Y (V variable of an event) caused by X (V variable) provides an X’ given U background variable. X’ becomes the cause of Y’ as the next step, and so forth. Note that U has features that change based on the effects of actions , and features that stay the same, a fact that defines the pathway of interest. Pathways as alluded to above are mostly about context in the ecosystem from the deterministic point of view. Context supplies meaning to the causal relations of model M by ordering U, V and F functions that link the two. Another way of saying this is to note how background U changes as one event leads to another successively.

The glue that holds causal ordering together in pathways is counterfactuals. To no one’s surprise the above notation is an oversimplification. Correlation established statistically is not causation because there is no one-way ordering of information, not unexpected when an = sign is the functional relationship between variables. Causal ordering is one way with the arrow denoting the functional relationship, which is illustrated graphically. Graphs are essential in visualizing functional relationships, which can be numerous when considering counterfactuals. For example, from the lens of a single action of an event, observed when a potential action is selected from many possible actions, the expectation of a future outcome is not one-to-one with the selected action causing a predetermined outcome. In the potential outcomes’ framework, many possible outcomes could be observed, those that are not are counterfactuals. The potential future outcomes may or not have been observable or realized somewhere in the ecosystem, and can include outcomes from inductive reasoning. Realistically, the range of potential future outcomes is infinite, and it is impossible to express this range with point estimates from statistical distributions of observables alone. This is the aspect of potential outcomes that is oriented to the past. Going to the other pole of the causal relationship, the future, the outcome Y given the action x (Do(X)=x in causal notation), looking to causes knowing the outcome also raise the potential of numerous possible causes. Managing the past and future together not a one to many nor a many to one relationship, but a combined many to many. These can be high dimensional relationships difficult to impossible to grasp as a humanoid.

Mathematical expressions giving a range of possible values for average causal effect (ACE) better describe cause and effect relationships than expectation of a single value with error terms. The acceptance of counterfactuals included both for cause and effects with range calculations showing causal effects equal to or greater than zero, expands the scope for mathematical approaches to distinguishing cause from correlation. One can see how point estimates fundamentally differ from range estimates. The former precisely define the past, the latter gives a strength of causal effect as an explanation for what could happen in the future. These mathematical subtleties as background for analysis of causal effects support the ladder of causation as it moves from the rung of observable to actions to the broad world of counterfactual possibilities. Clearly though, the ladder is illustrating a diffuse potential future rather than a precise one. Assuming the future replicates the past, cause is distinguished from correlation.

Healthcare in 3 Dimensions

Guide for Agency in a Stratified World of Worlds

The Causal Method’s power resides in the ability to include many types of information as a platform for decision support. It is not a problem to range from the thirty thousand foot lens of the broad ecosystem to the granularity of the single person as long as the causal equations permit the flow of complete information across these vast scales. This is the essence of interoperability, transparency, collaboration, accountability, and ultimately support for interventions at any level of the healthcare ecosystem. Of course all these desirable features run up against barriers, and the structure of causal equations (the U variables) identify the potential existence of these barriers which can be included in the structural causal equations.

Lacking in frequentist predictive modelling is acceptance of subjective data. Causal methods do allow subjective data curated by agents qualified as experts in a particular world of the ecosystem. These experts are a community of “knowers”. Causal modelling is work, and demands multidisciplinary collaboration to qualify data as candidates for inclusion. To be causally meaningful both objective and subjective data must be included if in the judgement of experienced domain experts, actions always proceed with diversity of inputs into decision-making.

With actions at any scale always existing in the context of an ecosystem, whether vast or local, agents collect and collaborate within and outside of their world. The ecosystem in fact is many worlds, with more or less interoperability and transparency among these worlds. The operation of the Ladder of Causation is designed for one world, if an action in this world includes input from another world, or many worlds, the Ladder becomes “augmented”. This augmented world is causal, if the agent of the original world accepts counterfactuals along with observed data. Again, correlation alone is hazardous, if causation is ignored by overlooking the type of subjective information used in everyday decision making.

Narrowing the discussion to the smallest scale, the single person (or patient), it becomes clear that carrying forward on the causal path, with all the information the single person entails, creates a geometric explosion of data. It is one thing to have complete information about a complex person for decision support, it is another to expect this data to be translated unaltered to another level. At these larger scales, subjective data becomes irrelevant, insofar as these do not result in a causal relation to agents of networks or populations. What can be carried forward from level to level (as per the Healthcare ecosystem graphic), are counterfactuals as causal principles. For example: disease prevention, cost effectiveness, compliance with standards of care, social determinants of health, psychosocial priorities, and others; are principles not directly linked to individuals, but are linked to populations. This interoperability of the person in the scale of the ecosystem means these principles are fashioned as quantitative inputs (yes or no binary checkboxes) easily applied to individuals. This satisfies interoperability, itself a principle; however, principles alone do not capture all the person level data. Currently it is a work in progress in the counterfactual field (Antonucci) to reduce the dimensionality of person level data. This person level data is fundamental, recognizing this offers the opportunity for interventions to augment the many objectives of agents in any world of the health care ecosystem

The Next Step

Scenarios as examples of Causal Methods to move from abstract explanations to quantitative support.

It takes a village, many skill sets come into play to execute graphical causal models from statistics to mathematics, to capturing qualitative expert domains and translating to quantitative structures. What is presented here is data architecture to build causal models, a prelude to sleuthing with the data.