History-Dependent Treatment Policies

Panel Data

Causal Inference

Evaluate a dynamic treatment regime inside a Gaussian panel scan, and contrast two regimes without collapsing posterior uncertainty.

do(set=) replaces a treatment with a schedule that is fixed before the first step. A dynamic regime is different: the action at time t is a rule of the simulated history. policy= evaluates that rule inside the scan, so a time-varying confounder can respond to earlier treatment and then affect the next action.

The call below uses the fitted greenhouse model: stress ~ lag(stress) + lag(water) + heat and growth ~ stress + water + stress:water. Only stress and water require initial states. Here data is the pandas frame used to fit model.

from pathmc import TimeSchedule, TreatmentPolicy, current, previous, where

n_times = data["time"].nunique()
responsive = TreatmentPolicy(
    "responsive",
    "water",
    where(previous("stress") > 0.5, 1.0, 0.0),
)
result = model.do(
    policy=responsive,
    simulate_over="time",
    horizon=n_times,
    initial={"water": 0.0, "stress": 0.0},
    random_seed=7,
)

Contract

policy must be a TreatmentPolicy. The rule is an expression (current, previous, where, arithmetic, and comparisons) or a TimeSchedule or a finite number. Python if, and, or, and not are rejected at expression-construction time. current(name) is legal only when that measurement is known before the action; an outcome caused by the current action cannot choose that action. previous(name) at the first fitted time is the explicit pre-sample state.

horizon is required and must equal the fitted time count. It is not inferred. simulate_over="time" is required. n_simulations defaults to 256 and must be at least 2. kind="predictive" is rejected because the policy path always integrates process noise. Omitting random_seed records the seed that was used.

The model must be a scan-compiled Gaussian lag panel. Latent variables, non-Gaussian families, adstock and other transforms, categoricals, and residual covariance are rejected rather than evaluated by a weaker executor. Do not add a scientifically meaningless lag just to unlock policy=.

initial must cover every observed lag base plus any previous() reference the rule reads. Extra keys that the rule or the scan does not use are rejected. Values are business units. A scalar broadcasts; a mapping must contain exactly the fitted unit labels.

What the result keeps

do(policy=...) returns a PolicyRun, not a DoResult. Population summaries are means over units and simulations, with dims (time, chain, draw). simulation_mcse(var) is the Monte Carlo standard error within each posterior draw. It keeps chain and draw, and keeps time until aggregate_time reduces it. aggregate_time(var, reduction="sum"|"mean"|"last") is the cumulative or terminal estimand. Pass keep_trajectories=True for unit paths; those dims are (chain, draw, simulation, unit, time).

Contrast two policy results only when they share the posterior, population, exogenous inputs, fixed interventions, seed, horizon, and simulation count. Initial values must agree for every state used by both policies. A rule using previous("rain") can be compared with a schedule that never reads previous rain: supply that initial value only to the rule that needs it. The contrast retains both policies’ baseline requirements, so a later comparison still rejects conflicting values.

Apply the same time reduction and reporting window to both results before subtraction, or subtract their trajectories first and then aggregate the contrast. For example, cumulative growth over the whole fitted grid cannot be paired with mean growth or a total over a shorter window. The contrast is a paired difference; it does not declare a winner. Report growth and water, or whatever the outcome and the treatment are, separately.

A threshold on a stochastic state does not match the noise-free do(set=..., kind="mean") path. The reported mean averages posterior draws and simulations. A mean-substitution implementation, which plugs the conditional mean in for the random state before applying the threshold, is not this estimand.

Assumptions

A causal reading needs sequential exchangeability, consistency, treatment support over relevant histories, model adequacy, and no cross-unit interference. Static backdoor checks do not prove longitudinal identification. A marginal min/max warning does not establish sequential positivity: support has to hold on the histories the rule visits, not only inside the observed range of the state.

See Water on a schedule—or when plants need it? for the greenhouse panel this contract is written against. The synthetic stress index is pedagogical, not agronomic advice.