Predictive Selection Is Not Causal Discovery

Selection Answers a Predictive Question

Lasso and elastic net can identify features that help predict an outcome in the data used to build a model. That is valuable when the task is to forecast claims, prioritize cases for review, or estimate future demand. It does not, by itself, answer a different question: what would happen to the outcome if we deliberately changed one feature or exposure? A feature can be predictive because it is a cause, because it is associated with a cause, or because it records information about how cases were selected or managed.

This distinction matters in actuarial work. A model might use an inspection indicator to predict losses accurately. Concluding that inspections cause losses would be a different claim and could lead to a poor decision. For predictive analysis, the central concern is how well the model predicts new cases under the intended conditions. A causal claim concerns the consequences of an intervention and requires evidence about how exposure and outcome are related.

Definition: A predictive association is a relationship between recorded features and an outcome that helps estimate the outcome for cases drawn from a relevant population. A causal effect compares outcomes under alternative interventions or exposure states. In potential-outcome notation, for a binary exposure \(A\), the average causal effect is \(E[Y(1)-Y(0)]\), where \(Y(1)\) and \(Y(0)\) are the outcomes the same target population members would have under exposure and non-exposure, respectively. Observed data usually reveal only one of those outcomes for each member.

For a continuous response, a lasso fit commonly minimizes squared prediction error plus an \(L_1\) penalty. Elastic net combines \(L_1\) and \(L_2\) penalties. For example, with standardized predictors \(x_{ij}\), an unpenalized intercept, and a Gaussian-response model, one form of the elastic-net objective is

\min_{\beta_0,\boldsymbol{\beta}} \left\{ \frac{1}{2n}\sum_{i=1}^n \left(y_i-\beta_0-\sum_{j=1}^p x_{ij}\beta_j\right)^2 +\lambda\left[\alpha\sum_{j=1}^p|\beta_j| +\frac{1-\alpha}{2}\sum_{j=1}^p\beta_j^2\right] \right\}.

Here \(n\) is the number of observations, \(p\) is the number of predictors, \(\lambda\) controls the penalty strength, and \(\alpha=1\) gives the lasso penalty while \(0<\alpha<1\) gives an elastic-net combination. A nonzero fitted coefficient means that the feature is retained in that penalized model at the specified settings. It does not mean the feature is a cause. The objective rewards predictive fit while controlling coefficient size; it contains no term that tests whether an intervention on a predictor would change the outcome.

The objective above describes a Gaussian-response example, not every lasso or elastic-net application. For other outcome types, the model’s fitting loss changes. The core interpretive point remains: selection is defined by the chosen prediction procedure, response, data, and penalty—not by causal status.

Confounding and Proxy Variables

A confounder is a variable that helps explain why an exposure varies across people and is also related to the outcome. If it is not accounted for, the observed exposure–outcome association can differ from the causal effect of the exposure. A proxy variable is a recorded feature that carries information about another factor, such as an unrecorded risk characteristic. A proxy may predict well even when changing the recorded feature itself would not change the outcome.

The reason confounding can produce an association is visible in the law of total probability. If \(Z\) is a risk group and \(A\) is an exposure, then

P(Y=1\mid A=a) =\sum_z P(Y=1\mid A=a,Z=z)P(Z=z\mid A=a).

The overall event rate combines the within-group rates with the group proportions among those exposed or unexposed. Even if the exposure has no effect within either group, different group proportions can make the overall rates differ. This mixture explains why a strong predictive association need not be a causal effect.

Worked Example: A Predictive App Feature Confounded by Risk

A hypothetical insurer records whether a policyholder uses a risk-monitoring app and whether a claim occurs during the year. App use does not change claim risk in this example. However, high-risk policyholders are more likely to use the app. Among high-risk policyholders, the claim probability is 0.40; among low-risk policyholders, it is 0.10, regardless of app use. Of 200 app users, 180 are high-risk and 20 are low-risk. Of 200 nonusers, 20 are high-risk and 180 are low-risk. Calculate the observed claim rates and interpret the association.

Method: standardize the group counts using the stated within-group probabilities. Among app users, expected high-risk claims are \(180(0.40)=72\), and expected low-risk claims are \(20(0.10)=2\). The total is \(72+2=74\), so the app-user claim rate is \(74/200=0.37\).

Among nonusers, expected high-risk claims are \(20(0.40)=8\), and expected low-risk claims are \(180(0.10)=18\). The total is \(8+18=26\), so the nonuser claim rate is \(26/200=0.13\). The observed difference is \(0.37-0.13=0.24\), or 24 percentage points.

Within each risk group, the claim probability is the same for app users and nonusers. Under the scenario’s assumption that app use has no effect, the causal effect is zero, even though app use strongly predicts claims in this population. A lasso model could retain app use because it helps distinguish groups with different risk compositions. Common mistake: interpreting the 24-point observed difference as the effect of adopting the app. The correction is to recognize that app use is associated with baseline risk, and the aggregate comparison mixes different proportions of high- and low-risk policyholders.

A proxy presents a related but distinct interpretation problem. The selected feature may be a convenient record of underlying risk rather than a mechanism that produces the outcome. Removing or changing the record may not change the risk it represents. This distinction is important when model features are codes, locations, prior administrative actions, or other measurements that stand in for more fundamental characteristics.

Worked Example: A Zone Code as a Proxy for Flood Exposure

A hypothetical portfolio has 200 properties. A legacy zone code \(C\) equals 1 for 100 properties and 0 for 100. The code is a proxy for underlying flood exposure \(H\), not a cause of flooding: changing the stored code while leaving the property and its exposure unchanged would not change its loss risk. Of the \(C=1\) properties, 80 have high exposure and 20 have low exposure. Of the \(C=0\) properties, 20 have high exposure and 80 have low exposure. The claim probabilities are 0.30 for high exposure and 0.05 for low exposure. Calculate the claim rates by code.

Method: compute expected claims within each code group from the exposure mix. For \(C=1\), expected high-exposure claims are \(80(0.30)=24\), and expected low-exposure claims are \(20(0.05)=1\). Thus, its rate is \((24+1)/100=0.25\).

For \(C=0\), expected high-exposure claims are \(20(0.30)=6\), and expected low-exposure claims are \(80(0.05)=4\). Its rate is \((6+4)/100=0.10\). The observed risk difference by code is \(0.25-0.10=0.15\), or 15 percentage points.

The code can be useful for prediction because it carries information about flood exposure. But the comparison does not imply that changing the code causes a 15-point change in claim probability. The underlying exposure explains the risk difference in the scenario. Common mistake: treating a selected code as an actionable risk lever. The correction is to ask what real-world intervention the code represents, if any, and whether that intervention changes exposure. Here, changing the recorded code alone does not.

What Would Support a Causal Conclusion?

Predictive selection alone does not establish causation, but this does not mean causal questions are impossible to study. Evidence comes from a design and analysis that justify a comparison of outcomes under alternative exposure states. Random assignment is one clear example: if assignment is genuinely random, treatment and control groups are comparable on average before treatment. The causal interpretation comes from that design, together with correct outcome measurement, adherence to the stated treatment definition, and appropriate handling of missing outcomes or departures from assignment—not from a variable being retained by lasso.

In observational data, a causal interpretation usually requires substantive assumptions. For example, measured confounders must be sufficient to make exposure groups comparable after conditioning on them; exposure and outcome must be defined consistently; and the data must contain relevant exposed and unexposed cases across the covariate patterns being compared. These conditions are not verified merely because a model selects a feature or predicts accurately. A predictive model may include useful proxies while still leaving important causes unmeasured.

Worked Example: Random Assignment Changes the Evidence

A hypothetical program randomly assigns 160 policyholders to receive a prevention reminder and 160 to usual practice. During a fixed follow-up period, 24 assigned to the reminder group and 30 assigned to usual practice have a claim. Calculate the observed event-rate difference and state what supports a causal interpretation.

Method: compare group rates under random assignment. The reminder-group rate is \(24/160=0.15\). The usual-practice rate is \(30/160=0.1875\). The difference, reminder minus usual practice, is \(0.15-0.1875=-0.0375\), or \(-3.75\) percentage points.

Because assignment was random, the groups are comparable on average before assignment, so the difference can estimate the effect of assignment to the reminder under the study conditions, subject to the stated design and follow-up assumptions. The estimate is not proof that every recipient benefits, and it does not establish the effect in a different population or setting. Lasso selection is not what makes this comparison causal; random assignment and the study design are the relevant evidence. Common mistake: saying that random assignment guarantees a precise or universally applicable effect. It supports causal comparison in this study, but sampling uncertainty and generalizability remain separate concerns.

Interpretation in Predictive Work

A selected feature can still be valuable even when it is not causal. If the objective is to predict future claims for a population similar to the development data, a stable proxy may improve predictions. Its usefulness depends on the deployment setting: if recording practices, population composition, or the relationship between the proxy and underlying risk changes, predictive performance may also change. Selection does not guarantee that a feature will remain useful under such changes.

When communicating a fitted model, separate three statements that are often mistakenly combined:

Selection statement: the feature had a nonzero coefficient in a specified penalized model.
Prediction statement: the feature contributed information useful for prediction under a stated evaluation setup.
Causal statement: intervening to change the exposure would change the outcome, under a defined target population and assumptions.

The first does not automatically establish the second, and neither establishes the third. Predictive performance should be evaluated for the intended use; causal claims need an appropriate causal design or defensible assumptions. In reports, describe selected features as predictive signals unless there is separate evidence supporting an intervention claim. This interpretation is aligned with the SOA Exam PA (Predictive Analytics) syllabus.

Key takeaway: Lasso and elastic net select predictors according to a penalized modeling objective. A selected variable can be a cause, a confounded correlate, or a proxy for underlying risk. Selection alone does not distinguish these possibilities or establish what would happen under an intervention.

Check Your Understanding

For each problem, distinguish what can be concluded predictively from what can be concluded causally.

A hypothetical book of 100 monitored accounts has 60 high-risk accounts with a claim probability of 0.30 and 40 low-risk accounts with a claim probability of 0.05. In a comparison group of 100 unmonitored accounts, there are 20 high-risk and 80 low-risk accounts. Monitoring has no effect within either risk group. Calculate both claim rates and explain the source of their difference. (Answer: monitored \(=20/100=0.20\); comparison \(=10/100=0.10\); the difference is due to the groups’ different risk composition, not a monitoring effect.)
A hypothetical location code marks 50 properties, 40 of which are high exposure and 10 low exposure. The other 50 properties include 10 high-exposure and 40 low-exposure properties. Claim probabilities are 0.20 for high exposure and 0.04 for low exposure. Calculate the claim rates by code and state whether changing only the code is causal. (Answer: marked \(=(40(0.20)+10(0.04))/50=0.168\); unmarked \(=(10(0.20)+40(0.04))/50=0.072\); changing only the code is not causal in the stated scenario.)
A randomized hypothetical trial assigns 120 customers to a new reminder and 120 to usual practice. Claims occur for 18 reminder-group customers and 24 usual-practice customers. Calculate the difference in rates, reminder minus usual practice, and name the source of causal support. (Answer: \(18/120-24/120=0.15-0.20=-0.05\), or \(-5\) percentage points; random assignment supports the comparison, subject to study assumptions.)
A lasso model retains a prior-inspection indicator when predicting next-year losses. Inspections are more common for accounts already judged to be high risk. What can be concluded from selection, and what cannot? (Answer: the indicator is a predictive signal in that fitted model; selection alone cannot show that inspections cause higher losses or that reducing inspections would lower them.)
A selected administrative code is highly predictive in the development portfolio, but coding procedures change before deployment. Give one reason predictions may deteriorate and one conclusion that selection still does not justify. (Answer: the code may no longer represent underlying risk in the same way, reducing predictive value; selection still does not establish that changing the code causes a change in outcomes.)

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