From a Validated Prediction to an Action
A validated model can estimate which cases are more likely to experience an event. That prediction alone does not determine what an organization should do. A recommendation must connect the prediction to a feasible action and explain why the action is expected to improve an outcome enough to justify its cost. For example, a model may identify policyholders at elevated risk of a costly event, but the organization still needs to decide whether to contact them, which cases to contact, and whether the contact is effective and operationally feasible.
The distinction matters: model validation assesses predictive performance, while the effect of an intervention requires separate evidence or an explicitly stated assumption. A model that ranks cases well does not, by itself, show that outreach, inspection, or review will prevent losses. A sound recommendation therefore identifies the decision-maker, the cases affected, the expected benefit and cost, and the conditions on which the estimate depends. This approach is aligned with the SOA Exam PA (Predictive Analytics) syllabus.
Expected Value Requires More Than a Risk Score
Let \(E\) denote the event that a case would experience a loss if no action were taken. Let \(C\) denote completion of the recommended action, \(e\) the probability that a completed action prevents the loss, \(L\) the loss avoided if prevention succeeds, and \(K\) the cost incurred for each assigned case. Under a model where the action can prevent the loss only when the baseline event would occur and the action is completed, expected net value per assigned case is:
Here \(P(E\cap C)\) is the joint probability that the case would experience the event without intervention and that the action is completed. It is not generally equal to \(P(E)P(C)\). That product is valid only if event occurrence and completion are independent, or if the stated completion rate is specifically conditional on event cases. A marginal completion rate alone does not establish the joint probability.
If an action is assigned to every eligible case whether or not it is completed, its assignment cost belongs in \(K\) even for incomplete cases. If costs are incurred only when the action is completed, the cost term instead needs to reflect the appropriate completion probability and cost structure. State which convention applies before calculating net value.
Why the Expected-Value Calculation Works
Define \(I_E\), \(I_C\), and \(I_R\) as indicators for the baseline event, action completion, and successful prevention, respectively. Under the stated setup, avoided loss is \(L I_E I_C I_R\). The expected avoided loss is therefore:
If the prevention probability conditional on both an event and completed action is \(e\), then \(P(R\mid E\cap C)=e\), giving \(P(E\cap C)eL\). Subtracting the assignment cost \(K\) gives expected net value. This derivation also shows why replacing \(P(E\cap C)\) with \(P(E)P(C)\) requires an independence assumption: by the multiplication rule, \(P(E\cap C)=P(E)P(C\mid E)\), not necessarily \(P(E)P(C)\).
Worked Recommendations
Worked Example: Prioritizing Preventive Outreach
A hypothetical insurer has validated a model for identifying accounts likely to incur a specified loss during the coming year. It assigns 80 accounts to an outreach program. The sum of their predicted probabilities of the loss in the absence of outreach is 16 expected losses. Based on separate intervention evidence, assume that among those baseline-event cases, 10 expected cases receive completed outreach, and that completed outreach prevents the loss with probability 0.40. Each prevented loss is valued at $600. The $25 assignment cost is incurred for every assigned account, whether or not outreach is completed. Recommend an action and calculate its expected net value. Assume no discounting; no mortality assumption is relevant. Event counts are expected counts from the model’s stated probabilities, and prevention is represented by the stated conditional probability.
Method. Calculate expected avoided losses using the joint event-and-completion count, then subtract the assignment cost. This avoids assuming that the marginal completion rate applies equally to accounts that would otherwise have a loss.
Expected prevented losses are \(10\times0.40=4\). Thus expected avoided loss is \(4\times\$600=\$2{,}400\). Total assignment cost is \(80\times\$25=\$2{,}000\). Expected net value is \(\$2{,}400-\$2{,}000=\$400\), or \(\$400/80=\$5\) per assigned account.
A specific recommendation is: the insurer’s outreach team should contact the 80 model-selected accounts, provided the separate intervention evidence applies to this population and the organization can achieve the assumed joint count of 10 baseline-event cases with completed outreach. The model’s expected 16 events alone would not establish that 10 event cases receive completed outreach; that quantity must be supported rather than inferred from an overall completion rate.
Check. The total expected benefit exceeds total assigned cost by $400, and the per-account value multiplied by 80 is also \(80\times\$5=\$400\).
Worked Example: Recommending a Limited Review Team
A hypothetical service organization can assign 30 cases to a rapid review team. A validated prediction model estimates nine events among these cases if no review occurs. For this example, separate operational evidence supports the assumption that 80% of those cases that would otherwise experience the event receive completed review. A completed review prevents the event with probability 0.50, conditional on the event and completed review. Each prevented event avoids $2,000 in cost. Assignment costs $150 per case, including cases that do not receive a completed review. Calculate expected net value and state the operational condition. No interest discounting or mortality assumption is involved; event indicators have the model-estimated probabilities, and prevention is represented by the stated conditional probability.
Method. Use the completion rate conditional on baseline event occurrence, so it directly determines the joint event-and-completion count. Do not multiply by an unrelated marginal completion rate.
The expected number of baseline-event cases with completed review is \(9\times0.80=7.2\). Expected prevented events are \(7.2\times0.50=3.6\). Expected avoided cost is \(3.6\times\$2{,}000=\$7{,}200\). Total assignment cost is \(30\times\$150=\$4{,}500\). Expected net value is \(\$7{,}200-\$4{,}500=\$2{,}700\), or \(\$2{,}700/30=\$90\) per assigned case.
The recommendation is for the organization’s review manager to assign the 30 selected cases to the team, conditional on maintaining the assumed 80% completion rate among cases that would otherwise experience the event and on the 0.50 prevention rate applying to completed reviews. The completion condition is about event cases, not merely the share of all assigned cases receiving review. If only a marginal completion rate is known, the needed joint probability is not yet established.
Check. The calculation gives 3.6 expected prevented events, a plausible amount below the 7.2 expected baseline-event cases with completed review. Multiplying 3.6 by $2,000 gives the stated $7,200 benefit.
Worked Example: Choosing a Targeted Program Over a Broad One
A hypothetical facilities operator is considering inspections for two groups selected using validated predictions. For 40 high-risk sites, predicted baseline-event count is 12; for 60 lower-risk sites, it is six. Separate evidence supports completion among baseline-event sites of 75% for the high-risk group and 50% for the lower-risk group. A completed inspection prevents an event with probability 0.60, conditional on a baseline event and completed inspection. Each prevented event avoids $1,000. Inspection assignment costs $100 per site, and a $500 setup cost applies once to any program operated. Compare inspecting the high-risk group alone with inspecting both groups. No interest discounting or mortality assumption is involved; the event counts are expected counts, and the stated completion and prevention probabilities apply to the indicated groups.
Method. Calculate each group’s expected benefit and cost separately, then include the fixed setup cost once for each proposed program. This avoids assuming that a lower-risk group is worthwhile merely because the broader program has a positive total benefit.
For the high-risk group, the expected number of baseline-event sites with completed inspections is \(12\times0.75=9\). Expected prevented events are \(9\times0.60=5.4\), so expected avoided loss is \(5.4\times\$1{,}000=\$5{,}400\). Variable inspection costs are \(40\times\$100=\$4{,}000\). Including setup, total cost is \(\$4{,}000+\$500=\$4{,}500\). Net value is \(\$5{,}400-\$4{,}500=\$900\).
For the lower-risk group, the expected number of baseline-event sites with completed inspections is \(6\times0.50=3\). Expected prevented events are \(3\times0.60=1.8\), giving expected avoided loss of \(1.8\times\$1{,}000=\$1{,}800\). Variable inspection costs are \(60\times\$100=\$6{,}000\). Adding the $500 setup cost for a program covering both groups gives total broad-program cost of \(\$4{,}000+\$6{,}000+\$500=\$10{,}500\). Total expected avoided loss is \(\$5{,}400+\$1{,}800=\$7{,}200\), so broad-program net value is \(\$7{,}200-\$10{,}500=-\$3{,}300\).
The recommendation is for the facilities manager to inspect the 40 high-risk sites and not extend the program to the lower-risk group under these assumptions. The targeted program has expected net value of $900, whereas the broad program has expected net value of negative $3,300. The recommendation depends on the group-specific completion and prevention assumptions and on the setup and variable costs being accurate.
Check. The broad option’s incremental value from adding the lower-risk group is its $1,800 expected benefit less $6,000 in additional variable cost, or negative $4,200. This equals the difference between broad and targeted net values: \(-\$3{,}300-\$900=-\$4{,}200\).
Make the Recommendation Operational
A recommendation should be actionable without asking the reader to infer what the model result means. Use a short sequence that connects the prediction to implementation:
Specify the role or team responsible for the decision or action, such as a review manager assigning cases.
State which population, time period, or model-selected group is covered. Do not leave the reader to guess what “high risk” means operationally.
Describe what will happen and report the expected benefit and cost in interpretable units, using a clearly named comparison such as no action.
Identify assumptions about action effectiveness, joint event-and-completion probabilities, costs, capacity, and relevance of the evidence to the proposed population.
If the recommendation uses a model threshold or ranking to choose cases, make clear that this is a selection rule, not evidence of intervention effectiveness. A score can help decide whom to consider for action; a separate link from action to outcome is needed to estimate avoided losses. When effectiveness is uncertain, present the result as conditional: “If the assumed completion and prevention rates hold, expected net value is …” Do not state a conditional calculation as a guaranteed outcome.
Common Traps
- Multiplying marginal rates without justification. In general, \(P(E\cap C)\ne P(E)P(C)\). Use the joint probability, or state and support independence or a completion rate conditional on event occurrence.
- Treating prediction as intervention evidence. A validated probability estimates event risk under the conditions represented in the data; it does not by itself estimate what an action will prevent.
- Omitting costs for unsuccessful implementation. If assignment costs are incurred even when an action is not completed, count them for all assigned cases.
- Recommending a broad program based only on aggregate benefit. Compare the incremental benefit and cost of including additional groups, as well as the total program value.
- Leaving out the operating condition. A positive expected value may depend on completion, capacity, timing, or effectiveness. State the condition that makes the recommendation viable.
Check Your Understanding
For each problem, identify the relevant joint event-and-completion information before calculating expected net value.
- A hypothetical program assigns 50 cases at $12 each. There are four expected baseline events among assigned cases; separate evidence indicates that 60% of those baseline-event cases receive the completed action. The action prevents an event with probability 0.50 when completed for a baseline-event case, and each prevented event is worth $400. What is expected net value? (Answer: Expected benefit is \(4\times0.60\times0.50\times\$400=\$480\); total cost is $600; net value is \(-\$120\).)
- A team assigns 20 cases at $30 each. The joint probability of a baseline event and completed intervention is 0.15 per assigned case. Conditional on both, intervention prevents the event with probability 0.80, and each prevention is valued at $500. What is expected net value per assigned case? (Answer: \(0.15\times0.80\times\$500-\$30=\$30\) per assigned case.)
- A hypothetical inspection program has 10 expected baseline events. Completion occurs for 70% of the event cases, and a completed inspection prevents an event with probability 0.40. Each prevention is worth $1,000; assignment costs $80 for each of 50 cases. What is total expected net value? (Answer: Benefit \(=10\times0.70\times0.40\times\$1{,}000=\$2{,}800\); cost \(=50\times\$80=\$4{,}000\); net value \(=-\$1{,}200\).)
- A program costs $100 per assigned case and $400 in setup cost. For 30 selected cases, expected baseline events equal six. Of these event cases, 75% are expected to receive completed action; the action prevents an event with probability 0.50, conditional on both. Each prevention is worth $1,500. What is total expected net value, and what operational condition should the recommendation state? (Answer: Benefit \(=6\times0.75\times0.50\times\$1{,}500=\$3{,}375\); cost \(=30\times\$100+\$400=\$3{,}400\); net value \(=-\$25\). State that 75% completion is assumed among cases that would otherwise experience the event.)
- For 25 assigned cases, the probability of a baseline event is 0.20 and the marginal probability of completed action is 0.60. The action prevents the event with probability 0.50 when both occur, each prevention is worth $1,000, and assignment costs $40 per case. Can expected net value be determined from these marginal rates alone? If independence is explicitly assumed, what is the expected net value? (Answer: Without the independence assumption or the joint probability, net value cannot be determined. Under independence, expected benefit is \(25\times0.20\times0.60\times0.50\times\$1{,}000=\$1{,}500\), cost is $1,000, and net value is $500.)