Sensitivity Analysis for Polygenic Risk Decisions

Why Sensitivity Analysis Matters

A polygenic risk estimate can look precise while relying on assumptions that are uncertain in a new population or clinical setting. Baseline incidence may differ from the reference population; competing events may occur at a different rate; treatment benefit may be less certain than the untreated risk; and the risk model may not transport exactly. If a small, plausible change in one of these inputs changes a person’s risk category or reverses an intervention decision, that result deserves more caution than a decision that remains the same across the tested scenarios.

Sensitivity analysis makes this dependence visible. It recalculates risks or decisions under specified alternative inputs while holding other inputs fixed, or varies several inputs in a structured set of scenarios. It does not establish which scenario is true. Nor does a set of scenarios automatically quantify statistical uncertainty: that requires a probability model for uncertain inputs. The practical question here is whether the classification or decision is stable under plausible changes.

Risk, Classification, and Decision Rules

For a fixed time horizon, a risk classification assigns an estimated absolute risk to a category using prespecified cut points. An intervention rule may use a risk threshold, or may compare the expected benefit of treatment with its expected harms. In either case, sensitivity analysis must keep the rule explicit: changing a risk estimate is not the same as changing the threshold or the trade-off used to make the decision.

Definition: A sensitivity analysis for a polygenic risk decision is a structured recalculation of predicted risks, risk categories, or intervention decisions under alternative plausible values or assumptions for quantities that affect them. A result is decision-robust across the tested scenarios when the decision remains unchanged in all of those scenarios. This is a statement about the scenarios examined, not a guarantee that the decision is correct.

The earlier material on competing risks distinguishes the event of interest from an event that prevents it from occurring. In a simple model with constant cause-specific hazards, let \(\lambda_1\) be the hazard of the event of interest and \(\lambda_2\) the hazard of a competing event. Over horizon \(T\), the cumulative incidence of the event of interest is:

F_1(T)=\frac{\lambda_1}{\lambda_1+\lambda_2} \left\{1-\exp[-(\lambda_1+\lambda_2)T]\right\}.

This expression assumes the cause-specific hazards are constant over the horizon and appropriate for the target population and risk group. The competing event precludes the event of interest. The formula uses both hazards because a person must remain free of either event to be at risk of experiencing the event of interest. It is not generally correct to calculate risk as though the competing event did not occur.

Interpretation: A sensitivity scenario changes one or more inputs to a model and reports the resulting risk or decision. Unless a probability distribution for those inputs is specified and used, a range across scenarios is not a confidence interval and is not a probability statement about the true risk.

A Short Justification for the Competing-Risk Calculation

Under constant hazards, the probability of remaining free of both events through time \(t\) is \(S(t)=\exp[-(\lambda_1+\lambda_2)t]\). During a short interval of length \(dt\), the probability of the event of interest is approximately \(S(t)\lambda_1dt\): the individual must still be event-free, and the event-of-interest hazard is \(\lambda_1\). Integrating these contributions over the horizon gives:

F_1(T)=\int_0^T \lambda_1\exp[-(\lambda_1+\lambda_2)t]\,dt =\frac{\lambda_1}{\lambda_1+\lambda_2} \left\{1-\exp[-(\lambda_1+\lambda_2)T]\right\}.

The derivation also explains why changing the competing-event rate can change absolute risk even if the event-of-interest hazard is held fixed. It does not require treating the two event times as independent latent outcomes; it relies on the specified cause-specific hazards in the event-free population.

Worked Scenarios

The examples use entirely hypothetical values. They illustrate how to set up a sensitivity analysis, not clinical recommendations. For clarity, all risks are for a five-year horizon, and the calculations use the constant-hazard model just defined.

Worked Example: Varying Baseline Incidence and Competing-Event Rates

Suppose a hypothetical model uses a reference cause-specific hazard of \(0.012\) per year. For a high polygenic-score group, assume a relative hazard of 2.0, giving an event-of-interest hazard \(\lambda_1=0.024\) per year. Let the competing-event hazard be \(0.010\) per year. Classify five-year risks as low below 5%, intermediate from 5% to below 10%, and high at 10% or more. First vary the baseline hazard by 25% in either direction, applying the same score multiplier of 2.0.

The event-of-interest hazards are \(0.012\times0.75\times2=0.018\), \(0.012\times1\times2=0.024\), and \(0.012\times1.25\times2=0.030\) per year. With the competing hazard fixed at \(0.010\), the risks are:

F_1(5;0.018,0.010)= \frac{0.018}{0.028}\{1-\exp(-0.140)\}=0.0840, $$ $$ F_1(5;0.024,0.010)= \frac{0.024}{0.034}\{1-\exp(-0.170)\}=0.1104, $$ $$ F_1(5;0.030,0.010)= \frac{0.030}{0.040}\{1-\exp(-0.200)\}=0.1360.

Thus, the classification is intermediate, high, and high across the three baseline scenarios. The category changes when the baseline hazard is reduced by 25%; the baseline assumption is therefore decision-relevant for this classification.

Now hold the event-of-interest hazard at \(0.024\) per year and vary the competing hazard. With \(\lambda_2=0.005\), the risk is \(\frac{0.024}{0.029}\{1-\exp(-0.145)\}=0.1117\). With \(\lambda_2=0.010\), it is \(0.1104\), as above; with \(\lambda_2=0.020\), it is \(\frac{0.024}{0.044}\{1-\exp(-0.220)\}=0.1077\). All three remain in the high category, although the absolute risk declines as the competing-event hazard increases. The classification is stable across these competing-rate scenarios, but the risk estimates are not identical.

Worked Example: Varying Treatment Benefit

Use the baseline high-score scenario from the preceding example: the untreated five-year event-of-interest risk is \(0.1104\), with \(\lambda_1=0.024\) and \(\lambda_2=0.010\) per year. Suppose a hypothetical treatment reduces the event-of-interest hazard by a relative amount \(e\), leaves the competing-event hazard unchanged, and has a harm weighted as equivalent to a 1.5 percentage-point increase in the event of interest. For this example, treat intervention as worthwhile only when the absolute risk reduction exceeds 1.5 percentage points. This is a stipulated decision rule, not a general clinical threshold.

For each benefit assumption, the treated event-of-interest hazard is \(\lambda_{1,\mathrm{treated}}=0.024(1-e)\). At a 10% hazard reduction, this is \(0.0216\) per year. The treated risk is:

F_{1,\mathrm{treated}}= \frac{0.0216}{0.0316}\{1-\exp(-0.158)\} =0.0999.

The absolute risk reduction is \(0.1104-0.0999=0.0105\), or 1.05 percentage points. It does not exceed the stipulated 1.5-point harm, so the decision rule does not favor intervention in this scenario.

At a 25% hazard reduction, \(\lambda_{1,\mathrm{treated}}=0.018\) per year, and:

F_{1,\mathrm{treated}}= \frac{0.018}{0.028}\{1-\exp(-0.140)\} =0.0840, \qquad \text{absolute risk reduction}=0.1104-0.0840=0.0264.

The reduction is 2.64 percentage points, which exceeds 1.5 points; the stipulated rule favors intervention. At a 40% hazard reduction, the treated hazard is \(0.0144\) per year and the treated risk is \(\frac{0.0144}{0.0244}\{1-\exp(-0.122)\}=0.0678\). The absolute reduction is \(0.1104-0.0678=0.0426\), or 4.26 percentage points, also exceeding the harm assumption. The decision therefore changes between the 10% and 25% benefit scenarios. The treatment-benefit assumption, not just the untreated genetic risk, is consequential.

Worked Example: Testing a Score-Effect Assumption

Suppose the reference event-of-interest hazard remains \(0.012\) per year and the competing hazard remains \(0.010\) per year. A model assumption assigns the high-score group a relative hazard of 2.0. The resulting event-of-interest hazard is \(0.012\times2.0=0.024\) per year, and the five-year risk is \(0.1104\), in the high category under the cut points used above.

As a sensitivity analysis, suppose the score effect is attenuated to a relative hazard of 1.5. Then \(\lambda_1=0.012\times1.5=0.018\) per year, and:

F_1(5)= \frac{0.018}{0.018+0.010} \{1-\exp[-(0.018+0.010)5]\} =0.0840.

The classification is now intermediate. If instead the relative hazard is 2.5, then \(\lambda_1=0.030\) per year and the risk is \(\frac{0.030}{0.040}\{1-\exp(-0.200)\}=0.1360\), in the high category. The category depends on the assumed score effect in this example, so it is not robust across the tested effect values.

This calculation tests sensitivity to the score-effect input while retaining the same model form and competing hazard. It does not show that any one relative hazard is the correct value. A separate structural sensitivity analysis might examine whether hazards are plausibly constant over the full five years, or whether the competing-event hazard varies over time. Those are different assumptions and should be changed and reported explicitly rather than blended into one unexplained range.

A Practical Sensitivity-Analysis Workflow

A transparent analysis states what is varied, why the alternatives are plausible, what is held fixed, and which result is being checked. A useful sequence is:

Specify the target and decision rule.
Name the event, time horizon, risk categories or intervention rule, and the relevant population. Keep the rule fixed while testing input sensitivity unless the rule itself is the subject of the analysis.

List influential assumptions.
Examples include local baseline incidence, competing-event hazards, the score effect, treatment benefit, and the risk model’s time and transport assumptions. State the units and reference values.

Choose plausible scenarios.
Use values justified for the intended setting, such as alternative local incidence estimates or a range of treatment effects. Vary one input at a time to identify drivers, then consider joint scenarios when inputs may change together.

Recalculate and compare.
For every scenario, report the risk with units and time horizon, its category, and the resulting decision. Show the calculation or enough information to reproduce it.

Describe robustness precisely.
Say which decisions stayed the same, which changed, and under which assumptions. Do not describe the tested range as exhaustive or as a confidence interval unless it was constructed as one.

One-at-a-time scenarios help locate influential inputs, but they do not necessarily describe realistic combinations. For example, baseline incidence and competing-event rates may both differ between populations. Joint scenarios can reveal whether a conclusion depends on their combination. The scenarios should be clinically and statistically plausible rather than selected merely to produce a desired result.

Common Mistake and Why the Analysis Matters

Wrong reasoning: “The risk stays above the threshold when the competing-event rate changes, so the decision is robust.” This conclusion is too broad if only competing-event rates were varied. As the examples show, a baseline-incidence or score-effect change can alter the category, and a treatment-benefit change can reverse an intervention decision.

Correction: State the scope of robustness: for example, “The risk category remained high across the three competing-event rates tested, but changed under the lower baseline-incidence and attenuated-score-effect scenarios.” A decision is robust only relative to the assumptions and range actually examined.

Sensitivity analysis matters because a genetic risk estimate is used in a chain of reasoning: model inputs produce an absolute risk, that risk is mapped to a category or decision rule, and the rule informs an action. Examining the chain can show whether uncertainty in a particular input is worth resolving before acting. It can also communicate why an estimate should be treated cautiously when it lies near a category boundary. It does not replace validation, calibration, or an assessment of clinical evidence; each answers a different question.

Key takeaway: Recalculate the risk and decision under explicit, plausible alternatives for baseline incidence, competing events, treatment benefit, and model assumptions. Report both stable results and changes, and limit every robustness claim to the scenarios tested.

Check Your Understanding

Answer using the definitions and calculations in this tutorial.

Why is a range of risks across chosen sensitivity scenarios not automatically a confidence interval?
In the first worked example, which baseline-incidence scenario changed the risk category, and what was the resulting category?
With the treatment rule in the second example, why does a 10% hazard reduction not lead to the same decision as a 25% reduction?
If a risk category stays unchanged across several competing-event rates, what can and cannot be concluded about robustness?
Name one model assumption, other than the score effect, that could be tested in a separate sensitivity analysis and describe what would need to be specified.