Baseline Risk

Baseline Risk: Sources, Relative Effects and Heterogeneity in Economic Models

In a health economic model, the baseline risk sets how many events would happen under the comparator, and the treatment effect from trials is then applied to it to give the events expected under the new intervention. Because absolute benefit is the product of the two, the choice of baseline risk can move the incremental cost-effectiveness ratio as much as the trial result does. This page explains how baseline risk and relative effects are combined, where baseline data come from and what the NICE manual and the NICE Decision Support Unit recommend for choosing them, how uncertainty and the scale of the effect measure matter, and why differences in baseline risk between patient groups lead to stratified decisions. An illustrative example follows one preventive treatment through two risk groups. Risk over time and its conversion to cycle probabilities are covered on the absolute risk page.

Two components: a baseline model and a relative effect model

NICE Decision Support Unit Technical Support Document (TSD) 5, by Dias, Welton, Sutton and Ades, describes most cost-effectiveness analyses as having two separate parts: a baseline model of the absolute natural history under a standard treatment in the comparator set, and a model for relative treatment effects. The baseline part may rest on trial or cohort evidence, while the relative effects usually come from randomised controlled trials. The natural history under the new treatment is obtained by putting the two together. For an odds ratio, TSD 5 adds the log odds ratio to the baseline log odds:

$$\text{logit}(p_1) = \text{logit}(p_0) + \ln(\text{OR})$$

where $p_0$ is the baseline probability of the event under standard care, $p_1$ is the probability under the new treatment, $\text{logit}(x) = \ln(x/(1-x))$ and OR is the odds ratio for the new treatment against standard care. In the TSD 5 example a baseline probability of 0.25 and an odds ratio of 0.8 give $p_1$ = 0.21. With a relative risk the step is a multiplication:

$$p_1 = p_0 \times \text{RR}$$

where RR is the risk ratio. The Cochrane Handbook (chapter 15) calls the baseline in this calculation the assumed comparator risk and gives an example in which a risk ratio of 0.92 and an assumed comparator risk of 0.3 mean 24 fewer events per 1000 people. TSD 5 notes that the same approach applies to models that are linear in log relative risks or log hazard rates, so a hazard ratio is applied to a baseline hazard in the same way.

Where baseline risk comes from

TSD 5 says the baseline response should be as specific as possible to the population of interest, so recent trials, relevant cohort studies, register studies or, in some cases, expert opinion may be more suitable than the full set of trials used for relative effects. A common approach takes the comparator arms of the same trials that supply the relative effects. TSD 5 accepts this but says it needs to be justified in each case, asking whether every trial represents the absolute response expected in the target population under current circumstances, especially if some trials are old or had very restrictive inclusion criteria. It states that simply calculating the unweighted mean of the baseline arms is not recommended under any circumstances.

The NICE manual (PMG36, sections 4.6.15 and 4.6.16) makes a similar point. Trial data collected to estimate treatment effects may not quantify the risk of some outcomes well enough for the population of interest, or over a long enough period. Quantifying baseline risk and the natural progression of the condition with the comparators can be informed by observational studies, and relative effects from randomised trials may then be applied to the baseline risk of the populations or subgroups of interest. The choice of data sets should be justified by their suitability to the population in the evaluation.

When baseline risk depends on patient characteristics such as age, sex or disease severity, TSD 5 prefers risk equations estimated from individual patient data in large trial databases, registers or cohort studies. The treatment effect is then added to the equation as if it were another risk factor. TSD 5 identifies the main difficulty as justifying the data source and its relevance to the target population, and it asks, where necessary, for sensitivity analyses of the choice of source.

Separate estimation and uncertainty in the baseline

TSD 5 recommends building the baseline model separately from the model for relative effects, so that assumptions about the baseline cannot alter the treatment effects and because the two usually draw on different data. Joint modelling can help when evidence is very sparse or when there are strong reasons to believe a particular baseline model, but TSD 5 says it has considerable impact on the relative effect estimates and always needs justification.

How baseline uncertainty is carried into the model also matters. TSD 5 suggests using the predictive distribution of the baseline in a new setting, in place of the fixed or random effects mean, because the predictive distribution reflects the observed variation between studies. In its smoking cessation example both approaches give a baseline quit probability of about 0.07 to 0.08, but the 95% credible interval widens from 0.05 to 0.09 under the posterior mean to 0.02 to 0.20 under the predictive distribution. The predictive distribution carries that wider uncertainty into probabilistic sensitivity analysis. TSD 5 notes that the choice has very little effect on the differences between treatments but adds uncertainty to the natural history model, and so to the absolute costs and QALYs.

Choosing the scale for the relative effect

The same trial evidence can predict different absolute benefits depending on which effect measure is carried into the model. The Cochrane Handbook (chapter 10) reports empirical evidence that relative effect measures are, on average, more consistent across studies than absolute measures, and advises against meta-analysis of risk differences unless there is a clear reason to expect them to be consistent. It also warns that when the assumed comparator risk differs from the typical comparator risk in the trials, predictions of absolute benefit will differ according to whether a risk ratio or an odds ratio was used. The NICE manual (PMG36, section 4.9.7) asks that subgroup analyses specify the scale on which any effect modification is defined.

Heterogeneity in baseline risk and cost-effectiveness

The Cochrane Handbook (chapter 15) notes that even if relative effects are similar across subgroups, absolute effects will differ according to baseline risk. In an economic model the consequence reaches costs as well as health: higher-risk patients avoid more events, so they gain more QALYs and offset more of the treatment cost through events avoided. The NICE manual (PMG36, section 4.9.5) states that the overall net treatment effect is determined by baseline risk or the relative effects of the technology, and section 4.9.6 requires systematic identification of data to quantify baseline risk when subgroups are based on it, with the methods reported in enough detail to allow replication. Section 4.9.1 asks for clinical and cost-effectiveness estimates for each relevant subgroup in cost-utility analyses.

Espinoza, Manca, Claxton and Sculpher, citing earlier work by Phelps, list baseline risk alongside treatment efficacy, costs and patient preferences as sources of heterogeneity in cost-effectiveness, and note that baseline risk may sometimes be correlated with the relative treatment effect. They call the gain in health from making different recommendations for different subgroups using existing evidence the static value of heterogeneity. A subgroup analysis by baseline risk is one route to that value, while treatment effect heterogeneity concerns differences in the relative effect itself.

Worked example: one preventive treatment in two risk groups

All numbers are illustrative. A preventive treatment costs GBP 2,000 per patient over five years and has a relative risk of 0.70 for a single event, assumed constant across risk levels. Each event costs GBP 10,000 and causes a loss of 2.0 QALYs; discounting is ignored. The population is 60% low risk, with a five-year baseline risk of 0.05, and 40% high risk, with a baseline risk of 0.20. The decision uses an illustrative threshold of GBP 20,000 per QALY.

1. Absolute risk reduction. For the low-risk group:

$$\text{ARR} = p_0 \times (1 - \text{RR}) = 0.05 \times 0.30 = 0.015$$

where ARR is the absolute risk reduction, $p_0$ the baseline risk and RR the relative risk. For the high-risk group 0.20 × 0.30 = 0.06.

2. QALYs and costs. QALYs gained are ARR × 2.0, giving 0.03 (low risk) and 0.12 (high risk). Event costs avoided are ARR × 10,000, giving GBP 150 and GBP 600, so incremental costs are 2,000 − 150 = GBP 1,850 and 2,000 − 600 = GBP 1,400.

3. ICER and net monetary benefit by group.

The ICER is incremental cost divided by QALYs gained (1,850 / 0.03 and 1,400 / 0.12), and net monetary benefit is 20,000 × QALYs gained minus incremental cost. The pooled row uses the average baseline risk, 0.6 × 0.05 + 0.4 × 0.20 = 0.11.

4. The decision. On the pooled baseline the ICER of GBP 25,303 exceeds the threshold, so the single best decision for everyone is not to treat (net monetary benefit 0). Treating only the high-risk group gives 0.4 × 1,000 = GBP 400 of net monetary benefit per member of the population, a gain over both treating everyone (−350) and treating nobody (0). That GBP 400 per person, equal to 400 / 20,000 = 0.02 net QALYs at the threshold, is the static value of recognising heterogeneity in baseline risk in this example.

5. The scale of the effect. Suppose the trials were run at a baseline near 0.05, where a relative risk of 0.70 gives a treated risk of 0.035 and an equivalent odds ratio of (0.035/0.965)/(0.05/0.95) = 0.689. Applying that odds ratio to the high-risk baseline gives odds of 0.25 × 0.689 = 0.172 and a treated risk of 0.172/1.172 = 0.147, an ARR of 0.053 instead of 0.06. QALYs gained fall to 0.106 and the ICER rises to about GBP 13,854. The high-risk group stays cost-effective here, but the gap shows why the scale used to transport the effect to a new baseline should be stated and tested.

Common errors with baseline risk

Baseline risk is the risk under the comparator on which relative effects act, so it overlaps with absolute risk but differs from attributable risk, the excess risk linked to an exposure. Most errors arise in choosing or applying it.

1. Unrepresentative source. Comparator arms of old or narrowly selected trials taken as the baseline for current practice without justification.
2. Mismatched time periods. The Cochrane Handbook (chapter 10) notes that comparator group risk depends on the length of follow-up, which often differs between studies.
3. Spurious risk relationships. A plot of trial effects against comparator group risk can show a false correlation through regression to the mean, for which the Cochrane Handbook recommends correction methods and statistical expertise.
4. Average baseline only. Running the model on a single pooled baseline hides subgroups for whom the decision would differ.
5. Understated uncertainty. Using the posterior mean of the baseline where TSD 5 recommends the predictive distribution.

Sources

• Deeks JJ, Higgins JPT, Altman DG, McKenzie JE, Veroniki AA (editors). Chapter 10: Analysing data and undertaking meta-analyses (last updated November 2024). In: Higgins JPT, Thomas J, Chandler J, et al (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.5. Cochrane; 2024. https://training.cochrane.org/handbook/current/chapter-10
• Dias S, Welton NJ, Sutton AJ, Ades AE. NICE DSU Technical Support Document 5: Evidence synthesis in the baseline natural history model. Sheffield: Decision Support Unit, ScHARR, University of Sheffield; 2011, last updated April 2012. https://doi.org/10.15131/shef.data.33737536
• Espinoza MA, Manca A, Claxton K, Sculpher MJ. The value of heterogeneity for cost-effectiveness subgroup analysis: conceptual framework and application. Medical Decision Making. 2014;34(8):951-964. https://doi.org/10.1177/0272989X14538705
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). London: NICE; 2022, last updated 31 March 2026. Sections 4.6.15, 4.6.16, 4.9.1, 4.9.5, 4.9.6 and 4.9.7. https://www.nice.org.uk/process/pmg36/chapter/economic-evaluation
• Schünemann HJ, Vist GE, Higgins JPT, Santesso N, Deeks JJ, Glasziou P, Akl EA, Guyatt GH. Chapter 15: Interpreting results and drawing conclusions (last updated August 2023). In: Higgins JPT, Thomas J, Chandler J, et al (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.5. Cochrane; 2024. https://training.cochrane.org/handbook/current/chapter-15