Adverse Event Rate

Adverse Event Rates as Cost-Effectiveness Model Inputs

An adverse event rate turns a count of harmful or unwanted occurrences into a frequency that can be compared between treatments and carried into an economic model. The name is used in patient-safety measurement, which counts injuries caused by care, and in clinical trials, which count unfavourable occurrences after a treatment whether or not the treatment caused them. In health economics the trial sense is the relevant one, and the rate becomes an event probability in a decision tree or Markov model and carries a cost and a loss of quality of life for each event. The resulting model input depends on the choice of denominator, on converting rates correctly to cycle probabilities and on how costs and disutilities are attached to each event.

Two definitions behind the same number

A rate is only as clear as the definition of the event being counted. Trial safety reporting and patient-safety research define an adverse event differently, so two figures with the same label can measure different things.

The ICH E2A guideline on clinical safety data defines an adverse event as an untoward medical occurrence in a patient given a medicinal product that does not necessarily have a causal relationship with the treatment. A trial adverse event rate therefore includes background illness as well as drug effects, which is why the difference between randomised arms, not the rate in one arm, carries the information about harm caused by the treatment. The Harvard Medical Practice Study took the patient-safety view, defining adverse events as injuries caused by medical management, and found them in 3.7% of hospitalisations in 30,121 records from New York hospitals in 1984. That denominator is hospital admissions, a different quantity from the share of trial patients with an event.

ICH E2A also separates severity, which describes intensity, from seriousness, which rests on outcomes such as death, a threat to life or hospital admission. Oncology trials grade severity with the National Cancer Institute's Common Terminology Criteria for Adverse Events (CTCAE), in which grade 3 is typically severe or medically significant with hospitalisation indicated, grade 4 is life-threatening and grade 5 is death. Some terms, such as febrile neutropenia, start at grade 3, so a severity cut-off does not affect every event in the same way.

Choosing the denominator between proportions and person-time rates

Trial publications usually report adverse events either as a proportion of patients with at least one event or as a rate per unit of time at risk. The form decides how the figure can be used in a model.

$$P = \frac{n}{N}$$

where $P$ is the proportion of patients with at least one event during the follow-up period, $n$ is the number of patients with one or more events, and $N$ is the number of patients at risk at the start. This is the cumulative incidence over that period.

$$r = \frac{d}{PT}$$

where $r$ is the event rate, $d$ is the number of events counted, and $PT$ is the total person-time at risk, for example in patient-years. This is an incidence rate; it can exceed one and depends on the time unit.

The difference matters when trial arms are treated for different lengths of time. A drug stopped early because of toxicity or progression accumulates less time at risk, so its crude proportion can understate the event frequency per unit of treatment time. Counting patients with any event also differs from counting all events, because a model that costs every episode needs the event count, while a model that moves patients into a post-event state needs the number of first events.

Converting an adverse event rate into a model probability

State-transition models move patients between states once per cycle, so they need a probability for the cycle length rather than a published rate or a proportion over another period. The standard conversion assumes that the event rate is constant over the interval.

$$p = 1 - e^{-r t}$$

where $p$ is the probability of at least one event within an interval of length $t$, $r$ is the constant event rate in the same time unit as $t$, and $e$ is the base of the natural logarithm. This rate-to-probability conversion gives the transition probability for a cycle.

When the source reports a proportion over a period that differs from the model's cycle length, the proportion is turned into a rate and back into a probability for the new interval, as follows.

$$r = \frac{-\ln(1 - P)}{T} \quad \text{and} \quad p_t = 1 - (1 - P)^{t/T}$$

where $P$ is the proportion with an event over the observed period $T$, $r$ is the implied constant rate, and $p_t$ is the probability for a cycle of length $t$. Dividing $P$ by the number of cycles is not equivalent, because probabilities do not add over time in the way rates do.

These formulas hold only when the adverse event is the single exit from the state concerned. When patients can also die, progress or stop treatment in the same cycle, the transitions compete, and the tutorial by Gidwani and Russell shows that converting each transition separately with the two-state formula gives incorrect numbers of patients moving to each state. A model with competing risks needs the rates converted jointly, or the model restructured so each node has two branches.

Attaching costs and health losses to each event

Once each adverse event has a probability, the model attaches the resources used to manage it and the health it costs. The calculation is a weighted sum over the events included.

$$C_{AE} = \sum_{k} p_k \, c_k \quad \text{and} \quad Q_{AE} = \sum_{k} p_k \, u_k \, \tau_k$$

where $C_{AE}$ is the expected adverse event cost per patient, $Q_{AE}$ is the expected loss of quality-adjusted life years per patient, $p_k$ is the probability of event type $k$, $c_k$ is the cost of managing one episode, $u_k$ is the disutility during the episode, and $\tau_k$ is its duration as a fraction of a year.

Episode costs are built up from the care each event triggers, such as admissions, visits and drugs, often by micro-costing. The health loss enters the QALY total in a cost-utility analysis, as a one-off decrement or, for events with lasting effects, as a separate health state. The NICE manual (PMG36, section 4.10.4) asks for a table that includes disaggregated costs and the decrements associated with further interventions and adverse events. Such a table makes the contribution of adverse events to the result visible.

Double counting is a specific risk. A review by Craig and colleagues of 80 NIHR health technology assessment reports found that over half of the models using utilities took them from patients on treatment, so those values could already reflect adverse effects. Adding a separate disutility per event on top of such values can count the same loss twice.

Choices that change the cost-effectiveness result

Several choices sit between a trial safety table and a model input, and each can move the incremental results. Most are structural choices rather than uncertain parameter values, so they are best stated and tested in scenario analysis.

1. Which events are included. A model can be restricted to events above a severity grade or a frequency cut-off, or to events that differ between arms; each restriction removes costs and health losses and needs a reason.

2. All-cause or treatment-related counts. All-cause counts in both arms keep the comparison randomised; counts judged related to the drug depend on investigator attribution.

3. Exposure and recurrence. Arms with unequal exposure need person-time rates, and a per-cycle probability applied throughout treatment assumes events can recur, whereas a single decrement assumes they cannot.

4. Source of the estimates. Rates may come from one trial, a network meta-analysis or observational data; a methods paper by Ghabri, Dawoud and Drummond lists the lack of relevant real-world safety data among the issues that limit how adverse events are modelled.

In probabilistic sensitivity analysis, a beta distribution suits a proportion of patients with an event, and a gamma distribution is a common choice for a rate per unit of person-time.

Worked example of a 24-week trial result in four-week cycles

The figures below are illustrative. A trial follows 200 patients on a new drug and 200 on a comparator for 24 weeks. Grade 3 or higher diarrhoea occurs in 36 patients on the new drug and 16 on the comparator. The model has four-week cycles and everyone stays on treatment for six cycles. It tracks event-free patients, so a patient leaves the at-risk pool after a first episode, so only first episodes are counted.

1. Calculate the observed proportions. The new drug has $P = 36/200 = 0.18$ and the comparator has $P = 16/200 = 0.08$ over 24 weeks.

2. Convert to four-week probabilities. With $t/T = 4/24$ the probabilities are as follows.

$$p_{new} = 1 - (1 - 0.18)^{4/24} = 1 - 0.82^{1/6} = 0.0325$$

where $p_{new}$ is the probability of a first episode in a four-week cycle on the new drug. The rate route gives the same result, since the implied rate is $r = -\ln(0.82)/24 = 0.00827$ per patient-week, and $p_{new} = 1 - e^{-0.00827 \times 4} = 0.0325$.

$$p_{comp} = 1 - (1 - 0.08)^{4/24} = 1 - 0.92^{1/6} = 0.0138$$

where $p_{comp}$ is the corresponding four-week probability on the comparator.

3. Check against the naive shortcut. Dividing the 24-week proportion by six gives 0.03 per cycle for the new drug. Over six cycles that implies a cumulative risk of $P_6 = 1 - 0.97^6 = 0.167$, not the 0.18 observed, whereas the converted probability reproduces the trial result, with $P_6 = 1 - (1 - 0.0325)^6 = 0.180$.

4. Attach costs and health losses. Each episode costs an illustrative £1,800 to manage and reduces utility by 0.10 for 14 days, as follows.

$$q = 0.10 \times \frac{14}{365} = 0.00384$$

where $q$ is the QALY loss per episode. Over 24 weeks the expected adverse event cost is 0.18 × £1,800, or £324 per patient, on the new drug and 0.08 × £1,800, or £144, on the comparator. The expected QALY losses are 0.18 × 0.00384, or 0.00069, and 0.08 × 0.00384, or 0.00031.

5. Interpret. The new drug adds £180 in adverse event costs and loses about 0.00038 QALYs per patient. At an illustrative threshold of £20,000 per QALY the health loss is worth about £8, so for a short-lived event the management cost dominates the effect on net monetary benefit. Because the model removes patients from the at-risk pool after a first episode, the naive shortcut would have understated the new drug's cumulative risk by 1.3 percentage points and its adverse event cost by about £23 per patient. If a per-cycle probability were instead applied to the whole cohort in every cycle, the naive figure would give exactly £324 and the converted one about £351, so the size and direction of the error depend on the model structure. Events that cause death, long admissions or lasting disability can reverse the balance, which is why severe events often need their own health states.

Reading adverse event rates in appraisal decisions

Adverse event inputs shape the cost side of an appraisal and the credibility of claims that two treatments are similar. Their role differs between cost-utility and cost-comparison analyses.

For NICE cost-comparison appraisals, PMG36 (sections 4.2.19 and 4.2.20) states that costs of differing health outcomes, such as managing adverse events, should be captured when relevant, and that substantial differences in costs directly relating to health outcomes such as adverse events indicate that the technologies may not provide similar overall health benefits. A large difference in adverse event costs can therefore undermine the cost-comparison route. In a cost-utility analysis, when the events are short-lived and moderately costly, as in the worked example, a difference in rates moves the incremental cost-effectiveness ratio more through costs than through QALYs; severe or lasting events can change that balance.

Practice has been uneven. The review by Craig and colleagues covered NIHR health technology assessment reports published between 2004 and 2007 and found that 54% of the decision models included adverse effects; of those, 79% used a cost parameter and 67% a clinical adverse effects parameter. The authors called for much clearer reporting of how adverse effects were included or why they were left out, and Ghabri, Dawoud and Drummond add that some consequences of adverse events are not adequately captured by current health-related quality of life measures.

Adverse event rate, harm rate and related measures

Several neighbouring measures share the same arithmetic but answer different questions. Keeping them apart avoids using one in place of another when building model inputs. In patient-safety work the person-time counterpart is the harm rate, the frequency of a defined adverse outcome per unit of person-time at risk or exposure.

A relative risk or incidence rate ratio applied to a baseline risk or rate is a common way to obtain the rate for a new treatment when direct data are thin. The number needed to harm uses the same inputs for communication but plays no part in the model calculation.

Rare serious events and zero counts

Trials are seldom large enough to estimate rare serious adverse events precisely. A zero count in one arm is therefore not evidence of zero risk, and a model that sets the probability to zero removes both the expected harm and its uncertainty.

Sources

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• Fleurence RL, Hollenbeak CS. Rates and probabilities in economic modelling: transformation, translation and appropriate application. PharmacoEconomics. 2007;25(1):3-6.
• Ghabri S, Dawoud D, Drummond M. Methods for including adverse events in economic evaluations: suggestions for improvement. Value in Health. 2024;27(7):936-942.
• Gidwani R, Russell LB. Estimating transition probabilities from published evidence: a tutorial for decision modelers. PharmacoEconomics. 2020;38(11):1153-1164.
• International Council for Harmonisation. E2A Clinical safety data management: definitions and standards for expedited reporting. Step 4 version; 1994.
• National Cancer Institute, Cancer Therapy Evaluation Program. Common Terminology Criteria for Adverse Events (CTCAE), version 6.0. 2025.
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). London: NICE; 2022, last updated 13 October 2026. Sections 4.2.19, 4.2.20 and 4.10.4.