Decision Making in Health and Medicine​: Understanding Risk and Uncertainty in Health Studies

Medical decisions are rarely made with absolute certainty. In reality, choices, often urgent ones, must be made using the best available evidence. This decision-making process applies not only to major public health decisions, such as those made during a pandemic, but also to everyday clinical situations.

Whether setting new medical policies or determining the right treatment for an individual patient, effective decision making in health and medicine must be rational, weighing context, risks, and possible outcomes.

Looking at clinical results or personal health metrics, professionals aren’t just looking at numbers; they are weighing probabilities. To make sense of this, you need to understand the tools used to measure the possible outcomes.

Here is a step-by-step guide to the core concepts of decision-making in health and medicine:

• Step 1: Relative risk;
• Step 2: Absolute risk;
• Step 3: Absolute risk reduction;
• Step 4: Conditional probability;
• Step 5: Bayes’ rule; and
• Step 6: Expected value.

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When you hear that a specific diet increases the risk of a heart condition threefold, or that regular exercise lowers the risk of diabetes by half, you are dealing with relative risk (RR), a comparison of risk between groups.

It is important to remember that relative risk doesn‘t tell us about the absolute probability of the disease, so how likely a disease is to happen in total. Instead, it compares the likelihood between two groups, e.g., those who exercise versus those who don’t.

Calculation

Relative risk is a ratio that compares the probability (P) of an outcome in an exposed group to the probability in a non-exposed group. You calculate it by dividing the probability of an event in the exposed group by the probability in the unexposed (control) group:

where:

• $\mathrm{RR}$ — Relative risk; and
• $\mathrm{P}$ — Probability.

Interpreting the Results

When calculating the relative risk, your result falls into one of the three categories:

• $\mathrm{RR > 1}$ — Increased risk (exposure makes the outcome more likely);

• $\mathrm{RR < 1}$ — Decreased risk (exposure is protective, e.g., like a vaccine); and

• $\mathrm{RR = 1}$ — No difference (exposure has no measurable effect on the outcome).

Application

Relative risk is the gold standard for cohort studies. Cohort studies are observational studies that follow a group of people over time to examine how specific exposures, such as smoking or diet, affect health outcomes. They are commonly used in epidemiology to measure how often diseases occur and to identify risk factors.

While relative risk shows how a behavior or treatment compares to a control group, absolute risk gives the actual probability of experiencing a health event over a specific time period.

For instance, a particular lifestyle habit may double your risk of a disease (relative risk), but the absolute risk of getting that disease can be low. So even if you have a double risk of a disease due to a certain habit, if the absolute risk of that disease in the general population is only 1 in 10,000, doubling it only raises your absolute risk to 2 in 10,000. That means your actual chance of getting sick went from 0.01% to 0.02%.

Calculation

To determine the absolute risk, you simply divide the number of people who affected by the event by the total number of people in that group:

Relevance

This parameter is crucial for the decision-making process in health and medicine​ and is widely used in several medical aspects:

• Cohort/prospective studies — monitoring the incidence of a certian health outcome;
• Epidemiological studies — to understand patterns and trends in health and disease; and
• Clinical prognosis — to estimate an individual’s risk of developing conditions such as cancer, cardiovascular disease, or adverse effects from medical intervention.

It is also used in clinical studies to calculate the absolute risk reduction (ARR).

Once the baseline absolute risk is determined, the next logical step in evaluating a new medication or intervention is to calculate the absolute risk reduction (ARR).

Calculation

To find the ARR, you simply need to subtract the absolute risk of the treatment group from the absolute risk of the control group:

where:

• $\mathrm{ARR}$ — Absolute risk reduction; and
• $\mathrm{AR}$ — Absolute risk.

Application:

ARR tells you the actual difference a treatment makes.

For example, if a clinical trial found that 12 out of 100 people without any treatment develop a certain condition while the group that was treated with a drug shows 3 out of 100 develop the disease, you have an absolute risk of 12% and 3%, respectively.

To understand the difference the treatment makes, you subtract the value of the general incidence without any intervention from the one with the treatment:

ARR = 12% - 3% = 9%

This gives you deeper information than the absolute risk in the treatment group (3%), because now you know that, compared to untreated individuals, the drug decreases the risk of developing the disease by 9%.

Until now, we have focused on the link between the impact of lifestyle or medication on health outcomes. Now, we will take a look at factors that are already known to influence the chances of developing a certain disease. This is because the risk of developing a disease can be influenced by genetic markers, previous events, or test results, which are a predisposition that makes the occurrence of a disease more or less likely than in people without these factors. This adjusted probability is called conditional probability.

Conditional probability depends on a previous probability. It takes into account known circumstances that affect the overall probability. For example, the total probability of having diabetes will differ from the probability of having diabetes under the condition that the person is overweight.

Calculation

In short, conditional probability is the probability of event $\mathrm{A}$ under the condition that event $\mathrm{B}$ has already occurred:

Relevance & application

This information is particularly valuable for research and clinical trial design. Considering conditional probability helps to:

• Reasonably adjust exclusion/inclusion criteria for study participants — how the person’s medical history influences this particular medical intervention;
• Risk assessment — identifying risk factors of a certain condition; and
• Provides a rationale for the hypothesis — what outcome can be expected from a previous condition.

Bayes’ rule is a mathematical formula that uses conditional probability in reverse. It is a crucial tool in decision making in health and medicine​, as instead of looking at the outcome based on the conditions, it determines the possibility of having the condition, based on the outcome:

Basically, Bayes’ rule calculates the probability of A given B, using the probability of B given A, together with the prior probability of A and the overall probability of B. This allows updating the (posterior) probability.

For example, if a doctor receives a new test result, they update the probability that the patient has a certain disease — it may be higher or lower than it would be without considering that test result. Therefore, Bayes’ rule is essential for interpreting diagnostic tests and understanding true positive rates. It also enables personalized treatment, because therapeutic decisions can be based on the individual’s probability rather than the overall population risk.

Now that we know how to adjust conditional probabilities, we can take the next step and determine the expected value (EV). Expected value accounts for every possible outcome of a treatment, weighting each by its probability. In this way, probabilities become a practical tool for decision-making in health and medicine​, enabling comparisons of the feasibility of different therapies.

Calculation

To find the expected value, you multiply the value or utility of each outcome by its probability, then sum those results together:

where:

• $\mathrm{P_i}$ — Probability of the outcome; and
• $\mathrm{V_i}$ — Value/utility of the outcome.

Application

In a clinical setting, expected value is often used when a patient faces several options. For instance, a surgery might have a higher success rate but also a higher risk and a slower recovery time. An alternative therapy has a lower risk but also a lower success rate and takes longer.

This is where the utility score comes into play. Often measured in Quality-Adjusted Life Years (QALYs), a physician can calculate which treatment option provides the highest expected quality of life over the long term, like so:

Surgery:

• Full recovery success = 80% probability and 90 QALYs; and

• Complications = 20% and 30 QALYs.

  EV surgery = (0.80 × 90) + (0.20 × 30) = 78

Alternative treatment:

• Partial relief = 95% probability and 70 QALYs; and

• Severe side effects = 5% probability and 20 QALYs.

  EV alternative = (0.95 × 70) + (0.05 × 20) = 67.5

In this scenario, the surgery would give the best expected overall outcome for the patient.

This article was written by Julia Kopczyńska and reviewed by Steven Wooding.