Data Presentation in Therapeutics

(Treatment Calculations)

Control Event Rate (CER):

The proportion of events occurring in the control group.

Experimental Event Rate (EER):

The proportion of events occurring in the experimental group.

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The Experimental Treatment Reduces the Risk for a Bad Event

Relative Risk (RR):

• Relative risk (RR) is a statistical measure used to compare the risk of a certain event (like developing a disease) happening in two different groups.
• Relative risk tells us how much more or less likely something is to happen in one group compared to another.
  • RR = 1: No difference in risk between the groups.
  • RR > 1:  Increased risk in the exposed group (e.g., a risk factor increases the chance of disease – harmful effect).
  • RR < 1: Decreased risk in the exposed group (e.g., a treatment reduces the chance of disease – beneficial effect).
  • Example:
    • If a drug reduces the risk of stroke from 10% (CER) to 5% (EER):
      • RR= [ 5% / 10% ] = 0.5
    • This means the treatment reduces the risk of stroke by 50% relative to the control group.
• Is accompanied by 95% Confidence Interval (CI)
  • Key Rules:
    • If CI includes 1 → The result is not statistically significant (no clear difference between groups).
    • If CI is entirely <1 → Treatment significantly reduces risk.
    • If CI is entirely >1 → Treatment significantly increases risk.
    • Narrow CI → More precise estimate (larger studies).
    • Wide CI → Less precise estimate (small sample size or high variability
  • 📌 Example:
    • RR = 0.75 (95% CI: 0.60 – 0.90) → Statistically significant reduction in risk.
    • RR = 0.75 (95% CI: 0.50 – 1.10) → Not statistically significant because CI includes.

example 1 :

• Hart et al., 2011 has an RR of 1.18, and the 95% CI is 0.95 to 1.48 :
  • the true RR could be as low as 0.95 (a possible 5% reduction in risk) or as high as 1.48 (a 48% increase in risk), and since the CI includes 1, the result may not be statistically significant.
• Krewski et al., 2009 has an RR of 1.09 (95% CI: 1.05, 1.13).
  • The CI is narrow and does not include 1, indicating a statistically significant result. The narrow CI suggests that the estimate is precise.
• Lepeule et al., 2012 has an RR of 1.37 (95% CI: 1.07, 1.75).
  • This RR is higher, meaning it suggests a 37% increased risk, and the CI also does not include 1, indicating statistical significance.
  • However, the CI is slightly wider compared to Krewski’s study, meaning the estimate is less precise

example 2:

Key Features of the Plot:

1. Each horizontal line represents a study’s 95% Confidence Interval (CI).
2. The blue dot represents the point estimate (Relative Risk, RR) for each study.
3. The vertical dashed line at RR = 1 represents the null effect (no difference between groups).
4. Interpretation of Confidence Intervals (CIs):
   • Green labels (“Significant”) → CI does not cross 1, meaning the result is statistically significant.
   • Red labels (“Not Significant”) → CI crosses 1, meaning the result is not statistically significant.

Interpretation of Studies:

• Study 1 (RR = 0.75, CI: 0.60 – 0.90) → Significant (treatment reduces risk).
• Study 2 (RR = 1.2, CI: 0.95 – 1.50) → Not Significant (CI includes 1, no clear effect).
• Study 3 (RR = 0.85, CI: 0.65 – 1.05) → Not Significant (CI includes 1, uncertain effect).
• Study 4 (RR = 1.5, CI: 1.1 – 2.0) → Significant (treatment increases risk).
• Study 5 (RR = 1.0, CI: 0.85 – 1.15) → Not Significant (CI includes 1, no clear effect).

Key Takeaways:

✅ CIs that cross 1 mean the result is not statistically significant.
✅ Narrow CIs indicate more precision, while wider CIs suggest greater uncertainty.
✅ This visualization helps quickly determine which studies have meaningful effects.

Relative Risk Reduction (RRR)

is a measure used in clinical studies to compare the risk of a certain outcome between two groups—typically one receiving an experimental treatment and the other receiving a placebo or standard treatment. It helps to understand how much a treatment reduces the risk of a negative outcome in relative terms.

• CER (Control Event Rate): The rate of the outcome in the control group (i.e., those receiving the placebo or standard treatment)
• EER (Experimental Event Rate): The rate of the outcome in the experimental group (i.e., those receiving the new treatment).

Alternatively, it can also be expressed as:

Absolute Risk Reduction (ARR):

Absolute difference in bad event rates between control (CER) and experimental (EER) groups.

Number Needed to Treat (NNT):

• Number of patients needed to be treated to prevent one additional bad outcome.
• Focuses on preventing negative events, such as preventing a heart attack, stroke, or death.
• Example:
  • If a medication is given to prevent heart attacks, the NNT tells us how many people need to take that medication for one person to avoid a heart attack.
  • Lower NNT: example NNT = 2 – means you only need to treat 2 people to prevent 1 heart attack.) indicates that the treatment is more beneficial, meaning fewer patients need to be treated to prevent one adverse event.
  • Higher NNT: example NNT = 25 – you need to treat 25 people to prevent 1 heart attack.) means that the treatment is less effective, and many more patients need to be treated to achieve the same benefit.
  • NNT should always be reported with a 95% confidence interval (CI) to express the range within which the true NNT might lie.
  • Example:
    • If NNT = 25 with a 95% CI of 20–30, it means that the true NNT might be as low as 20 or as high as 30, depending on the population variability or study design. (ie : with 95% confidence that the true number lies within somewhere between 20 and 30)

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example 1 : Scenario: A clinical trial is conducted to evaluate the effectiveness of an experimental cardiac drug in preventing heart attacks. Participants in the study are divided into two groups:

1. Control Group: Receives standard care (without the experimental drug).
2. Treatment Group: Receives the experimental cardiac drug in addition to standard care.

Study Results:

• In the Control Group, 15 out of 100 participants had a heart attack (i.e., 15% or 0.15).
• In the Treatment Group, 9 out of 100 participants had a heart attack (i.e., 9% or 0.09).

Step-by-Step Calculation of RRR:

• Calculate the Risk in Each Group:
  • Risk in Control Group (without experimental drug): 15% = 0.15
  • Risk in Treatment Group (with experimental drug): 9% = 0.09
• Calculate the Absolute Risk Reduction (ARR):
  • ARR is the difference in risk between the control group and the treatment group:
  • 𝐴𝑅𝑅 = Risk in Control Group −Risk in Treatment Group
  • ARR = 0.15 – 0.09 = 0.06 (or 6%)}
• Calculate the Relative Risk Reduction (RRR):
  • RRR represents the proportional reduction in risk due to the experimental cardiac drug compared to the control group:
  • 𝑅𝑅𝑅 = (Risk in Control Group − Risk in Treatment Group)/ Risk in Control Group
  • RRR = {0.15 – 0.09}/{0.15} = 0.40 (or 40%)}

Interpretation of RRR:

• The Relative Risk Reduction (RRR) of 40% means that the experimental cardiac drug reduces the risk of having a heart attack by 40% compared to those who do not receive the drug.
• In other words, patients taking the experimental drug have a 40% lower relative risk of experiencing a heart attack compared to those in the control group.

Practical Meaning of RRR in This Scenario:

• RRR provides a sense of how much the experimental cardiac drug is helping reduce the relative risk of heart attacks.
• For example, if a patient has an initial 15% risk of having a heart attack without treatment, using the experimental drug reduces that risk to 9%, which means 40% relative reduction compared to not taking the drug.

Consider the Absolute Risk:

While RRR shows an impressive reduction in relative risk, it’s also important to consider the Absolute Risk Reduction (ARR) and Number Needed to Treat (NNT) for a complete understanding of the drug’s effectiveness:

• ARR in this scenario is 6%, meaning that 6 fewer heart attacks per 100 patients occur when using the drug compared to not using it.
• NNT can be calculated as: NNT=1/ARR= 1/0.06 ≈17
• This means that 17 patients need to be treated with the experimental drug to prevent one additional heart attack.

Summary:

• The Relative Risk Reduction (RRR) of 40% shows that the experimental cardiac drug is effective in reducing the risk of heart attacks relative to the control group.
• However, looking at ARR (6%) and NNT (17) also gives insight into how many patients actually benefit, helping balance expectations and provide a clear understanding of the overall impact of the treatment.

Using both RRR and other measures like ARR and NNT provides a comprehensive view of the effectiveness of the experimental cardiac drug, guiding clinical decision-making.

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example 2 – Dumbing it Down RRR, ARR, and NNT

You’re testing a new heart attack prevention drug. You compare two groups:

• Control Group (No Drug) → 10% (10 out of 100) have a heart attack.
• Treatment Group (With Drug) → 5% (5 out of 100) have a heart attack.

1. Absolute Risk Reduction (ARR) – “How much the risk drops in real numbers”

ARR tells us the actual difference in event rates between the groups. ARR=CER−EERARR = \text{CER} – \text{EER}ARR=CER−EER

🔹 Interpretation: The drug reduces the absolute risk of heart attack by 5 percentage points.

2. Relative Risk Reduction (RRR) – “How much the risk drops compared to the original risk”

RRR tells us how much the risk was reduced relative to the control group.

🔹 Interpretation: The drug cuts the risk in half (50% reduction compared to no drug).

3. Number Needed to Treat (NNT) – “How many people need to take the drug to help ONE person”

NNT tells us how many people need to be treated to prevent one bad outcome.

🔹 Interpretation: You need to treat 20 people to prevent 1 heart attack.

Simple Takeaway

Measure	Meaning	Example Interpretation
ARR	How much the risk drops in real numbers	Risk drops by 5 percentage points (10% → 5%)
RRR	How much the risk drops compared to the original risk	The risk is cut in half (50% reduction)
NNT	How many people need treatment to prevent 1 bad outcome	Need to treat 20 people to prevent 1 heart attack

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The Experimental Treatment Increases the Probability of a Good Event

Relative Benefit Increase (RBI):

Increase in rates of good events between experimental (EER) and control (CER) groups.

Absolute Benefit Increase (ABI):

Absolute difference in good event rates between experimental (EER) and control (CER) groups.

Number Needed to Treat (NNT):

• Number of patients needed to receive the experimental treatment to create one additional improved outcome.
• achieving a positive outcome, such as recovery from an illness, improved quality of life, or remission of a disease.
• Example:
  • If a new drug is being tested to improve recovery rates from an infection, the NNT tells us how many people need to receive the drug for one additional person to recover compared to a control group
  • Lower NNT: example NNT = 12 – every 12 patients treated with the new drug, 1 additional person recovers compared to placebo, This means the drug is more effective
  • Higher NNT: example NNT = 56 – every 56 patients treated with the new drug, 1 additional person recovers compared to placebo. This indicates that the drug is less effective, as more patients need to be treated to see the same benefit.
• NNT should always be reported with a 95% confidence interval (CI) to express the range within which the true NNT might lie.

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The Experimental Treatment Increases the Probability of a Bad Event

Relative Risk Increase (RRI):

Increase in rates of bad events between experimental (EER) and control (CER) groups.

Absolute Risk Increase (ARI):

• Absolute difference in bad event rates between experimental (EER) and control (CER) groups.

Number Needed to Harm (NNH)

• Number of patients needed to receive the experimental treatment for one additional person to be harmed compared with control treatment.