Statistics

Diagnostic Test Calculations

Treatment Calculations

Definitions of Allocation and Blinding in Clinical Trials

Allocation Concealment

• Allocation Concealed:
  • Adequate measures were taken to conceal allocation to study group assignments from those responsible for assessing patients for entry in the trial.
  • Examples:
    • Central randomization
    • Sequentially numbered, opaque, sealed envelopes
    • Numbered or coded bottles and containers
    • Drugs prepared by the pharmacy
    • Other descriptions with convincing elements of concealment
• Allocation Not Concealed:
  • Inadequate measures were taken to conceal allocation to study group assignments.
  • Examples:
    • No concealment procedures
    • Sealed envelopes that were not opaque
    • Other descriptions not convincing of concealment
• Unclear Allocation Concealment:
  • The article did not report or provide a description of the allocation concealment sufficient to classify as concealed or not concealed.

Blinding

• Blinded:
  • Any or all of the following groups were unaware of who received which study intervention:
    • Clinicians
    • Patients
    • Participants
    • Outcome assessors
    • Statisticians
  • If “initially” is indicated (e.g., “blinded [patients and outcome assessor initially]”), it means the code was broken during the trial, possibly due to adverse effects.
• Blinded (Unclear):
  • The authors did not report or provide an indication of who, if anyone, was unaware of who received which study intervention.
• Unblinded:
  • All participants in the trial, including clinicians, patients, participants, outcome assessors, and statisticians, were aware of who received which study intervention.

Definitions Relating to Data Presentation in Therapeutics

Definitions

• Control Event Rate (CER): The proportion of events occurring in the control group.
  • Formula:

• Experimental Event Rate (EER): The proportion of events occurring in the experimental group.
  • Formula:

The Experimental Treatment Reduces the Risk for a Bad Event

• Relative Risk Reduction (RRR): Proportional reduction in bad event rates between experimental (EER) and control (CER) groups.
  • Accompanied by 95% Confidence Interval (CI)

• 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.
  • Rounded up to the next whole number
  • Accompanied by 95% CI

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.

3. 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.

Additional Terms

• Confidence Interval (CI): Quantifies uncertainty in measurement; usually reported as 95% CI, indicating the range within which we can be 95% sure the true value for the whole population lies.
• Weighted Event Rates: Contributions of individual studies to the total in a meta-analysis, determined by sample size and number of events in each study.

Diagnostic Test Calculations

Diagnostic Standard

• Diagnostic Standard: The method used to confirm the presence or absence of the target disorder, often referred to as the “gold” or “reference” standard.

Definitions and Formulas

1. True Positive (a): Individuals who have the target disorder and a positive test result.
2. False Positive (b): Individuals who do not have the target disorder but have a positive test result.
3. True Negative (d): Individuals who do not have the target disorder and have a negative test result.
4. False Negative (c): Individuals who have the target disorder but have a negative test result.

Sensitivity

• Sensitivity: The proportion of individuals with the target disorder who have a positive test result.
• Formula:

Specificity

• Specificity: The proportion of individuals without the target disorder who have a negative test result.
• Formula:

Pre-Test Probability (Prevalence)

• Pre-Test Probability (Prevalence): The proportion of individuals who have the target disorder before the test is carried out.
• Formula:

Pre-Test Odds

• Pre-Test Odds: The odds that an individual has the target disorder before the test is carried out.
• Formula:

Post-Test Probability

• Post-Test Probability: The proportion of individuals with a particular test result who have the target disorder.
• Formula:

• Post-Test Odds: Derived from the likelihood ratios and pre-test odds.

Visual Representation

By applying these formulas, one can determine the sensitivity, specificity, and probabilities associated with a diagnostic test, thereby understanding its effectiveness and predictive value.

Diagnostic Test Calculations: Additional Definitions

Post-Test Odds

• Post-Test Odds: The odds that the patient has the target disorder after the test has been carried out.
• Formula:

Positive Predictive Value (PPV)

• Positive Predictive Value (PPV): The proportion of individuals with a positive test result who have the target disorder.
• Formula:

Negative Predictive Value (NPV)

• Negative Predictive Value (NPV): The proportion of individuals with a negative test result who do not have the target disorder.
• Formula: ( \text{NPV} = \frac{d}{c + d} )

Likelihood Ratios

• Likelihood Ratio: The ratio of the probability of a test result among individuals with the target disorder to the probability of that same test result among individuals who are free of the target disorder.
• Positive Likelihood Ratio (LR+): Ratio of the probability of a positive test result among individuals with the target disorder to the probability of a positive test result among individuals without the target disorder.
  • Formula:

• Negative Likelihood Ratio (LR-): Ratio of the probability of a negative test result among individuals with the target disorder to the probability of a negative test result among individuals without the target disorder.
  • Formula:

Diagnostic Accuracy

• Diagnostic Accuracy: The proportion of true positive and true negative test results among all individuals tested.
• Formula:

Visual Representation

By applying these formulas, one can determine the predictive values, likelihood ratios, and diagnostic accuracy of a test, thereby understanding its effectiveness and predictive value.

Summary of Formulas