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.
- Any or all of the following groups were unaware of who received which study intervention:
- 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
- True Positive (a): Individuals who have the target disorder and a positive test result.
- False Positive (b): Individuals who do not have the target disorder but have a positive test result.
- True Negative (d): Individuals who do not have the target disorder and have a negative test result.
- 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.