Reference Equations
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| Equation | Description |
|---|---|
| SEM = SD / √(sample size) | Standard Error of the Mean measures the accuracy with which a sample represents a population. |
| SD = √(variance) | Standard Deviation quantifies the amount of variation in a set of data values. |
| LR- = (1 – sensitivity) / specificity | Negative Likelihood Ratio indicates how much the odds of the disease decrease when a test is negative. |
| LR+ = sensitivity / (1 – specificity) | Positive Likelihood Ratio indicates how much the odds of the disease increase when a test is positive. |
| False Positive Rate = 1 – specificity | The probability that a test incorrectly indicates presence in a disease-free individual. |
| True Positive Rate = sensitivity | The probability that a test correctly indicates presence in an affected individual. |
| Sensitivity = TP / (TP + FN) = a / (a + c) | Sensitivity measures the ability of a test to correctly identify those with the condition (true positives) from all those who actually have the condition (true positives + false negatives). It reflects how well a test can detect the condition when it is truly present. |
| Specificity = TN / (TN + FP) = d / (d + b) | Specificity measures the ability of a test to correctly identify those without the condition (true negatives) from all those who do not have the condition (true negatives + false positives). It reflects how well a test avoids false positives. |
| PPV = TP / (TP + FP) = a / (a + b) | Positive Predictive Value (PPV) indicates the likelihood that someone who tests positive for the condition truly has the condition. It measures the proportion of true positives out of all positive test results. |
| NPV = TN / (TN + FN) = d / (d + c) | Negative Predictive Value (NPV) indicates the likelihood that someone who tests negative for the condition truly does not have the condition. It measures the proportion of true negatives out of all negative test results. |
| Pre-test Probability = (a + b) / (a + b + c + d) = (TP + FN) / total | Pre-test probability is crucial for interpreting diagnostic tests because it influences the positive predictive value (PPV) and negative predictive value (NPV) of the test. A high pre-test probability means that a positive test result is more likely to represent true disease, while a low pre-test probability increases the chances that a positive result could be a false positive. In summary, pre-test probability is the estimated chance that a person has the disease before the test results, often derived from the disease prevalence or clinical suspicion. |
| NNT = 1 / (CER – EER) | Number Needed to Treat is the average number of patients who need to be treated to prevent one additional bad outcome. |
| Variance = SD² | Variance measures the dispersion of a set of data points around their mean value. |
| Odds Ratio = (ad) / (bc) | Odds Ratio compares the odds of an event occurring in one group to the odds of it occurring in another group. |
| Risk Ratio or Relative Risk = (a / (a + b)) / (c / (c + d)) = EER / CER | This means that the Risk Ratio compares the probability of an event occurring in the experimental group (EER) to the probability of the event occurring in the control group (CER). If the RR is 1, it indicates no difference in risk between the two groups. An RR less than 1 suggests a reduced risk in the experimental group, while an RR greater than 1 suggests an increased risk in the experimental group. |
| Precision = TP / (TP + FP) | Precision measures the accuracy of the positive predictions made by a test. |
| ROC Curve = sensitivity vs 1-specificity | Receiver Operating Characteristic curve evaluates the diagnostic ability of a binary classifier system. |
| AR = (CER – EER) / CER | Attributable Risk calculates the difference in risk between exposed and unexposed groups. |
| ARR = CER – EER | Absolute risk reduction, measures the decrease in the rate of an undesired/harmful outcome due to the treatment |
| RRR = (CER – EER) / CER = ARR / CER | RRR quantifies how much the risk is reduced in the treatment group compared to the control group, relative to the control group’s risk. |
| ARI = EER – CER | Absolute risk increase measures the increase in the risk of an undesirable event/outcome due to the treatment or intervention. |
| ABI = EER – CER | Absolute benefit increase measures the increase in the rate of a desired/beneficial outcome due to the treatment. |
| *Note regarding ARI and ABI: The key difference is whether you are looking at an undesirable event to calculate the risk increase (ARI), or a desired outcome to calculate the benefit increase (ABI). They are complementary ways to express the absolute effect of a treatment. | |
| Type 1 Error | Rejecting a true null hypothesis. |
| Type 2 Error = 1 – power | Accepting a false null hypothesis. Type 2 error is denoted by Beta. So if the power is set at 80%, the chance of a type 2 error is 20%. |
| Pre-test Odds = prevalence / (1 – prevalence) | The odds that a patient has the condition before a test is performed. |
| Post-test Odds = pre-test odds x LR+ | The odds that a patient has the condition after a positive test result. |
| Pre-test Odds = pre-test probability / (1 – pre-test probability) | An alternative way to calculate the post-test odds when you are only provided with the pre-test probabilities. |
Here’s a glossary of the acronyms used:
- SEM: Standard Error of the Mean
- SD: Standard Deviation
- LR-: Negative Likelihood Ratio
- LR+: Positive Likelihood Ratio
- NNT: Number Needed to Treat
- ROC: Receiver Operating Characteristic
- AR: Attributable Risk
- TP: True Positives
- FP: False Positives