Statistics for Clinical Research – A practical Guide

The hazard ratio (HR) is a measure of the relative risk of an event occurring in one group versus another. It is commonly used in survival analysis and clinical trials to compare the risk of an event (such as death or disease progression) between a treatment group and a control group. The HR is calculated as the ratio of the hazard (or risk) of the event occurring in the treatment group to the hazard of the event occurring in the control group. A HR greater than 1 indicates that the treatment group has a higher risk of the event, while a HR less than 1 indicates that the treatment group has a lower risk of the event. A HR of 1 indicates that the risk of the event is the same in both groups.

Risk is the probability that an event will occur. It is typically expressed as a decimal or percentage. For example, a risk of 0.1 (or 10%) means that there is a 10% chance that an event will occur.

Odd ratio (OR) is a measure of the association between an exposure and an outcome. It is a ratio of the odds of the outcome occurring in the exposed group compared to the odds of the outcome occurring in the unexposed group. OR is commonly used in case-control studies. An OR greater than 1 indicates that the exposed group is more likely to have the outcome than the unexposed group, while an OR less than 1 indicates that the exposed group is less likely to have the outcome. An OR of 1 indicates that there is no association between the exposure and the outcome.

It's important to note that Risk and Odds Ratio are different. Risk is a probability and Odds Ratio is a ratio of two probabilities. OR tends to be used more in case-control studies, while HR tends to be used more in cohort studies and clinical trials.

Number needed to treat (NNT) is a measure of the effectiveness of a treatment. It represents the number of patients who need to be treated in order for one additional patient to benefit from the treatment. NNT is calculated as the reciprocal of the absolute risk reduction (ARR). For example, if a treatment reduces the risk of a certain event by 20%, the NNT would be 5, meaning that 5 patients need to be treated for 1 additional patient to benefit from the treatment. Lower NNTs indicate that a treatment is more effective, as fewer patients need to be treated to achieve a beneficial outcome.

Number needed to harm (NNH) is a similar measure to NNT, but it represents the number of patients who need to be treated in order for one additional patient to be harmed by the treatment. NNH is calculated as the reciprocal of the absolute risk increase (ARI). Like NNT, lower NNHs indicate that a treatment is safer, as fewer patients need to be treated to observe harm.

It's important to note that NNT and NNH are related to the treatment effect size, a larger effect size will have a smaller NNT or NNH and vice versa.

A life table, also known as a mortality table or actuarial table, is a statistical tool that is used to model the survival of a population. It is typically used in actuarial science, demography, and epidemiology. A life table is constructed by collecting data on the number of deaths and the number of survivors at each age within a given population.

A basic life table includes two columns, one showing the number of people alive at the beginning of a specific age interval (the "exposure" or "population"), and the other showing the number of deaths that occurred within that age interval (the "cases").

From this information, a number of important statistics can be calculated, including:

• Life expectancy: the average number of years that a person can expect to live, given the current mortality rates

• Mortality rate: the number of deaths per unit of population

• Survival rate: the proportion of people in a population who are still alive at a certain age

• Age-specific death rate: the number of deaths per unit of population at a specific age

Life tables are often used to compare mortality rates between different populations, or to track changes in mortality over time within a population. They can also be used to project future mortality rates, which is important for financial planning and forecasting.

Sensitivity and specificity are two important measures of the performance of a diagnostic test.

Sensitivity is the proportion of true positive cases (people with the disease) that are correctly identified by the test. It is calculated as the number of true positive cases divided by the total number of true positive and false negative cases. A test with high sensitivity will correctly identify most people who have the disease, while a test with low sensitivity will miss many people who have the disease.

Specificity is the proportion of true negative cases (people without the disease) that are correctly identified by the test. It is calculated as the number of true negative cases divided by the total number of true negative and false positive cases. A test with high specificity will correctly identify most people who do not have the disease, while a test with low specificity will incorrectly identify many people as having the disease.

It's important to note that a high sensitivity test will tend to have a lower specificity, and vice versa. Therefore, it's essential to consider both sensitivity and specificity together when evaluating a diagnostic test. It also depends on the clinical context, for example, a screening test for a rare disease will have a different sensitivity and specificity cutoff than a test for a common disease.