Rates, Risks, and Odds
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Introduction
Risks, rates, and odds describe how often events happen.
Rates
Rates measure the frequency of an event, usually in a defined population and over a set period of time. The use of rates in place of raw numbers allows for comparision between populations at different times and places.
Rates can be crude, relating to the overall defined population, or specific for different subgroups.
- incidence
- prevalence
Incidence
Incidence is the the number of new events/cases over a specific time period, in an at-risk population. A cumulative index rate (CIR) is usually given, with the time period commonly being a year.
Person-time incidence only counts the time that participants were actually at risk, and is the number of new events / total person-time units at risk
Prevalence
Prevalence is the total number of people who have a condition at any one time point. Prevalence = incidence x duration. Chronic diseases have a higher prevalence than incidence, while many infectious diseases have high incidence but low prevalence.
Prevalence changes the positive and negative predictive value of screeing tests.
Usually described per unit of population.
( # existing cases in a time / total population ) x unit population
Entire population
Good for looking at burden of disease
Comparing Rates
Adjustment or standardization can remove the effects of confounders when comparing two or more populations.
Direct adjustment uses the averages of specific rates of a study population, weighted according to the distribution of a standard population.
Indirect adjustment is used to compare populations whose specific rates are unknown. Instead, the rates of a standard population are combined with the rates of the study population to yield the 'standardized morbidity ratio'. I have no idea what this means.
Risks
Risk, or probability, is the likelihood an event will occur. It is measured by # of events / # of trials. Risks range from 0 to 1.
- absolute risk
- relative risk
- attributable risk
Absolute Risk
Absolute risk is the actual percentage associated with a given risk factor.
Relative Risk
Relative risk, also called risk ratio, is the incidence probability of an exposed population divided by the incidence probability of the unexposed, or IRE / IRUE. It is very important to report time period.
In a 2x2 table, RR = [A / (A+B)] / [C / (C + D)]
A relative rate of 1 means there is no association; the further from 1, in either direction, the stronger the association, with a strong association being above 3.01 or below 0.40. H0wever, a high RR does not necessarily mean there is a high risk difference - attributable risk (risk difference) provides a better picture of the absolute impact of an effect.
Attributable Risk
While relative risk indicates the strength of an association, the attributable risk (risk difference) provides absolute value of size of the effect. It is calculated as the arthmetic difference of incidence rates in exposed minus unexposed rates, or [A/(A+B) - C/(C+D)].
It assumes causality, in that the level of absolute risk in the exposed group is due to exposure.
The number needed to treat (NNT) = 1 /AR
Population Attributable Risk
The population attributable risk (PAR) is the amount of absolute risk due to a given exposure, and is the attributable risk x the prevalence of exposure in the population.
Odds and Odds Ratios
Odds are the probability of an event happening / the probability of an event not happening. Thus the odds of throwing a three with one die is 1/5.
odds = probability / (1 - probability)
and conversely
probability = odds / (1 + odds)
Odds Ratio
Odds ratio is the ratio of odds for the exposed group vs the unexposed group. It approximates RR, especially for rare outcomes, is more universally appropropriate than RR, and has mathematical advantages over RR.
In a 2x2 table, OR = ( A/B ) / (C/D) = AD / BC
Resources and References
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