For example, when the odds are 1:10, or 0.1, one person will have the event for every 10 who do not, and, using the formula, the risk of the event is 0.1/(1+0.1) = 0.091. The simplest way to ensure that the interpretation is correct is to first convert the odds into a risk. The interpretation of an odds is more complicated than for a risk. Odds can be converted to risks, and risks to odds, using the formulae: For example, an odds of 0.01 is often written as 1:100, odds of 0.33 as 1:3, and odds of 3 as 3:1. It is commonly expressed as a ratio of two integers. In gambling, the odds describes the ratio of the size of the potential winnings to the gambling stake in health care it is the ratio of the number of people with the event to the number without. The odds is the ratio of the probability that a particular event will occur to the probability that it will not occur, and can be any number between zero and infinity. Odds is a concept that is more familiar to gamblers. In a sample of 1000 people, these numbers are 100 and 500 respectively. For example, when the risk is 0.1, about 10 people out of every 100 will have the event when the risk is 0.5, about 50 people out of every 100 will have the event. It is simple to grasp the relationship between a risk and the likely occurrence of events: in a sample of 100 people the number of events observed will on average be the risk multiplied by 100. In ‘Summary of findings’ tables in Cochrane reviews, it is often expressed as a number of individuals per 1000 (see Chapter 11, Section 11.5). In research, risk is commonly expressed as a decimal number between 0 and 1, although it is occasionally converted into a percentage. Risk describes the probability with which a health outcome (usually an adverse event) will occur. Risk is the concept more familiar to patients and health professionals. When the difference between them is ignored, the results of a systematic review may be misinterpreted. In statistics, however, risk and odds have particular meanings and are calculated in different ways. In general conversation the terms ‘risk’ and ‘odds’ are used interchangeably (as are the terms ‘chance’, ‘probability’ and ‘likelihood’) as if they describe the same quantity. For the current version, please go to /handbook/current or search for this chapter here. This is an archived version of the Handbook.
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