should not have decimal places if the number of subjects in total is less than 100.Summary statistics:6 If a relative risk is quoted, what is the ARD? Is this a very small number? Beware of reports that only quote relative risks and give no hint of the absolute risk!
7 If an odds ratio is quoted, is it a reasonable approximation to the relative risk? (Ask what the size of the risk in the two groups are).
3.3 Exercises
Table 3.9 shows the results of randomised controlled trial in primary care in patients with venous leg ulcers to compare a new specially impregnated bandage, called ‘Band aid’, with usual care. Usual care will be treatment by district nurses with standard bandages and wound dressings. The primary outcome for the study will be whether or not the index or reference leg ulcer has completely healed at a 12‐month post‐randomisation.
1 3.1 What proportion of patients in the Band‐aid group had a completely healed leg ulcer at 12 months?0.300.400.600.650.70
2 3.2 What proportion of patients had a completely healed leg ulcer at 12 months in the control group?0.300.400.600.650.70
3 3.3 What is the difference in response (leg ulcer healing rates at 12 months) between the Band‐aid and control groups?−0.10−0.050.000.050.10
4 3.4 Calculate the number of people needed to be treated with Band‐aid dressing in order for an additional person to have a completely healed leg ulcer at 12 months compared to people usual care?6 78810
5 3.5 What is the relative risk for the leg ulcer healing at 12 months in the Band‐aid group compared to the control group?0.640.861.171.562.33
6 3.6 What is the relative risk for the leg ulcer healing at 12 months in the control group compared to the Band‐aid group?0.640.861.171.562.33
7 3.7 What are the odds for the leg ulcer healing at 12 months in the Band‐aid group?0.640.861.501.562.33
8 3.8 What are the odds for the leg ulcer healing at 12 months in the control group?0.640.861.501.562.33
9 3.9 Calculate the odds ratio for the leg ulcer healing at 12 months in the Band‐aid group compared to the control group?0.640.861.171.562.33
10 3.10 Calculate the odds ratio for the leg ulcer healing at 12 months in the control group compared to the band‐aid group?0.640.861.171.562.33
4 Probability and Distributions
2 4.2 The Binomial Distribution
3 4.3 The Poisson Distribution
4 4.4 Probability for Continuous Outcomes
8 4.8 Points When Reading the Literature
Summary
Probability is defined in terms of either the long‐term frequency of events, as model based or as a subjective measure of the certainty of an event happening. Examples of each type are given. The concepts of independent events and mutually exclusive events are discussed. Several theoretical statistical distributions, such as the Binomial, Poisson and Normal are described. The properties of the Normal distribution and its importance are stressed and its use in calculating reference intervals is also discussed.
4.1 Types of Probability
There are a number of ways of looking at probability and we describe three as the ‘frequency’, ‘model‐based’ and ‘subjective’ approaches as shown in Figure 4.1.
Figure 4.1 Three types of probability.
We all have an intuitive feel for probability but it is important to distinguish between probabilities applied to single individuals and probabilities applied to groups of individuals. In recent years about 600 000 people die annually from about 65 million people in the United Kingdom. Hence, for a single individual, with no information about their age or state of health, the chance or probability of dying in any particular year is 600 000/65 000 000 = 0.009 or just under 1 in 100. This is termed the crude mortality rate as it ignores differences in individuals due, for example, to their gender or age, which are both known to influence mortality. From year‐to‐year this probability of dying is fairly stable (see Figure 4.2), although there has been a long‐term decline over the years in the probability of dying. This illustrates that the number of deaths in a group can be accurately predicted but, despite this, it is not possible to predict exactly which particular individuals are going to die.
Figure 4.2 Crude mortality rates in the United Kingdom from 1982 to 2016.
(Source: data from ONS 2017, https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/datasets/deathregistrationssummarytablesenglandandwalesdeathsbysingleyearofagetables).
The basis of the idea of probability is a sequence of what are known as independent trials. To calculate the probability of an individual dying in one year we give each one of a group of individuals a trial over a year and the event occurs if the individual dies. As already indicated, the estimate of the (crude) probability of dying is the number of deaths divided by the number in the original group. The
