Medical Statistics Made Easy, fourth edition

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The same equation can be applied to look at how multiple independent variables influence the dependent variable. Here's what the reviewer said: "This is a practical guide to the use of statistics in medical literature and their application in clinical practice. The numerous examples help make the conceptualization of complex ideas easy. It is a great resource for healthcare students and clinicians in the field." Regression analyses are other methods to elucidate the relationships between variables. Using these methods we can determine how we could expect one variable to change in relation to the other. The type of regression analysis that should be used differs based on the characteristics of the variables. Let’s say we wanted to find the mean blood cholesterol of patients in a hospital. We would probably do this by taking a sample of patients from the hospital, and then calculate a sample statistic (in this case, mean blood cholesterol). Inferences could then be made based on this and extrapolated to the population of interest (i.e. from some of the patients in the hospital (our sample) to all of them (our population of interest)). If we do this lots of times we would generate lots of means – plotting the distribution of these means would give us the sampling distribution of the mean. If the sample size is large, the sampling distribution of the mean will have a normal distribution regardless of the actual distribution in the population. If the sample size is smaller, the sampling distribution of the mean will only be normal if the actual distribution in the population is normal.

Although the normal distribution is very common in medical statistics, it is not the only way in which data can be distributed. Data distributed in a pattern that is not normal is described as nonparametric. Below are summarised the names of tests that should be performed in certain situations for parametric data (table 2). The corresponding test for nonparametric data is also given. In some cases, more than one test can be used to get identical results. Purpose Risk Ratio 39 EXAMPLES A cohort of 1000 regular football players and 1000 non-footballers were followed to see if playing football was significant in the injuries that they received. After 1 year of follow-up there had been 12 broken legs in the football players and only four in the non-footballers. The risk of a footballer breaking a leg was therefore 12/1000 or The risk of a non-footballer breaking a leg was 4/1000 or The risk ratio of breaking a leg was therefore 0.012/0.004 which equals three. The 95% CI was calculated to be 0.97 to As the CI includes the value 1 we cannot exclude the possibility that there was no difference in the risk of footballers and non-footballers breaking a leg. However, given these results further investigation would clearly be warranted.

Watch out for... If a value (or a number of values) is a lot smaller or larger than the others, “skewing” the data, the mean will then not give a good picture of the typical value.

CORRELATION How important is it? Only used in 10% of medical papers. How easy is it to understand? LLL When is it used? Where there is a linear relationship between two variables there is said to be a correlation between them. Examples are height and weight in children, or socio-economic class and mortality. The strength of that relationship is given by the correlation coefficient. What does it mean? The correlation coefficient is usually denoted by the letter r for example r = 0.8 A positive correlation coefficient means that as one variable is increasing the value for the other variable is also increasing the line on the graph slopes up from left to right. Height and weight have a positive correlation: children get heavier as they grow taller. A negative correlation coefficient means that as the value of one variable goes up the value for the other variable goes down the graph slopes down from left The arrows point to the modes at ages 10–19 and 60–69. Bi-modal data may suggest that two populations are present that are mixed together, so an average is not a suitable measure for the distribution. Confounding variables are those which are linked to the outcome but have not been accounted for in the study. For example, we may observe that as ice cream sales increase, so do the number of drownings. This is because ice cream sales will increase in the summer; simultaneously more people will be going for a swim. Therefore there is not a direct causative link between ice creams and drownings, but there is an indirect correlation that we have not accounted for.MEAN Otherwise known as an arithmetic mean, or average. How important is it? A mean appeared in 2 3 papers surveyed, so it is important to have an understanding of how it is calculated. How easy is it to understand? LLLLL One of the simplest statistical concepts to grasp. However, in most groups that we have taught there has been at least one person who admits not knowing how to calculate the mean, so we do not apologize for including it here. When is it used? It is used when the spread of the data is fairly similar on each side of the mid point, for example when the data are normally distributed. The normal distribution is referred to a lot in statistics. It s the symmetrical, bell-shaped distribution of data shown in Fig. 1. Le T, Bhushan V, Sochat M. First aid for the USMLE step 1 2016. New York: McGraw-Hill Education; 2016. In statistics, we want to draw conclusions about a population based on a smaller sample. The estimates we make about the broader population based on the sample are called sample statistics. If we were to take lots of samples, it is not likely that the sample statistics for each sample would be the same (this is due to sampling variation); however, there should be a tendency towards the true value for the population. EXAMPLE Let us say that a group of patients enrolling for a trial had a normal distribution for weight. The mean weight of the patients was 80 kg. For this group, the SD was calculated to be 5 kg. 1 SD below the average is 80 – 5 = 75 kg. 1 SD above the average is 80 + 5 = 85 kg. ±1 SD will include 68.2% of the subjects, so 68.2% of patients will weigh between 75 and 85 kg. 95.4% will weigh between 70 and 90 kg (±2 SD). 99.7% of patients will weigh between 65 and 95 kg (±3 SD). See how this relates to the graph of the data in Fig. 6. 14 Montalban X, Hauser SL, Kappos L, Arnold DL, Bar-Or A, Comi G et al. Ocrelizumab vs placebo in primary progressive multiple sclerosis. New England Journal of Medicine 2017;376(3):209-220.

Let’s now apply the information in table 6 to a theoretical population of 5,000 stroke patients. We can see that without the drug we could expect 2,500 of these patients to die (), but with the new treatment, this would be reduced to 2,000 (). In other words, for every 10 patients who are treated with the new drug, there is 1 patient whose life will be saved who would otherwise have died. In a population of 5,000, this means 500 lives will be saved (Table 6). The worked examples that demonstrate the statistical method in action have been updated to include current articles from the medical literature and now feature a much wider range of medical journals. What do they mean? “Per cent” means per hundred, so a percentage describes a proportion of 100. For example 50% is 50 out of 100, or as a fraction 1⁄2. Other common percentages are 25% (25 out of 100 or 1⁄4), 75% (75 out of 100 or 3⁄4). To calculate a percentage, divide the number of items or patients in the category by the total number in the group and multiply by 100.Imagine we are conducting a study looking at the effect of an exposure on an outcome (e.g. the effect of smoking on GFR). We have two groups (an exposure and a control) and two mean outcome values (one for each group). Calculating the difference between the means and dividing this by the standard error gives a z-score. The z-score is the number of standard deviations away from the mean that the mean difference lies (or the value on the x-axis on the graph of the standard normal distribution (see the section on SND)). Biases are systematic differences between the data that has been collected and the reality in the population. There are numerous types of bias to be aware of, some of which are listed below: Measurement bias: when information is recorded in a distorted manner (e.g. an inaccurate measurement tool).