Medical Statistics Made Easy, fourth edition

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Let’s say we are trying to establish whether there is a link between smoking and lung cancer. Our sample can be split into four groups: exposed with cancer, exposed without cancer, unexposed with cancer and unexposed without cancer (table 5). Life tables are useful for showing the trend of survival over time when the survival data for each individual is not known. An example of a cohort life table is shown below (Table 7). It is important to consider that death is not the only way that subjects may leave a study. They may be lost to follow-up or they may have to be withdrawn deliberately (this is the ‘number censored’). The risk and chance of survival for any given interval may also then be calculated. RISK REDUCTION AND NUMBERS NEEDED TO TREAT How important are they? Although only quoted in 5% of papers, they are helpful in trying to work out how worthwhile a treatment is in clinical practice. How easy are they to understand? LLL Relative risk reduction (RRR) and absolute risk reduction (ARR) need some concentration. Numbers needed to treat (NNT) are pretty intuitive, useful and not too difficult to work out for yourself. When are they used? They are used when an author wants to know how often a treatment works, rather than just whether it works. What do they mean? ARR is the difference between the event rate in the intervention group and that in the control group. It is also the reciprocal of the NNT and is usually given as 100 a percentage, i.e. ARR = NNT NNT is the number of patients who need to be treated for one to get benefit. those studies by showing the mean changes and 95% CIs in a chart. An example is given in Fig. 8. Study A Study B Study C Study D Study E Combined estimate –40

This can look far more daunting than it really is. The symbols x and y denote the exposure and outcomes respectively – x‾ and ȳ represent the means of these. A value of r=0 means that there is no correlation and the data will exhibit a straight line when plotted. When r = 1 there is a perfect positive correlation – when r = -1 there is a perfect negative correlation. Correlation is no longer reliable when looking at data that exhibits curvilinear relationships, as it is likely to identify these data sets as having no correlation. If we have two sets of data with the same mean but different SDs, then the data set with the larger SD has a wider spread than the data set with the smaller SD. For example, if another group of patients enrolling for the trial has the same mean weight of 80 kg but an SD of only 3, ±1 SD will include 68.2% of the subjects, so 68.2% of patients will weigh between 77 and 83 kg (Fig. 7). Compare this with the example above. 14 A mean appeared in 2⁄3 papers surveyed, so it is important to have an understanding of how it is calculated. 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."Dr Michael Harris MB BS FRCGP MMEd is a GP and lecturer in General Practice in Bath. He teaches nurses, medical students and GP registrars. Until recently he was an examiner for the MRCGP. Dr Gordon Taylor PhD MSc BSc (Hons) is a senior research fellow in medical statistics at the University of Bath. His main role is in the teaching, support and supervision of health care professionals involved in non-commercial research. Procedure bias: subjects in different arms of the study are treated differently (other than the exposure or intervention). Medical Statistics Made Easy EXAMPLE Mann Whitney U test A GP introduced a nurse triage system into her practice. She was interested in finding out whether the age of the patients attending for triage appointments was different to that of patients who made emergency appointments with the GP. Six hundred and forty-six patients saw the triage nurse and 532 patients saw the GP. The median age of the triaged patients was 50 years (1st quartile 40 years, 3rd quartile 54), for the GP it was 46 (22, 58). Note how the quartiles show an uneven distribution around the median, so the data cannot be normally distributed and a non-parametric test is appropriate. The graph in Fig. 9 shows the ages of the patients seen by the nurse and confirms a skewed, rather than normal, distribution. 300 Number of patients Ages of patients Fig. 9. Graph of ages of patients seen by triage nurse. 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)).

Medical Statistics Made Easy RRR is the proportion by which the intervention reduces the event rate. EXAMPLES One hundred women with vaginal candida were given an oral antifungal, 100 were given placebo. They were reviewed 3 days later. The results are given in Table 4. Table 4. Results of placebo-controlled trial of oral antifungal agent Given antifungal Given placebo Improved No improvement Improved No improvement ARR = improvement rate in the intervention group improvement rate in the control group = 80% 60% = 20% NNT = = =5 ARR 20 So five women have to be treated for one to get benefit. The incidence of candidiasis was reduced from 40% with placebo to 20% with treatment, i.e. by half. Thus, the RRR is 50%. In another trial young men were treated with an expensive lipid-lowering agent. Five years later the death rate from ischaemic heart disease (IHD) is recorded. See Table 5 for the results. Table 5. Results of placebo-controlled trial of Cleverstatin Given Cleverstatin Given placebo Survived Died Survived Died 998 (99.8%) 2 (0.2%) 996 (99.6%) 4 (0.4%) ARR = improvement rate in the intervention group improvement rate in the control group = 99.8% 99.6% = 0.2% What does it mean? Statisticians can calculate a range (interval) in which we can be fairly sure (confident) that the “true value” lies. For example, we may be interested in blood pressure (BP) reduction with antihypertensive treatment. From a sample of treated patients we can work out the mean change in BP.Mann Whitney and Other Non-Parametric Tests 33 The statistician used a Mann Whitney U test to test the hypothesis that there is no difference between the ages of the two groups. This gave a U value of with a P value of < Ignore the actual U value but concentrate on the P value, which in this case suggests that the triage nurse s patients were very highly significantly older than those who saw the GP. Watch out for... The Wilcoxon signed rank test, Kruskal Wallis and Friedman tests are other non-parametric tests. Do not be put off by the names go straight to the P value. 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 Medical Statistics Made Easy EXAMPLES Out of 50 new babies on average 25 will be girls, sometimes more, sometimes less. Say there is a new fertility treatment and we want to know whether it affects the chance of having a boy or a girl. Therefore we set up a null hypothesis that the treatment does not alter the chance of having a girl. Out of the first 50 babies resulting from the treatment, 15 are girls. We then need to know the probability that this just happened by chance, i.e. did this happen by chance or has the treatment had an effect on the sex of the babies? The P value gives the probability that the null hypothesis is true. The P value in this example is Do not worry about how it was calculated, concentrate on what it means. It means the result would only have happened by chance in in 1 (or 1 in 140) times if the treatment did not actually affect the sex of the baby. This is highly unlikely, so we can reject our hypothesis and conclude that the treatment probably does alter the chance of having a girl. Try another example: Patients with minor illnesses were randomized to see either Dr Smith or Dr Jones. Dr Smith ended up seeing 176 patients in the study whereas Dr Jones saw 200 patients (Table 2). Table 2. Number of patients with minor illnesses seen by two GPs Dr Jones Dr Smith P value i.e. could have (n=200) a (n=176) happened by chance Patients satisfied 186 (93) 168 (95) 0.4 Four times in 10 with consultation (%) possible Mean (SD) consultation 16 (3.1) 6 (2.8) <0.001 < One time in 1000 length (minutes) very unlikely Patients getting a 58 (29) 76 (43) 0.3 Three times in 10 prescription (%) possible Mean (SD) number of 3.5 (1.3) 3.6 (1.3) 0.8 Eight times in 10 days off work probable Patients needing a 46 (23) 72 (41) 0.05 Only one time in 20 follow-up appointment (%) fairly unlikely a n=200 means that the total number of patients seen by Dr Jones was 200.

There are tables which correlate the percentage of the area under the curve to the value on the x-axis of the SND. A sample of such a table can be found below (table 1). Odds Ratio 41 Next, odds ratios. They are calculated by dividing the odds of having been exposed to a risk factor by the odds in the control group. An odds ratio of 1 indicates no difference in risk between the groups, i.e. the odds in each group are the same. If the odds ratio of an event is >1, the rate of that event is increased in patients who have been exposed to the risk factor. If <1, the rate of that event is reduced. Odds ratios are frequently given with their 95% CI if the CI for an odds ratio does not include 1 (no difference in odds), it is statistically significant. EXAMPLES A group of 100 patients with knee injuries, cases, was matched for age and sex to 100 patients who did not have injured knees, controls. In the cases, 40 skied and 60 did not, giving the odds of being a skier for this group of 40:60 or In the controls, 20 patients skied and 80 did not, giving the odds of being a skier for the control group of 20:80 or We can therefore calculate the odds ratio as 0.66/0.25 = The 95% CI is 1.41 to If you cannot follow the maths, do not worry! The odds ratio of 2.64 means that the number of skiers in the cases is higher than the number of skiers in the controls, and as the CI does not include 1 (no difference in risk) this is statistically significant. Therefore, we can conclude that skiers are more likely to get a knee injury than non-skiers. Standard Deviation 19 range for the variable. For example, if we have some length of hospital stay data with a mean stay of 10 days and a SD of 8 days then: mean 2 SD = = = -6 days. This is clearly an impossible value for length of stay, so the data cannot be normally distributed. The mean and SDs are therefore not appropriate measures to use. Good news it is not necessary to know how to calculate the SD. It is worth learning the figures above off by heart, so a reminder ±1 SD includes 68.2% of the data ±2 SD includes 95.4%, ±3 SD includes 99.7%. Keeping the normal distribution curve in Fig. 6 in mind may help. E X A M T I P Examiners may ask what percentages of subjects are included in 1, 2 or 3 SDs from the mean. Again, try to memorize those percentages. Medical Statistics Made Easy those studies by showing the mean changes and 95% CIs in a chart. An example is given in Fig. 8. Study A Study B Study C Study D Study E Combined estimate Change in BP (mmhg) Fig. 8. Plot of 5 studies of a new antihypertensive drug. See how the results of studies A and B above are shown by the top two lines, i.e. 20 mmhg, 95% CI for study A and 20 mmhg, 95% CI -5 to +45 for study B. The vertical axis does not have a scale. It is simply used to show the zero point on each CI line. The statistician has combined the results of all five studies and calculated that the overall mean reduction in BP is 14 mmhg, CI This is shown by the combined estimate diamond. See how combining a number of studies reduces the CI, giving a more accurate estimate of the true treatment effect. The chart shown in Fig. 8 is called a Forest plot or, more colloquially, a blobbogram. Standard deviation and confidence intervals what is the difference? Standard deviation tells us about the variability (spread) in a sample. The CI tells us the range in which the true value (the mean if the sample were infinitely large) is likely to be.Not easy, but worth persevering as it is used so frequently. It is not important to know how the P value is derived – just to be able to interpret the result. MEDIAN Sometimes known as the mid-point. How important is it? It is given in over a third of mainstream papers. How easy is it to understand? LLLLL Even easier than the mean! When is it used? It is used to represent the average when the data are not symmetrical, for instance the skewed distribution in Fig. 2. Fig. 2. A skewed distribution. The dotted line shows the median. Compare the shape of the graph with the normal distribution shown in Fig. 1. What does it mean? It is the point which has half the values above, and half below. Risk ratios (or relative risks) are one way of comparing two proportions. They are calculated with the following equation: Hazard is defined as the risk at any given time of reaching the endpoint outcome in a survival analysis. This outcome is most often death, but it can be other things also such as disease progression. Let’s see an example. Below is a graph from a paper looking at the effect of the humanised monoclonal antibody ocrelizumab on the progression of multiple sclerosis (figure 5) (1). Figure 5 1 Medical Statistics Made Easy The χ 2 test is simpler for statisticians to calculate but gives only an approximate P value and is inappropriate for small samples. Statisticians may apply Yates continuity correction or other adjustments to the χ 2 test to improve the accuracy of the P value. The Mantel Haenszel test is an extension of the χ 2 test that is used to compare several two-way tables.

The data exhibited in life tables can be used to construct survival curves. We encountered such a graph (a Kaplan-Meier curve) when discussing hazard ratios (figure 5). Risk Reduction and Numbers Needed to Treat 47 You may see ARR and RRR given as a proportion instead of a percentage. So, an ARR of 20% is the same as an ARR of 0.2 E X A M T I P Be prepared to calculate RRR, ARR and NNT from a set of results. You may find that it helps to draw a simple table like Table 5 and work from there. Medical Statistics Made Easy Fig. 1. The normal distribution. The dotted line shows the mean of the data. What does it mean? The mean is the sum of all the values, divided by the number of values. EXAMPLE Five women in a study on lipid-lowering agents are aged 52, 55, 56, 58 and 59 years. Add these ages together: = 280 Now divide by the number of women: = 56 So the mean age is 56 years. 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. If you want a statistics course • Work through from start to finish for a complete course in commonly used medical statistics. Whereas probabilities can only adopt a value between 0 and 1, odds may have any value from 0 to infinity.Sensitivity and specificity tell us about the diagnostic capacity of the test. However, the predictive values demonstrate how likely it is that an individual does or does not have the disease based on their test result. A love of statistics is, oddly, not what attracts most young people to a career in medicine and I suspect that many clinicians, like me, have at best a sketchy and incomplete understanding of this difficult subject. Delivering modern, high quality care to patients now relies increasingly on routine reference to scientific papers and journals, rather than traditional textbook learning. Acquiring the skills to appraise medical research papers is a daunting task. Realizing this, Michael Harris and Gordon Taylor have expertly constructed a practical guide for the busy clinician. One a practising NHS doctor, the other a medical statistician with tremendous experience in clinical research, they have produced a unique handbook. It is short, readable and useful, without becoming overly bogged down in the mathematical detail that frankly puts so many of us off the subject. I commend this book to all healthcare professionals, general practitioners and hospital specialists. It covers all the ground necessary to critically evaluate the statistical elements of medical research papers, in a friendly and approachable way. The scoring of each brief chapter in terms of usefulness and ease of comprehension will efficiently guide the busy practitioner through his or her reading. In particular it is almost unique in covering this part of the syllabus for royal college and other postgraduate examinations. Certainly a candidate familiar with the contents of this short book and taking note of its