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And good morning. My name is Waseem Khan. I'll be talking about statistics today. Can I say thank you to professor. Can do you for inviting me and also to George and well done George on organizing such an excellent uh day with a brilliant lineup of speakers and a good range of topics that I'm sure everyone would find very useful before I start. Can I highlight um this paper in uh JBs as it was? Then it was published in 2006 and is a very clear and concise paper that covers everything that we would need to know as uh orthopedic surgeons and something that would would help us say if we did need to get statisticians involved, then this gives us a basic understanding of what we would need to know and how to approach statisticians in how to, how to give them the relevant information to it so that they could help us. So it would take an hour or two to read, but I would highly recommend it. So I will talk about a number of things and firstly, data and tests. So it is um it is, it is not a good use of resources to get information on everyone that is in a target population. So instead, what we do is we take a sample and get information from that sample. We make a number of assumptions, we assume that the information will get from the sample would represent the target population that the sample has the same characteristics as the target population. Um But at the end of the target population may not be the same as the general population. I'll talk about variables. We know that there are different types of variables. Variables could be categorical or they could be numerical with categorical variables. They could be either in an order. So orginal for example, disease stages or um or guess tolerance and classification for open practice or they could be nominal in which case, there is no order to them. So uh a log handsome classification with no fractures, for example, with numerical data, they could be discreet or continuous. So discreet data would be uh where there are defined numbers. And so a number of visits to clinic or number of operations or continues where the data is continuous. For example, with blood loss, how the data is illustrated is also different. So with, with categorical data, we could use a bar chart or or a party chart for illustrating the data with numerical data, we use histograms. So with, with histograms, there is no gap between the different different uh readings with with the bar chart and there would be gaps as, as the data would be in categories rather than in, in, in, in a numerical order. The choice of statistical tests that are done is also different between the variables. So if we have categorical variables, then we'd be using a different set of statistical tests to compare the, the readings that we have the data that we have and with numerical, they would be different as well. So here we've got the tests that I used with categorical data. So we've got um one group, we've got two groups or more than two groups. And the test that we do are based on how many groups there are and then further down characteristics of the, of the data. So with two groups, um when we are comparing to proportions, we wouldn't want to know whether the data is independent of each other or whether it's paired and based on that, we would go ahead and do our statistical test. So with independent, if we, if we've got two groups and they are independent, we would be doing a chi square test or a Fisher's exact test, the chi square test. If the uh sample sizes are, are large, officious, exact test use when sample sizes are small or the or the number of occurrences in a group is is slow. So as I said, the choice of test does vary. We, we spoke by categorical data with numerical data. It does depend on whether the data is normally distributed or not. So uh the example above shows data that is normally distributed uh with data at the bottom, it is not normally distributed. Once we've got this information that could help us decide what test you use. So with numerical data, just like we had with the categorical data, we do need to know how many groups there are. So one group to groups or more than two groups and then some information about the uh the groups. And so for example, the two groups, whether they are independent of each other or whether they are paired. And then the test would depend on whether the data is normally distributed or not. The tests that are highlighted in the shaded boxes are the test that would be used for um for uh normally distributed data, um parametric data. And the tests um in the boxes below are for data that is not normally distributed. So in our example, um numerical data, if you've got two groups, the test that we'd be doing with normally distributed data would be a two sample T test or repaired T test depending on whether the data is independent or paired. Um If the data is not normally distributed, then the test would be different. So it would be for independent data would be with Coxon ranks test or Mann Whitney test with pear data. It would be Wilcox's signed rank test how the data is uh summarized is also different. So as as we said before, the cat for categorical data, which is on the left, we'd be using uh bar charts or pie charts. Whereas with numerical data, we'd be using histograms with the categorical data, how the summary is measured is different as well. So it would be described as a proportion or a percentage and estimating the mean. We use something called the standardized error of the proportion with numerical data. Something that we are generally more familiar with. There are a number of summary, summary measures including the average and the spread average would be mean medial mode which I'm sure we all know the spread. There. There are different ways of determining the spread, the spread of how, how widely spread the data is. This gives us an idea of the estimate, estimates a spread for us. This could be described with range into quartile range variants, which is a corrected sum of squares about the mean and the standard deviation, which is the square root of the variants. Uh The number of data points that would be included within certain standard deviations is defined as well. So uh in 12, in three standard deviations, we'd have 63 95 and 99.7% of the data points. Uh This was to estimate the spread or to estimate the precision. Uh We use something called the standard error of the mean or we could use the 95% confidence interval. So this will be useful for all uh data that we get with its simple data that we get from uh smaller studies, looking at a small number of patient's or even with the large amounts of data that we we could get using uh different different pathways that uh I think Professor Snellings got to talk later on. So I'm sure she'd be talking about different pathways involved in osteoarthritis, Intended attending pathologies. We with the amount of data we get is very large. But the principles of how we express that data is is the same as what's summarized here. Next, I'll talk about studies and hypotheses testing. So studies could be observational which are descriptive studies where the investigator observes the outcome, but it does not do any intervention. Uh There's no assigning of treatments and so this could be prospective retrospective or it could be a cross sectional study. A cross sectional study is at a single time point where you're not looking at what's happened previously or how things are progressing in as as time progresses, you're just looking at things at a single time point. A cohort study is a longitudinal prospective observational study. So again, you're not intervening, you're just observing and seeing what happens. So an example would be having a group of interest and the comparison group. So a group of interest could be smokers, a comparison group, nonsmokers and then seeing then following them over time to see what happens. So here, for example, we're looking at patient's to um smoke and then end up with a condition. We're, and then comparing it to a group who don't smoke and the number of patients who end up with a particular conditions. So let, for example, if we're looking at non union, so if we say uh 10% of patient's who are smoking, end up with a non union and compare that to 5% of patient's who were nonsmokers and end up with non union. And then we, then we compare the group's using that information. So the instant risk of yes. And that is the patient's who were smokers getting it particularly instants. And so that would be uh 10 10%. So 10% of those patients in, in uh non union and the incidence of know would be the incidence of uh non union in the comparison group, which would be 5%. So the information we get from a cohort study is relative risk. So the relative risk of getting uh non union if, if you were a smoker is um it's too, so it's that 10% and the risk that the smokers had divided by the 5% which is the risk of the non smokers. And that, that was just a simple example. And so uh artificial example, just, just to give you an idea of how, how the calculations are done right. Next is a case control study, which is a retrospective observational study. Um So this is different to a cohort study because what we're doing is we're going uh back in time. So we, we look at a group of interest. So for example, we're looking at patient's to uh develop a, a certain condition and compared to a group of patients who don't develop that condition. So for example, we could say patient's who develop nonunion and compare it to patient's who, who progress on to union, who don't have any issues with the union. Uh So we look at those patients' and then we go back and take a history and then we could identify um come compare something in the history. So we could, we could use the same example, we could look at patient's who are smokers or non smokers and then we could compare the histories and then draw conclusions. So it's different from the cohort study because rather than following patient's following the smokers, nonsmokers and seeing how they do, we are going back. So we're looking at patient's who had union or non union and then going back and see if they were smokers or not. So here, what we do is we get something called the, the odds ratio. So the odds ratio of developing non union, for example, so if we use the same example, if we say 10% of the patient's were smokers who developed nonunion, compared to 5% of the patient's were smokers who progress on to union. Here. Again, the odds ratio of uh developing non union would be um to so 10% divided by 5%. So these were all observational studies that we, we spoke about with no interventions made by the investigator. The other type of study is an experimental study where the investigator intervenes. Um again, these longitudinal and uh these are longitudinal in prospective studies. Um and a randomize controlled trial is a, is a type of experimental study. So Iran buys controlled trial, it reduces bias, increases the validity and you have controls which are positive or negative. And there's a comparable group at the baseline and they are then randomized. There's a modification of randomization, for example, with, with stratification and then there's blinding or masking which could be single or double and this reduces assessment bias. So I'll talk about experimental trials. Uh No, not in too much detail. I understand professor can do J is talking on clinical trials as well and I'm sure he'll cover all of this in, in far more detail. Um uh So what you have is you have uh patient's um and then you allocate them to a treatment group or a control group and then you follow them up over time and then you compare the results. So here it's, it's different from the other observation studies because you are and you are intervening by delivering a treatment. So how you always have a hypotheses and you're the hypotheses could be that whatever you're doing to intervene would improve the function, for example. Um And, and you have a control group where the patient's are not getting uh the particular treatment, but getting a controlled treatment, this could be blinded, it could be double blinded and then you have an outcome measure. Uh So you need to define all of these things before you do the study. So you need to define who you are going to include you. Inclusion exclusion criteria, you need to define the treatment, the controls and the different measures you take to improve the validity of the study. And and also you need to identify what outcome measures you will be using. This is a very useful document. The consult statement, it's the framework for randomized controlled trials and do look this up. Uh uh won't, as I said, I won't go into this into much detail. So bias is um uh is um a flaw in impartiality. Um That we, we do a number, we take a number of steps to reduce bias and uh the bias comes in different forms. So this bias could be selection bias, observation, observers bias and designed bias and in how the study is designed in sampling in observation in the experiments. Um So a number of biases from before or during the study being conducted, conducted and biases from afterwards as well, how the data is reported, how, how the, how the results are reported and published. In due course, I'll talk briefly about testing hypotheses. And so how hypotheses are tested in an experimental study? So the nulla hypotheses assumes that there is no difference between the two groups for uh a standard we use is the P value. That's the probability of obtaining the sample values or values. Uh More extreme if the null hypotheses was true. So when we uh if you, if you get a P value of point, not for that means there's a 4% chance that the null hypothesis is true. And we are, we are, we are accepting a difference when they're, there is no difference um where the P value is set and does vary. But generally, we put the P value down is 9.5. There are a number of errors in testing hypotheses. And so type one error. Uh We, the clinical significance um uh uh we, we could always reduce um reduce the type one error by increasing the sample size. So type one area is where the null hypothesis is rejected even though it is true. So a type two areas on the other hand, where we accept annul high hypoxi is when it is false, the power of a study is one minus the type two error. So the power of the study is normally set at 80%. But increasing this would mean an increase in the sample size as well. So it's always a balance between using resources effectively um cost effectively and getting a, getting an answer that is reliable enough. So sample size calculations depend on a number of things. Um Again, as I said, it's, it's always a balance between detecting a difference and not racing resources. Um So it's a sample size calculations are done in a number of ways. They could either be done on computer programs using input trauma statistician. Some, some people use a modified formula for working out sample sizes or you could use uh the image on the right, which is an uh organs, normal, normal gram. So the information that we need for a sample size calculation would be the P value that we've set the P value. The second thing we would want to know is the power of the study which as I said, we generally set at uh 80% but we can change it. But that would affect the sample size. The other important thing we do need to know we exist and standardize difference. So for example, if we were going to look at tranexamic acid in joint replacements, um we would want and we, we are looking at two groups where we're looking at a group where trans trans exam Kassid is given and a group where it's not given and trying to see if there is a difference. The information that we will need to find out whether there is a difference or not would be the standard deviation of the observations. So if, if for example, we, we get normally, if we end up with some patient with 50 mils blood loss in some patient with 400 if that would suggest that there's a big standard deviation, so that standard deviation would mean that that would affect the number of patient's we need to include in the study. The other important thing would be the um important clean, their clinically important difference in the means. So if for example, we have a small difference, that's a significant five meals or whether we want a larger difference at 50 mil difference in blood loss to be significant. So that that would have, that would determine the number of patient that we will need to include to um to look at that study. So um on, on just as an example, on the right, we have the the normal gram. So here we could look at the power on, on the right hand side. So as I said, we normally set it at uh 0.8 or 80%. The significance level we normally keep there's no 0.5. But if we do want to increase it, we want to go to North Point no one that would increase the number of samples uh that we need to include and on the left the standardized difference. So power and significance level, we set ourselves with the standardized difference. We work out by dividing the clinically important difference in the mean that we want. So say, for example, we want to 50 mils to be a significant difference between the two divided by the standard deviation, which is uh 400 mills. For example, if we look at previous studies and you know, if you get a range that is broad enough standard deviation 400. So 2 50/400 would give us the standardized difference which would probably end up being around uh 0.6 ish. So drawing a line from 0.62 0.8 which is the power that we set up would give us an idea of how many the number of patient's we need to include. And as I said, if we change the significance level, if we change the P value, the number of samples will change as a result of that. Indeed. And for example, size calculations, it's um it's very often we would be using a statistician, we would be getting help from a statistician. Next, I'll talk briefly about relationship between variables. If you've got two variables, we use um uh a scattered diagram. Um So the image here on the right is a study looking at on the y axis, we've got pink pressure's great toe pressures. And on the bottom, we've got the weight of the patient. So we get a, a correlation between the two, it's a Pearson correlation coefficient which which ranges from minus 1 to 21, the slope of the curve gives us an idea of what the correlation is. Um But uh are two, sorry R squared is probably a more clinically relevant uh clinically relevant measure. So, uh and the slope of the line, if, if it measures 0.4 for example, are four would be 0.16 that would mean that 16% of the difference between the greater pressure is explained by the weight. So it's, it's not too significant. So closer you get to one would, would be 100 if it's one, then it's 100%. But as you go down, if it's 0.5 RS 0.5 if the person correlation coefficient is 0.5 then it would only be 25% of uh the difference that would be explained by, by weight. So our squared is, is more, is more useful than just looking at our because our square ways in the fact that the numbers are values closer to one are much more significant than closer to minus one. If you have more than two variables, uh we can use multi variant linear regression. So for example, if we look at all the lower limb patient's who are having various treatments and looking at DVT prophylaxes or DVT risks, then because it's not just two variables, there's lots of variables in something like that. We'd be using multi variant linear regression. Uh Survival analysis are a type of uh type of analysis. We're looking at more than two variables So we're coupling my curve is an example of this. So here we've got a Captain Meier survival analysis curve. Um It has a number of advantages and disadvantages. So it uses uh non parametric log rank test to compare uh compare curves between compared to curves. The drawbacks are that uh there's a lot of short term data, not much long term data. As time progresses, uh failures need to be specified and these are, these curves cannot be extrapolated. Um There are other forms of analysis as well. So uh specificity or uh sensitivity and specificity which relate to a particular test where they negative predictive value or a positive predictive value, they tend to relate to your patient. Um So if, if, for example, we are looking at CRP values in uh very prosthetic infections, then we, we could see that the sensitivity and specificity of the tests of uh CRP for prosthetic infection, they are quite high. But what is more important for us is um the results in our patient. So we uh positive predictive value of uh a race CRP would only be 74%. But importantly, the negative predictive value is is much higher. It's 99%. There are other forms of analysis as well. So reliability studies, um they quantify the variation or measurement areas. So inter observer and intro observer variation. So Kappa statistic is what's used for that. Again, it's measured up to one and 0.8 to one is is very good with less than 0.2 is considered poor with questionnaires. Every time we devise questionnaires, we do need to assess the validity, the reliability responsiveness uh of these questionnaires to see whether they can be used. Um So questionnaires validity is assessed by a number of measures. And uh it's it's useful to see to compare it to a gold standard. If there is a gold standard, responsiveness, for example, would be looking at the same questionnaire over time and seeing if with a change in um within intervention, whether the questionnaire responds to that change or not, reliability is measuring the questionnaire at time at two different time points where there's been no change in ensuring that it remains the same. And all questionnaires need to be free from uh from, from bias as well. So with, with languages, for example, whenever a dash questionnaire, for example, is introduced to another country in a different language, it has to go through all of these assessments um to make sure it is still reliable to be used in that particular setting with evidence. Um There there is a hierarchy of evidence with uh editorials, expert opinions at the bottom. And as we progressed and as as we, we spoke about a lot of these things, so case series, case control studies, cohort studies, randomized control trials. So uh the strength of the evidence increases as we go up up this pyramid, I understand that uh Mr Osmani is talking about levels of evidence. So I won't uh won't steal his thunder uh lastly clinical evidence based medicine. So uh what, what is important is to identify the patient or population that is being looked at the intervention, uh the comparison, what has been compared with and the outcome, right? So that brings me to the end of the talk. I hope it has been useful. Uh If, if there are any questions, I'm sure the uh faculty there would be able to, to answer. I think professor mcdonald is there who uh has a much better understanding of statistics and research methodology than I have. So I'm sure you'll be very happy to answer any questions. Thank you very much.