Equipment and preparation required for one group (2-4 students) to complete the workshop
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1 Your career today is a Pharmaceutical Statistician Leaders notes Do not give to the students Red text in italics denotes comments for leaders and example answers Equipment and preparation required for one group (2-4 students) to complete the workshop One printed worksheet and one pen or pencil for each student Two packs of cards (with the same backs). Label one of the packs as Treatment A and the other as Treatment B. From the Treatment A pack remove two Tens, two Jacks, two Queens and two Kings and put them into the Treatment B pack. From the Treatment B pack remove two Aces, two 2 s, two 3 s and two 4 s and put them into the Treatment A pack do not tell the students. This weights the packs so that the students get different results for the two treatments. One dice, one calculator and some spare paper
2 Your career today is a Pharmaceutical Statistician Today you ll be taking on the role of a pharmaceutical statistician. You will work through some scenarios faced by pharmaceutical statisticians in their day-to-day job and you ll see how important the use of statistics is in the development of drugs which will ultimately be used to treat diseases and save lives. What is the pharmaceutical industry? The pharmaceutical industry is involved in the research, development, manufacture and marketing of products for the prevention, diagnosis and treatment of diseases. Companies aim to gather enough evidence to convince government agencies, doctors and patients that their drug is safe (not harmful to the patient) and effective (improvement in the patient s disease). What does a pharmaceutical statistician do? Pharmaceutical statisticians can be involved at all stages of the drug development process, from drug discovery and pre-clinical work with scientists through to clinical trials on human beings and right into post-marketing work (long term safety reviews) after the drug has been approved. 2
3 This workshop will focus on clinical trials where statisticians are involved in: Designing studies to investigate the safety and efficacy of new drugs Randomising patients to treatments Applying appropriate statistical analysis Presenting and interpreting results to company executives and doctors Pharmaceutical statisticians work with medical experts, doctors, scientists, data managers, regulators and others during the drug development process. As a pharmaceutical statistician, drugs which you help to develop may end up being available to treat the people around you (or even yourself!) What skills does a pharmaceutical statistician need? Good applied analytical skills (but not necessarily an expert in statistical or mathematical theory) Excellent communication skills Where do pharmaceutical statisticians work? There are a wide range of companies large and small that develop drugs for people in the UK and worldwide. Here a few of the companies you could work for. For more details, see 3
4 Today s objective You are going to simulate a clinical trial and then use statistical analysis to determine whether a drug is safe (has no adverse side effects) and effective (helps prevent or reduce the disease it is intended to treat). You will learn some key concepts such as randomisation and blinding. STEP 1: Introduction Suppose you work for a pharmaceutical company which has developed a new treatment for high blood pressure. You need to work with medical experts to design a clinical trial to see if this new treatment is safe, and if it actually reduces high blood pressure. As a team, you will: Recruit 20 patients who have high blood pressure. Give approximately 10 patients the new drug and 10 patients a placebo drug (i.e. a sugar tablet that will have no effect on the patient s blood pressure). Measure each patients blood pressure before they take their assigned drug (i.e. at baseline), and again after they ve taken the drug (i.e. post-baseline). Look at the reduction in blood pressure from baseline in order to see if the new drug has reduced blood pressure more than the placebo drug. Look at the safety of the drug by recording any side-effects experienced by the patients. There are two keys points to consider when you design a clinical trial What is randomisation? Randomisation is the process of randomly assigning patients to a treatment group. Each patient should have a known (usually equal) chance of being assigned to each treatment group, and there should be no way of predicting which treatment group will be assigned in advance. Randomisation helps to prevent any bias in the results by balancing both known and unknown patient characteristics in each treatment group. What is a blinded trial? Most clinical trials are double-blinded, which means that the patient and the doctor do not know which treatment group the patient has been assigned to. The medication packets are masked (unmarked) so that they can t tell which treatment they re receiving. Blinding helps to reduce conscious or subconscious bias which would invalidate the results. For example, if the patient or doctor knew that they were assigned to the new drug, they may think they should feel better and unintentionally affect the results. 4
5 Decide in your group who will write notes and who will report back at the end of the session. Questions shown in BOLD should be used to report back to the rest of the class at the end of the session. 1: Briefly describe the pharmaceutical industry, the role of a pharmaceutical statistician and the skills you need to make this your career? The pharmaceutical industry is involved in the research, development, manufacture and marketing of products for the prevention, diagnosis and treatment of diseases. Pharmaceutical statisticians can be involved at all stages of the drug development process, from drug discovery and pre-clinical work with scientists through to clinical trials on human beings and right into post-marketing work after the drug has been approved. Required skills: a) Good applied analytical skills (but not necessarily an expert in statistical or mathematical theory) b) Excellent communication skills 2: What was the trial objective? To see if this new treatment is safe, and if it actually reduces high blood pressure 5
6 STEP 2: Run a clinical trial As you will not be able to run a real-life clinical trial, we will use artificial devices (such as dice and cards) to generate realistic data. Keeping in mind the concepts of randomisation and blinding, you will now assign patients to each treatment group; Treatment A and Treatment B. One is the new drug and one is the placebo drug, but you will need to remain blinded until all the data has been collected. Follow the steps to randomise your patients and to generate results. Randomise your patients to treatments For each patient, roll the dice. If you get an odd number (1, 3, 5) then assign the patient to Treatment A. If you get an even number (2, 4, 6) then assign the patient to Treatment B. Record the treatment assignments (A or B) in the Randomised treatment column 1 on the data sheet on the next page. You will fill in columns 2 and 3 later in the workshop. 3: How many patients did you randomise to each group? Do you have 10 patients on each treatment? Students should have rolled the dice 20 times and completed column 1 of the table on the next page. Odd dice numbers get assigned to Treatment A, even numbers to Treatment B. Students will hopefully have patient counts (on A and B) of 7 & 13, 8 & 12, 9 & 11 or 10 & 10. If they have a larger imbalance, they may want to try again after thinking about what problems a large imbalance might cause in the questions below. 4: If you did get more patients on one treatment than the other, why did this happen and what problems might this cause? Students only randomise 20 subjects. This is a small sample and so could get an imbalance by chance. Larger samples are less likely to have imbalance. A large imbalance could result in more patients on one drug than the other preventing a fair comparison. Fewer than 6 patients on a treatment might not be enough to assess whether one drug is better than the other. 6
7 Data Sheet An example set of results have been provided in case you want to shorten the workshop and remove the data generation section. Patient number Column 1 Randomised treatment Column 2 Decrease from baseline in blood pressure Column 3 Severity of worst side-effect 1 A 7 Mild 2 A 5 Severe 3 B 6 Severe 4 B 8 Mild 5 B 10 Mild 6 B 5 Moderate 7 A 6 Moderate 8 A 3 Moderate 9 B 9 Moderate 10 B 5 Mild 11 B 6 Mild 12 A 3 Severe 13 A 2 Mild 14 B 6 Mild 15 A 5 Mild 16 B 5 Moderate 17 A 7 Moderate 18 A 1 Mild 19 B 7 Moderate 20 A 8 Mild 7
8 Collect results to investigate whether the drug works Now that you have randomised patients in a blinded fashion, we need to generate some realistic results so that you can complete the next step. Select the pack of cards labelled as Treatment A: With the pack facing downwards (so that you can t see the numbers), pick a card from the pack and record the card number as the Decrease from baseline in blood pressure result in column 2 on your datasheet, for the first patient assigned to Treatment A. NOTE: count Aces as a 1 and picture cards as 10. Put the card back in the pack, give a quick shuffle and repeat this step, filling in the data in order for all of the patients on Treatment A. Pick up the set of cards labelled as Treatment B. Follow the same steps as above to generate a decrease from baseline result for each of the patients on Treatment B and enter them on your datasheet. 5: What is the mean decrease from baseline for the subjects on Treatment A? Students should calculate the mean of the results in column 2 for all subjects on Treatment A (as indicated in column 1). The result should be something in the region of in the region of 3 to 6, however the result may be different by chance. 6: What is the mean decrease from baseline for the subjects on Treatment B? Students should calculate the mean of the results in column 2 for all subjects on Treatment B (as indicated in column 1). The result should be something in the region of 6 to 9: however the result may be different by chance. Until all the data has been collected you are not informed of which treatment (New drug or Placebo) corresponds to A or B. This ensures that all information is collected and any data corrections can be made in an unbiased way. Collect results to look at the safety of the drug: The change from baseline results will help you to assess whether the new drug effectively reduces blood pressure (i.e. the efficacy of the drug). However, we also need to assess how safe the new drug is. For each patient, throw the dice to generate the severity of worst side-effect which each patient experienced during the trial. Record the severity for each patient on your datasheet in column 3. 1 or 2 = Mild 3 or 4 = Moderate 5 or 6 = Severe You should now have a completed datasheet for the 20 patients in your trial. 8
9 7: Complete this table Treatment A Treatment B Number of subjects Copy from question 3 Copy from question 3 Mean decrease from baseline Copy from question 5 Copy from question 6 Number of subjects with a mild side effect Number of subjects with a moderate side effect Number of subjects with a severe side effect Students should count the number of patients on Treatment A with a mild side effect (as recorded in column 3 of the datasheet). As above for moderate As above for severe Students should count the number of patients on Treatment B with a mild side effect (as recorded in column 3 of the datasheet). As above for moderate As above for severe 8: Which treatment (A or B) do you think is the best? (i.e. which has the higher mean decrease from baseline and fewer cases of moderate and severe side-effects?) Students should compare the results recorded in the table in question 7. A larger mean decrease indicates a better treatment in terms of efficacy. In terms of safety, you want the new drug to have the same or fewer moderate and severe side effects compared to placebo. You ll need to wait until unblinding to see which treatment is which. If it s difficult to decide, then in practice, we would probably need more advanced statistical methods and input from medical experts in order to decide which drug is better. Once we have checked the data for any errors and made any corrections, we can lock the database so that no further changes can be made. At this point we can unblind ourselves so that we know which treatment (new drug or placebo) corresponds to treatments A and B. 9
10 STEP 3: Statistical analysis Lock your database Your clinical trial is now complete, all of your data has been entered and you can focus on the analysis of the trial results one of the most important stages for a pharmaceutical statistician. Before you can be unblinded (i.e. told which treatment is the new drug and which is placebo), you first need to decide which statistical test you are planning to perform. Perform your statistical analysis of the efficacy data For efficacy (does the drug work?), you ve got a continuous measure for each patient (decrease from baseline), and two independent groups of patients. As a statistician, you have to decide what analysis you are going to do. Although you may not have covered this yet on your course, given this type of data, you choose to perform a two-sample t-test in order to see if there is a statistically significant difference between treatment groups. How to do this is explained later. 9. Ask your workshop assistant to unblind you (tell you which treatment is A and which treatment is B). Before the students perform the two-sample t-test, you need to unblind them. Ask the following questions before you tell them which treatment is which (this is in line with the questions we re asked in the industry): 1) Have all the data been collected? Answer = YES 2) Are the data correct to the best of your knowledge? Answer = YES 3) Have you decided which statistical analysis test you plan to perform? Answer: Two sample t-test Once the students have answered these questions, you can tell them the following: Enter which treatment (New Drug or Placebo) corresponds to A and B below: Treatment A = Placebo Treatment B = New drug 10. What is the difference between treatment groups (new drug placebo) in the mean decrease from baseline in blood pressure? They need to use the results from question 10, and calculate the following: Mean for Treatment B Mean for Treatment A 10
11 You may have observed a difference (new drug placebo 0) however how do you know if the difference could have occurred by chance (because of a few unusual values for your subjects) and in fact there is no true difference between the treatments. To estimate whether we are likely to have observed this result by chance, we calculate the probability of the difference occurring (assuming there was actually no true difference between the treatments). If the probability of this difference occurring is small (say less than a 5% chance of us finding this difference if no true difference exists) then we conclude that we have evidence that there is a true difference between the treatments. We say we have a statistically significant difference between the two treatment groups. If this result could easily have occurred by chance alone (say >5% likely), then we cannot conclude that there is any evidence of a true difference between the treatment groups. In order to calculate the probability of observing the result, we have to use probability distributions. The relevant distribution depends on your trial. We have two independent treatment samples, with quite a small sample size (20 subjects) and we want to test for a difference between two means. Therefore in this case, the most appropriate test and distribution to use is the two-sample t-test with the Student t-distribution. You will learn about many statistical distributions at university but this graph shows you how the Student t-distribution is used. Using calculus we can work out areas under the curve between various points on the t-test statistic axis. The shaded area, which represents 95% of the total area under the curve, lies between the vertical lines at ± This tells us: If no true difference existed between our two treatments and we repeated the clinical trial using 20 subjects many times, we would expect 95% of them get a t-test statistic between (within) ± Therefore 5% of the trials would have a t-test statistic greater than (outside) ± The shape of this distribution curve can change based on your assumptions and your sample size but this is beyond what we can explore today. 11. What does statistically significant mean? That the difference calculated is not likely to have occurred by chance if there truly is no difference between the treatment groups. 12. Using the table in Question 7, copy the results into the following table making sure you get Treatment A and B the correct way around. New drug Placebo Number of subjects n 1 = n 2 = Mean decrease from baseline in blood pressure ȳ 1 = ȳ 2 = 11
12 You now have the values for n 1, n 2, ȳ 1 and ȳ 2. Insert them into the equation below and calculate the value for the t-test statistic. Note: To save you time, we have provided in the equation the value of 4.4 which corresponds to the pooled variance. In practice this is calculated from your collected data, however you can just use the value given for today. More advanced students can be given the following formula to calculate their own pooled variance (i.e. to replace 4.4 in the calculation of the t-test statistic). They will have to calculate S 1 and S 2 which are the standard deviations for the new drug and placebo (remembering to square these values in the S 2 p formula below). 2 s p 2 n1 1s 1 n2 1 n n s 2 2 t-test statistic = y y n1 n2 As described above for your data, there is a statistically significant difference between treatment groups if the absolute value of the t-test statistic (the value ignoring any minus sign) is greater than What is the value of your t-test statistic and is it statistically significant (greater than 2.101)? They should think about the direction of the difference and double-check that the difference (ȳ1 ȳ2) is in the right direction (i.e. new drug placebo). Students may or may not have a statistically significant result. If the difference is not statistically significant, then they may want to consider why it s not significant. For example, it could be due to the very small sample size or high variability in the results. They could consider how to reduce the variation in a real trial perhaps by standardising doctors practices or by limiting the people allowed to enter the study to a narrower selection of patients. 14. If you had a family member with hypertension (increased blood pressure) which treatment would you recommend they take? If they have a statistically significant result they should choose the new drug. If there is some evidence that the new drug has a better effect than placebo, however it was not a statistically significantly difference, they may conclude there is no difference between the treatments, or they may recommend a new larger trial if they think the 20 subjects was not enough to assess efficacy reliably. 12
13 Perform your statistical analysis of the safety data You might have shown that your new drug is effective in reducing high blood pressure, or you might have found that it is no more effective than placebo. Either way, you also need to assess the safety of your new drug. 15. Complete the frequency table below which shows the number of patients in each treatment group (N), the number (n) of patients experiencing each severity category (mild, moderate, or severe) and the percentage of patients ( n x 100) in each treatment group experiencing each N severity category (mild, moderate or severe). The table below should be completed using the counts (n) recorded in the table in question 10. Percentages should be calculated using 100(n/N). They could round to 1 decimal place. Table of the number and percentage of patients experiencing each severity category New drug (N = ) n (%) Placebo (N = ) n (%) Example 5 patients (50%) 2 patients (20%) Mild ( %) ( %) Moderate ( %) ( %) Severe ( %) ( %) 16: Does it look like there is a difference between the treatment groups in the percentage of subjects with mild, moderate and severe side effects? They need to comment on whether there are any differences between treatment groups in terms of the percentage of mild, moderate and severe side effects. If there is a difference, they need to decide whether this could have happened by chance, or if there is strong enough evidence to conclude that one drug is not as safe as the other. 13
14 STEP 4: Conclusions from your clinical trial 17: Considering the efficacy and safety of your new drug would you recommend this treatment for reducing blood pressure? They should write a summary concluding their results and using the size of the differences to justify their conclusion. Prepare to feedback to the rest of the class a 5 minute summary of what you were tasked with today, what statistical tools you used to solve the problem and what your conclusions were. See over for further questions. Only attempt them if you find that there is time remaining once you have completed the exercise above in full. Make sure the students have completed all questions (particularly the ones in BOLD) before they go on to answer the additional questions. Credits Produced by the RSS Careers in Statistics Workshop group with support from the Royal Statistical Society and in association with PSI (see for more information). Published July Images: Page 1 Drugs: Flickr/emagineart, used under CC-BY licence Page 1 Timeline: RSS, information from Time to flourish Inside innovation: the medicine development process, ABPI, 16/03/2012 Page 2 Doctor: Thinkstock/ Digital Vision / Thomas Northcut / sb ab-001 Page 2 Multi pipette: Thinkstock / istock / Luchschen Page 2 Autosampler: Thinkstock / istock / Jeng_Niamwhan Page 2: Images of company names copyright their respective owners, used for illustrative purposes only Page 3: Hat: Thinkstock / istock / James Steidl / and Doctor: Thinkstock / istock / Chunumunu / Page 9: Monitor: Thinkstock / istock / zentilia / Page 9: Calculator: flickr dottiemae used under CC-BY licence Page 10: Graph drawn by Lyn Taylor, RSS Careers in Statistics Workshop group 14
15 If you have spare time here are some additional questions Briefly describe what is meant by randomisation in a clinical trial, and why it s so important? Randomisation is the process of randomly assigning patients to a treatment group. Each patient should have a known (usually equal) chance of being assigned to each treatment group, and there should be no way of predicting which treatment group will be assigned in advance. Randomisation helps to prevent any bias in the results by balancing both known and unknown patient characteristics in each treatment group Following on from question 3: If by chance the patients assigned to treatment A were more ill at the start of the study before they were given any treatments (i.e. had a higher blood pressure) than those assigned to treatment B what impact would that have on your clinical trial? Can you think of any way this could be avoided? (HINT: In clinical trials we use a technique called stratified randomisation, you may have heard it called stratified random sampling). Subjects who are severe at baseline are likely to be more severe after the study compared to milder disease patients even if the treatments work. Therefore, if more subjects with a severe disease are on one treatment compared to the other, this would lead to the treatment looking worse because of a baseline imbalance in severity (not because it actually performs worse). This could bias the trial and you may not be able to compare the treatments and conclude which works the best. You could design the randomisation to ensure balance in disease severity across the treatment groups by creating separate randomisation lists for each disease severity category. What benefit does randomly assigning patients have over assigning the first 10 patients to treatment A and the second 10 patients to treatment B? If the first 10 are assigned to treatment A, then the doctor may guess what drug each patient is receiving (for example, if they all see an improvement, then the doctor can assume they re on the new drug rather than placebo). They may feel unethical about putting a severely ill patient onto placebo and therefore delay randomisation until they think they will get the new treatment. This could lead to more severe subjects getting the new drug which then makes the new drug look worse than it really is. Do you think you had enough patients to make a conclusion? Statisticians are often involved in sample size calculations during the clinical trial design stage in order to ensure that enough patients are included. They will probably conclude that they need more subjects to be confident of the results. 15
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