Biostats Review P4 Orientation 2023 (1)

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Apr 3, 2024

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Biostatistics Review June 2023 Types of Study Data  Categorical Data= discrete variables o These come in only a fixed number of values – like dead/alive, obese/overweight/normal/underweight.  Continuous Data o These can have any value between a theoretical minimum and maximum, like birth weight, BMI, temperature, WBC. Data Description Examples Nominal Data (Categorical) No Set Order No True Zero Gender, ethnicity, mortality, yes/no, colors Ordinal Data (Categorical) Ordered & Ranked No True Zero Survey scale, Pain scale, NYHA Heart Failure Scale Interval Data (Continuous) Magnitude No True Zero Temperature Scale (Celsius & Fahrenheit) E.g. Temp O°F does not mean there is no temperature outside Ratio Data (Continuous) Set Order Has True Zero Age, Height, Blood Pressure, Heart Rate, Respiratory Weight The Null Hypothesis  Null=none, no, or nothing  Null hypothesis states there is no statistically significant difference between groups  A researcher who is studying a drug versus placebo would write a null hypothesis that states there is no difference between the drug and placebo (drug=placebo effect).  In research, the null hypothesis is what the researcher tries to disapprove or reject. Example: A study compared lisinopril to placebo to determine which is better for blood pressure control. Null Hypothesis: Lisinopril is no different from placebo in blood pressure control. P-value  When investigators design a study, they select a maximum error margin, known as alpha. o Alpha is the threshold for rejecting the null hypothesis. o Alpha typically set at 5% (0.05) or 1% or (0.01).  P-value: The level of statistical significance.  A value of p<0.05 means that the probability that the result is due to chance is less than 1 in 20.  The smaller the p-value, the greater the statistical significance  The p-value does not provide any information about the size of an effect. It only describes the strength of the result.  IF alpha is 0.05 the study, the study reports 95% Confidence Intervals.  IF alpha is 0.01, the study is reporting 99% Confidence Intervals. 1 | P a g e

Alpha P-Value Meaning 0.05 ≥0.05 Not statistically significant. 0.05 <0.05 95% probability (Confidence) that the conclusion is correct. Less than 5% chance it’s not. 0.01 <0.01 99% probability (Confidence) that the conclusion is correct. Less than 1% chance it’s not. 0.001 <0.001 99.9% probability (Confidence) that the conclusion is correct. Less than 0.1% chance it is not. Examples Statistically Significant Yes or No? Accept or Reject the Null Hypothesis? P>0.87 P<0.001 Power  The statistical ability of a study to detect a statistically significant difference between treatment groups.  Usually the number of participants to detect a statistically significant difference in a study  Probability that a study will have a statistically significant result (p<0.05)  Usually calculated and set at least 80%  Power increases as sample size increases  1-beta (refute the null hypothesis)  Typically discussed in the methods section of the study 2 | P a g e

Type I & Type II Error  Type 1 Error- To conclude there is a difference between treatments when there is really no difference between them o Rejection of the null hypothesis when it is actually true. o Type I Error is more serious  Why?  Type II Error- To conclude there is a no difference between treatments when there really is a difference between them. o Accept the null hypothesis when it is actually false o Significantly affected by study sample size, Less participants enrolled, greater risk of Type II Error o Type II error is more common  Why? Example: A randomized controlled trial was conducted to compare rosuvastatin vs. placebo to determine which treatment reduces the rate of myocardial infarction. In the methods section, the power was set at 85%, with 450 patients needed in each treatment arm (rosuvastatin and placebo). At the end of the study, only a total of 675 patients were enrolled in the study. Question 1. Did the study meet its power? ________ Question 2. They study is at potential risk of what type of error? _________ Confidence Intervals (CI)  An estimate of the range within which the true treatment effect lies. The 95% CI is the range of values within which we are 95% certain that the true value lies.  If the confidence interval for the difference in efficacy (a difference in means or proportions) between two treatments includes zero, then you cannot exclude the possibility that there is no difference in efficacy between treatments.  The width of the confidence interval is determined by the number of patients studied, the variability of the data, and the confidence level.  The confidence level is usually 95%, but could be as narrow as 90% or as wide as 99%.  The values in the Confidence Interval range are used to determine whether statistical significance has been reached.  Determining statistical significance using the confidence interval alone (without the P-value) is required for the Naplex Exam.  You can tell statistical significance without a P-value!! 3 | P a g e

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Confidence Intervals Difference Data FOR DIFFERENCE DATA (Subtraction): The result is statistically significant if the CI does not include or cross zero (0). The results are not statistically significant if the CI includes zero (0). Example 1 A study was conducted to compare the drug roflumilast to placebo in improving lung function in patients. Lung Function Spirometry Roflumilast (N=745) Placebo (N=745) Difference (95% CI) Statistically significant Yes or No? FEV1 (mL) 46 8 38 (18-58) Example 2 Lung Function Spirometry Roflumilast (N=745) Placebo (N=745) Difference (95% CI) Statistically significant Yes or No? FEV1/FVC (%) 0.314 0.001 0.313 (-0.26-0.89) Confidence Intervals Ratio Data For Ratio Data: (Relative Risk (RR), Odds Ratio (OR), Hazard Ratio (HR)  The results are statistically significant if the CI does not include or cross one (1).  The results are not statistically significant if the CI does include or cross one (1). Example A study was conducted to compare the drug roflumilast to placebo in reducing COPD exacerbations in patients. Exacerbations Roflumilast (N=745) Placebo (N=745) Relative Risk (95% CI) Statistically significant Yes or No? Severe 0.11 0.12 0.92 (0.61-1.29) Exacerbations Roflumilast (N=745) Placebo (N=745) Relative Risk (95% CI) Statistically significant Yes or No? 4 | P a g e

Moderate 0.94 1.11 0.85 (0.72-0.99) Relative Risk  Relative risk (RR) is the ratio of risk in the exposed group (treatment group) divided by the risk in the control group o Risk= number of subjects in the group with the event Total Number of subjects in the group o RR= Risk in Treatment Group Risk in Control Group  RR=1 (or 100%) à no difference in the risk of the outcome between the groups  RR>1 (or 100%) à greater risk of the outcome in the treatment group  RR<1 (or 100%) à lower risk (reduced risk) of the outcome in the treatment group Example A placebo-controlled study was done to determine if carvedilol reduces disease progression in patients with HF. A total of 10,780 patients were enrolled and followed for a year. What is the relative risk of HF progression in the carvedilol treatment group versus the placebo group. HF Progression Carvedilol (N=5320) Placebo (N=5460) 772 1,425 1) Calculate the risk of HF progression in each group. 2) Calculate the Relative Risk (RR) for this study. What does this relative risk mean for this study? 5 | P a g e

Relative Risk Reduction (RRR)  Relative risk reduction is calculated after the RR and indicates how much the risk is reduced in the treatment group compared to the control group.  RRR= (% risk in control group-% risk in treatment group) OR 1-RELATIVE RISK % risk in the control group Example A placebo-controlled study was done to determine if carvedilol reduces disease progression in patients with HF. A total of 10,780 patients were enrolled and followed for a year. HF Progression Carvedilol (N=5320) Placebo (N=5460) 772 1,425 Calculate the RRR  Relative risk reduction can improperly reflect the true results of a treatment in a clinical trial (inflated results).. Absolute Risk Reduction (ARR)  (ARR) Absolute difference in rates of an outcome between treatment and control groups in a clinical trial  Absolute risk reduction is more useful because it is the true difference between the treatment and placebo group.  ARR= % Risk in control group – %Risk in treatment group  Example A placebo-controlled study was done to determine if carvedilol reduces disease progression in patients with HF. A total of 10,780 patients were enrolled and followed for a year. HF Progression Carvedilol (N=5320) Placebo (N=5460) 772 1,425  Calculate the ARR 6 | P a g e

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Number Needed to Treat (NNT) & Number Needed to Harm (NNH)  NNT & NNH help clinicians determine how many patients need to receive the drug for one patient to get benefit (NNT) or harm (NNH). o Helps guide clinical decision as it relates to efficacy of therapies.  Number needed to treat (NNT): The number of patients needed to treat with a specified therapy in order for one patient to benefit from treatment. The NNT is the inverse of the absolute risk reduction (1 divided by absolute risk reduction).  Number needed to harm (NNH): The number of patients treated with a specific therapy in order for one of them to have a bad outcome.  NNT= 1/ARR OR NNH 1/ARR  Rules for NNT/NNH o NNT-round up to the nearest whole number (can’t have partial patient & also to avoid overstating the benefit of an intervention). o NNH-round down to the nearest whole number (can’t have partial patient & avoid understating the potential harm of an intervention). o Should only calculate the NNT/NNH for the primary endpoint of the study. o Should only calculate the NNT/NNH when the results for the endpoint are statistically significant  Example A placebo-controlled study was done to determine if carvedilol reduces disease progression in patients with HF. A total of 10,780 patients were enrolled and followed for a year. HF Progression Carvedilol (N=5320) Placebo (N=5460) 772 1,425  Calculate the NNT.  What does this mean? 7 | P a g e

A study was conducted to determine the incidence of Rhabdomyolysis in patients taking statin vs. placebo. Below are the results. Example Incidence of Rhabdomyolysis in Patients on a Statin vs. Placebo Incidence Statin (N=275) Placebo (N=280) % 1.25% 0.1%  Calculate the NNH.  What does this mean? 8 | P a g e

Odds Ratio & Hazard Ratio  Similar to Relative Risk  Odds Ratio looks at the probability that an event will occur versus the probability that it will not occur.  Estimate of the risk of unfavorable events associated with a treatment or intervention  Hazard Ratio very similar but looks at survival analysis o HR= Hazard rate (risk) in the treatment group Hazard rate (risk) in the control group  OR AND HR are interpreted very similar to Relative Risk. o OR or HR =1 à the event rate is the same in the treatment and control group. No advantage to the treatment o OR or HR >1 à the event rate in the treatment group is higher than the event rate in the control group  e.g. HR of 2 for an outcome of death, indicates there are twice as many deaths in the treatment group o OR or HR<1 à the event rate in the treatment group is lower than the event rate in the control group  e.g. HR of 0.5 for an outcome of death indicates that there are half as many deaths in the treatment group. Example: A placebo-controlled study was performed to determine if aspirin would reduce the risk of stroke and death in atrial fibrillation patients compared to placebo. A total of 3,414 patients were enrolled and followed for three years. Primary Endpoint Stroke & Death Aspirin N=1,718 Placebo N=1,696 282 274 1) Calculate the Hazard Ratio. 2) What does this mean? 9 | P a g e

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Biostats Practice Questions 1. You read a clinical study for a new antiepileptic medication that has strong data to support its efficacy against other AEDs. The treatment duration studied was 18 weeks. However, clinical studies have shown the following data related to safety. Adverse Effect Placebo (N = 260) New Drug (N = 258) Nausea 14% 16% Diarrhea 12% 11% Serious Arrhythmia 1% 3.65% What is the number needed to harm (NNH) related to arrhythmia? A .1 B. 4 C. 25 D. 37 n= 5000 patients Cetirizine 10 mg daily Placebo Relative Risk (95% CI) Exacerbations 0.11 0.12 RR 0.92 (0.61-1.29) 2. A study compared the rate of exacerbations of asthma patients that were taking cetirizine daily vs placebo. Below are the results. Are these results statistically significant? A. Yes B. No 3. A clinical study showed that the difference in the LDL lowering potential of Atorvastatin 40 mg and Pravastatin 40 mg was 16% (see table below). LDL Lowering Atorvastatin 40 mg (n=200) Pravastatin 40 mg (n=200) (95% CI) 10 | P a g e

LDL Lowering (%) 35% 19% 16% (12%-42%) Are these results statistically significant? A. Yes B. No 4. You are evaluating the results and discussion of a journal club article to present to the pharmacy residents at your institution. The randomized, prospective, controlled trial evaluated the efficacy of a new controller drug for asthma. The primary end point was the morning forced expiratory volume in 1 second (FEV1 ) in two groups of subjects (men and women). The difference in FEV1 between the two groups was 15% (95% confidence interval [CI], 10%–21%). Which statement is most appropriate, given the results? A. Without the reporting of a p-value, it is not possible to conclude whether these results were statistically significant. B. There is a statistically significant difference between the men and women (p<0.05). C. There is a statistically significant difference between the men and women (p<0.01). D. There is no statistically significant difference between the men and women. 5. A prospective randomized study compared once daily enoxaparin with twice-daily enoxaparin when treating patients with venous thromboembolism (VTE). One of the study end points was the recurrence of VTE. The following table summarizes recurrence rates in all patients. Once Daily Enoxaparin Twice Daily Enoxaparin All patients n % 13/298 (4.4%) 9/312 (2.9%) The 95% confidence interval (CI) for the difference in recurrence rates between the two groups was (−1.5% to 4.5%). Which conclusion is most appropriate? A. Twice-daily enoxaparin is superior to once daily B. Superiority of twice-daily enoxaparin could not be established over once daily. C. Once-daily enoxaparin is not inferior to twice daily. D. No conclusion can be drawn because p-values are unavailable. 6. A pharmacist is charged with evaluating daptomycin efficacy for cellulitis as part of a research project. She is evaluating patients comparing them to vancomycin. The primary endpoint of the study is the clinical cure rate for the skin infection within 7 days. Her data collection sheet has two boxes for the primary endpoint (yes and no). What type of data is the pharmacist collecting in regards to the primary endpoint? A. Nominal B. Ordinal C. Interval 11 | P a g e

D. Ratio 7. A study was conducted to analyze the risk of a COPD exacerbation in patients (N=450) receiving tiotropium compared to placebo. At the end of the study, the relative risk (RR) of exacerbations between both groups was 0.82 (95% Confidence Interval [CI], (0.70-0.96). Which statement is most appropriate, given the results? A. There is a statistically significant difference between the tiotropium and placebo for COPD exacerbations. B. There is no statistically significant difference between the tiotropium and placebo for COPD exacerbations. C. Without the reporting of a p-value, it is not possible to conclude whether these results were statistically significant. D. None of the above. 8. A new drug, HART, was compared to aspirin for heart attack prevention. The trial enrolled 2,546 patients in the HART arm, 39 out of 1,281 had a stroke. In the aspirin arm, 64 out of 1,265 patients had a stroke (p=0.0012). What is the relative risk reduction (RRR) of stroke in this trial? A. 1 B. 0.9 C. 0.3 D. 0.4 9. Which of the following below is the definition of a type 1 error? A. The alternative hypothesis is rejected in error. B. The null hypothesis is rejected in error. C. The study is too small to detect a statistical difference between groups. D. The null hypothesis is accepted in error. 10. A clinical study reports that patients taking a new drug, ALLERGYX, experience fewer episodes of rhinitis. The number of rhinitis episodes (the primary endpoint) was 16.4% in the ALLERGYX group and 28.7% in the placebo group. The trial randomized 600 patients (300 patients in each arm). Which of the following below is the number needed to treat (NNT) to prevent one rhinitis episode? A. 8 B. 9 C. 25 D. Not enough information to answer the question. 12 | P a g e

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11. A study is comparing rosuvastatin vs. pravastatin at maximum dose, to determine the benefit in protection in cardiovascular events. The investigators aimed to enroll a total of 25,000 study participants (12,500 in each treatment arm). Below are the results for the study. Primary Endpoint (Cardiovascular Death after 4 years) Pravastatin 80 mg daily (N=9077) Rosuvastatin 40 mg daily (N=9067) 95% CI Hazard Ratio (%) Intention to treat 31.6% 23.5% (0.74-0.88) Per Protocol Analysis 32.4% 29.8% (0.87-1.15) a. Calculate the number needed to treat (NNT) for the intention to treat group based on the results of the study. Follow rounding rules for NNT. b. True or False. The results for the Per Protocol Analysis are statistically significant. c. True or False. This study has a risk for Type II Error. 12. A study evaluated the triglyceride lowering potential of Niacin compared to placebo. Below are the results. N=2500 patients Niacin Placebo (95% CI) Triglyceride Lowering (%) 22% 10% 12% (8.5%-24%) True or False. The results of this study are statistically significant. 13 | P a g e

13. A new drug is being evaluated for its adverse effects in a clinical trial compared to placebo. Based on the table below, calculate the Number Needed to Harm (NNH) for Liver Toxicity for this drug. Based on the table, calculate the Number Needed to Harm (NNH) for Liver Toxicity for this drug. Use appropriate rounding rules for NNH. Adverse Effects Placebo (N=125) Active Drug (N=130) Headache 0.25% 1.25% Liver Toxicity 0.34% 3.5% 14. In the ARISTOTLE Study the rate of death from any cause was 3.52% in Apixaban group per year Vs 3.94% in warfarin group. HR 0.89; 95% CI, 0.80 to 0.99. Which of the following statement is true based on the given information? A. The rate of death from any cause was lower in the Apixaban group than in Warfarin group. B. The rate of death from any cause was not significant in the Apixaban group Vs Warfarin group. C. Warfarin had significantly lower rate of death compared to Apixaban. D. Since there is no p value no conclusion can be drawn from the given data 15. Which of the following below is an example of ordinal data? A. Mortality (Alive or Dead) B. Blood Pressure C. PHQ-9 Depression Scale D. All of the above 16. In the US Nurses’ Health Study (NHS) cohort study, where they looked at association of regular aspirin use (≥two 325 mg tablets/week) and colorectal cancer in 82,911 women found (RR, 0.77; 95% CI, 0.67– 0.88) over 20 years of follow-up. What does this say about the mortality from colorectal cancer? A. Those who takes aspirin ≥2 times/week have 23% lower risk of colorectal cancer. B. Those who takes aspirin ≥2 times/week have 0.77% lower risk of colorectal cancer. C. Those who takes aspirin ≥2 times/week have 77% lower risk of colorectal cancer. D. Those who takes aspirin ≥2 times/week have 0.23% reduction in death from colorectal cancer. 14 | P a g e

17. Results from a Meta-analysis where they looked at frequency of postoperative arterial fibrillation in patients on Ascorbic acid after cardiac surgery found odds ratio, 0.44 (95% CI, 0.32 to 0.61). How can you interpret this data? A. Ascorbic acid increased frequency of postoperative arterial fibrillation after cardiac surgery by 44% B. Ascorbic acid decreased frequency of postoperative arterial fibrillation after cardiac surgery by 44% C. There was no statistically significant difference in frequency of postoperative arterial fibrillation after cardiac surgery. D. Ascorbic acid decreased frequency of postoperative arterial fibrillation after cardiac surgery by 56% E. None of the above. 18. The CAPRIE study was a randomized clinical trial published in Lancet in 1996 to assess the potential benefit of clopidogrel, compared with aspirin, in reducing the risk of ischemic stroke, myocardial infarction, or vascular death in patients with recent ischemic stroke, recent myocardial infarction, or peripheral arterial disease. The study's primary endpoint cluster of incidence of ischemic stroke, myocardial infarction, and or vascular death occurred in 5.32% of clopidogrel patients per year and 5.83% of aspirin patients per year (p=0.043). Assuming this p-value is statistically significant, what is the number needed to treat in order to prevent the primary endpoint by using clopidogrel compared to aspirin? 19. Calculate the value of RR if the risk of heart failure associated with an invention drug is 5% versus 9% with placebo? a. 1.25 b. 2.65 c. 0.55 d. 1.8 20. If the calculated absolute risk reduction (ARR) for heart attack event was 5.1%, what would be the number needed to treat? a. 11 b. 2.65 c. 3.2 d. 20 15 | P a g e

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Biostats Review P4 Orientation 2023 (1)

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