Biostats_RxPrep Book 2022_1-10.pdf

BIOSTATISTICS CHAPTER 14 BIOSTATISTICS PURPOSE OF BIOSTATISTICS Statistics involves the collection and analysis of all types of data, from the average number of cars on a freeway to the blood pressure reduction expected from a calcium channel blocker. When statistics on people and animals, the statistical analysis is called biostatistical analysis, or simply, biostatistics. A basic understanding of biostatistics is required to interpret studies in medical and pharmacy journals, such as the New England Journal of Medicine or Pharmacotherapy. Simple formulas and definitions, described here, prepare the reader to interpret most journal articles and feel confident tackling common practice-based situations, such as: A physician asks if a patient should be switched from standard of care treatment to a new drug based on the relative risk reduction reported in a clinical trial. A patient taking warfarin wants to know if he should switch to Xarelto because he saw a commercial claiming that "it prevents DVT or PE in 98% of patients." STEPS TO JOURNAL PUBLICATION ""':·~. 208 The path to publication for the classic type of research study is shown in the figure on the next page. A study manuscript (description of the research, with results) can be submitted for publication in a professional, peer-reviewed journal. The editor of the journal selects potential publications and sends them to experts in the topic area for peer review. Peer review is intended to assess the research design and methods, the value of the results and conclusions to the field of study, how well the manuscript is written, and whether it is appropriate for the readership of the journal. The reviewers make a recommendation to the editor to either accept the article (usually with revisions) or reject it. Data that contradicts a previous recommendation, or presents new information, can change treatment guidelines. RxPREP 2022 COURSE BOOK\ RxPR EP ©2021, ©2022 ih' ,.. ,(°' BEGIN with ;1 • "··• · ' \I)/' . "" RESEARCH QUESTION Write a null hypothesis to answer the research question, such as: New drug is not as effecti ve as current drug. DESIGN COLLECT the DATA , ~-~ ) ENROLL the the STUDY ·" Q,,::2., SUBJECTS Assign to a treatment group or control group, or identify subjects belonging to a cohort or other group. Is it randomized, placebo-controlled, a case-control or other type of study? Prospectively (going into the future for a set period of time) or retrospectively (looking back in time using medical records). ANALYZE the DATA Enter the data into statistical software; assess the results (e.g., risk reductions, confidence intervals). iKl.1 (,lRxPrep Rl'J iStock.com/dilyanah ORGANIZATION OF A PUBLISHED CLINICAL TRIAL A published clinical trial begins with an abstract that provides a brief summary of the article. The introduction to the study comes next, which includes background information, such as disease history and prevalence, and the research hypothesis. This is followed by the study methods, which describe the variables and outcomes, and the statistical methods used to analyze the data. The results section includes figures, tables and graphs. A reader needs to interpret basic statistics and common graphs in order to understand the study results. The researchers conclude the article with an interpretation of the results and the implications for current practice. TYPES OF STUDY DATA When data points, or values, are collected during a study, they can be analyzed to determine the degree of difference between groups, or some other type of association. The statistical tests used to perform the analysis depend on the type of data. CONTINUOUS DATA Continuous data has a logical order with values that continuously increase (or decrease) by the same amount (e.g., a HR of 120 BPM is twice as fast as a HR of 60 BPM). The two types of continuous data are interval data and ratio data. The difference between them is that interval data has no meaningful zero (zero does not equal none) and ratio data has a meaningful zero (zero equals none) . The Celsius temperature scale is an example of interval data because it has no meaningful zero (0°C does not mean no temperature; it is the freezing point of water). Heart rate is an example of ratio data; a HR of O BPM is cardiac arrest (zero equals none; the heart is not beating). DISCRETE (CATEGORICAL) DATA The two types of discrete data, nominal and ordinal, have categories, and are sometimes called categorical data. Nominal and name are derived from the same word; with nominal data, subjects are sorted into arbitrary categories (names), such as male or female (o = male, 1 = female or O = female, 1 = male). It is sometimes described as "yes/no" data. Ordinal comes from the word order; ordinal data is ranked and has a logical order, such as a pain scale. In contrast to continuous data, ordinal scale categories do not increase by the same amount; a pain scale rating of 4 is worse than a pain scale rating of 2, but it does not mean that there is twice as much pain. CONTINUOUS DATA DISCRETE (CATEGORICAL) DATA Data is provided by some type of measurement which has unlimited options (theoretically) of continuous values Data fits into a limited number of categories RAT IO DATA Equal difference between values, with a true, meaningful zero (0= NONE) Examples: age, height, weight, time, blood pressure INTERVAL DATA NOMINAL DATA ORDINAL DATA Equal difference between values, but without a meaningful zero Categories are in an arbitrary order Categories are ranked in a logical order, but the difference between categories is not equal (OtcNONE) Examples: Celsius and Fahrenheit temperature scales Order of categories does not matter Examples: gender, ethnicity, marital status, mortality Order of categories matters Examples: NYHA Functional Class I-IV; 0-10 pain scale r(l'; (i'!RxPrep 209 I BIOSTATI STI CS 14 SUMMARIZING THE DATA MEASURES OF CENTRAL TENDENCY • Descriptive statistics provide simple summaries of the data. The typical descriptive values are called the measures of central tendency, and include the mean, the median and the mode (see Study Tip Gal below for mean, median and mode calculation examples) . • Mean: the average value; it is calculated by adding up the values and dividing the sum by the number of values. The mean is preferred for continuous data that is normally distributed (described below}. Median: the value in the middle when the values are arranged from lowest to h ighest. When there are two center values (as with an even number of values), take the average of the two center values. The median is preferred for ordinal data or continuous data that is skewed (not normally distributed}. • Mode: the value that occurs most frequently. The mode is preferred for nominal data. SPREAD (VARIABILITY) OF DATA Two common methods of describing the variability, or spread, in data are the range and the standard deviation (SD) . Range: the difference between the highest and lowest values. Standard deviation (SD}: indicates how spread out the data is, and to what degree the data is dispersed away from the mean (i.e., spread out over a smaller or larger range} . A large number of data values close to the mean has a smaller SD. Data that is highly dispersed has a larger SD. Example ____ _______ The diastolic blood pressure (DBP mmHg) reduction for 9 patients in a trial 3, 2,3,8,6, 3,4,4,3 ::;:::::_ Put the ~umbers in order: 2+3+3+3+ 3 +4+4+6+8 l The MODE is 3 the value that occurs most frequently _ ' j The MEAN is 4 (36 + 9 = 4). The MEDIAN is 3, the value in the middle of the ranked (ordered) list. The RANGE is the highest value (8; minus the smallest value (2). The range in DBP reduction is 6. GAUSSIAN (NORMAL) DISTRIBUTIONS Lal'ge sample sets of continuous data tend to form a Gaussian, or "normal" (bell-shaped), distribution (see the figure at the top of the next page) . For example, if a researcher collects 5,000 blood pressure measurements (continuous data) from Idaho residents and plots the values, the graph would form a normal distribution. Characteristics of a Gaussian Distribution When the distribution of data is normal, the curve is symmetrical (even on both sides), with most of the values closer to the middle. Half of the values are on the left side of the curve, and half of the values are on the right side. A small number of values are in the tails. When data is normally distributed: A The mean, median and mode are the same value, and are at the center point of the curve. !\ 68% of the values fall within 1 SD of the mean and 95% of the values fall within 2 SDs of the mean. Normal Distribution Shapes The examples to the right show how the curve of normally distributed data changes based on the spread (or range) of the data. The curve gets taller and skinnier as the range of data narrows. The curve gets shorter and wider as the range of data widens (or is more spread out}. 210 ,J A A ,j, Range of Range of data narrows data widens Rx PREP 20 22 CO UR SE BOOK I RxPREP ©2 0 2 1, © 2022 GAUSSIAN (NORMAL) DISTRIBUTION ; I l l ! i I i ! I I I 2.5% Outliers- very low values .. I I I 35D i 25D 1SD mean median mode 1 SD 2 SD 3 ~D Outliers- : very high values ©RxPreµ SKEWED DISTRIBUTIONS Data that are skewed do not have the characteristics of a normal distribution; the curve is not symmetrical, 68% of the values do not fall within 1 SD from the mean and the mean, median and mode are not the same value. This usually occurs when the number of values (sample size) is small and/or there are outliers in the data. Outliers (Extreme Values) An outlier is an extreme value, either very low or very high, compared to the norm. For example, if a study reports the mean weight of included adult patients as 90 kg, then a patient in the same study with a weight of 40 kg or 186 kg is an outlier. When there are a small number of values, an outlier has a large impact on the mean and the data becomes skewed. In this case, the median is a better measure of central tendency. In the examples to the right, the median is right in the middle of the data and is not affected by outliers. The distortion of the central tendency caused by outliers is decreased by collecting more values; as the number of values increases, the effect of outliers on the mean decreases. More low Negative (left) skew Positive (right) skew More high values Skew Refers to the Direction of the Tail Data is skewed towards outliers. When there are more low values in a data set and the outliers are the high values, data is skewed to the right (positive skew). When there are more high values in the data set and the outliers are the low values, the data is skewed to the left (negative skew). DEPENDENT AND INDEPENDENT VARIABLES A variable in a study is any data point or characteristic that can be measured or counted. Examples include age, gender, blood pressure or pain. Variables can be clinical endpoints such as death, stroke, hospitalization or an adverse event, or they can be intermediate (or surrogate) endpoints used to assess an outcome, such as measuring serum creatinine to assess the degree of renal impairment. Independent variables are changed by the researcher The dependent variables can be affected by the Independent variables Examples: drugs, drug dose/s, placebos, patients included (e.g., age, gender, comorbid conditions) Examples: HF progression , hemoglobin A1C, blood pressure, cholesterol values, mortality An independent variable is changed (manipulated) by the researcher in order to determine whether it has an effect on the dependent variable (the outcome). Independent variables are the characteristics of the subject groups (treatment and control) selected for inclusion (e.g., age, gender, presence or absence of hypertension, diabetes or other comorbid conditions), or any other characteristic that could have an effect on the dependent variable. 211 14 I BIOSTAT IS TI CS TESTING THE HYPOTHESIS FOR SIGNIFICANCE If a drug or device manufacturer wants to sell their product and make money, they will want research data that demonstrates that their product is significantly better than (or superior to) the current treatment or a placebo (no treatment). To show significance, the trial needs to demonstrate that the null hypothesis is not true and should be rejected, and the alternative hypothesis can be accepted. The null hypothesis and alternative hypothesis are always complementary; when one is accepted, the other is rejected. THE NULL HYPOTHESIS AND ALTERNATIVE HYPOTHESIS Null means none or no; a null hypothesis (H 0 ) states that there is no statistically significant difference between groups. A researcher who is studying a drug versus a placebo would write a null hypothesis that states that there is no difference in efficacy between the drug and the placebo (drug efficacy= placebo efficacy). The null hypothesis is what the researcher tries to disprove or reject. The alternati ve hypothesis (HA) states that there is a statistically significant difference between the groups (drug efficacy-:;:. placebo efficacy) . The altemative hypothesis is what the researcher hopes to prove or accept. ALPHA LEVEL: THE STANDARD FOR SIGNIFICANCE When investigators design a study, they select a maximum permissible error margin, called alpha (a.). Alpha is the threshold for rejecting the null hypothesis. In medical research, alpha is commonly set at 5% (or 0.05). A smaller alpha value can be chosen (e.g., 1%, or 0.01), but this requires more data, more subjects (which means more expense) and/or a larger treatment effect. ALPHA CORRELATES WITH THE VALUES IN THE TAILS WHEN DATA HAS A NORMAL DISTRIBUTION 99.7% of all values are within 3 SDs on each side of the mean. 95% of all values are within 2 SDs on each side of the 111e;u1. Y X 2.5% on eacn side= 5%. ,,th w ith alpha ; 0 .05 = 0.01 Ulf Comparing the P-Value to Alpha Once the alpha value is determined, statistical tests are performed to compare the data, and a p-value is calculated. The p-value is compared to alpha. If alpha is set at 0 .05 and the p-value is less than 0 .05, the nuU hypothesis is rejected, and the result is termed stat istically significant. If the p-value is greater than or equal to alpha (p 0.05), the study has failed to reject the null hypothesis, and the result is not statistically significant. The Null Hypothesis: Reject or Accept? Write a Determine the Null Hypothesis Alpha Value (such as 5%) Run study, co11ect data, analyze My product =other product/placebo. Goal: reject the null hypothesis. data with statistical tests to calculate p-values. Compare p-value to alpha value. < p-vatue < alpha REJECT the Null Hypothesis Alternative Hypothesis Accepted (e.g.. p < 0.05) $$$$$ p•value alpha ACCEPT the Null Hypothesis Alternative Hypothesis Rejected DARN! (e.g.. p O.OS) (~)RxPrep 212 RxPREP 2022 COURSE BOOK I RxPREP ©2021, ©2022 CONFIDENCE INTERVALS A confidence interval (Cl) provides the same information about significance as the p-value, plus the precision of the result. Alpha and the CI in a study will correlate with each other. 1-a J If alpha is 0.05, the study reports 95% Cis; an alpha of 0.01 corresponds to a CI of 99%. The relationship between alpha, the p-value and the CI is described in the table here and in the figure on the previous page. P-VALUE ALPHA :. MEANING 0.05 I 2: o.o5 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's not. Not statistically significant -------------- Statistically _ _ _ _ _ __ _Si!niflca!!!_ The values In the Cl range are used to determine whether significance has been reached Determining statistical significance using the Cl alone (without a p-value) Is required for the exam COMPARING DIFFERENCE DATA(MEANS) Difference data is based on subtraction [e.g., the difference in t,. FEV1 between roflumilast and placebo (below) was 38 (46 - 8 = 38)) The result is statistically significant if the Cl range does not include zero (e.g., zero is not present in the range of values); for example: D The 95% Cl for the difference int,. FEV1 (18-58 ml) does not include the result is statistically significant D The 95% Cl for the difference int,. FEV1/FVC (-0.26-0.89%) includes the result is not statistically significant DRUG" (N = 745) LUNG FUNCTION . 46 t,.fEV1 (ml ) t,. FEV1/FVC (%) 0.314 PLACEBO (N = 745) DIFFERENCE (95% Cl) 8 38 (18- 58) 0.001 0.313 (-0.26-0.89) 'Roflumilast 95% Cl for LI FEVl does NOT include ("cross") zero STATISTICALLY SIGNIFICANT 95% Cl for LI FEVl/FVC DOES include ("cross") zero NOT STATISTICALLY SIGNIFICANT -0.26 1---+--------i 0.89 18 1--- - - - - - 58 -20 0 40 20 -1 60 -0.5 1 0.5 0 COMPARING RATIO DATA (RELATIVE RISK, ODDS RATIO, HAZARD RATIO) Ratio data is based on division [e.g., the ratio of severe exacerbations between roflumilast and placebo (below) was 0.92 (0.11/0.12 = 0.92)] The result is statistically significant if the Cl range does not include one (e.g., one is not present in the range of values); for example: D The 95% Cl for the relative risk of severe exacerbations (0.61-1.29) includes the result is not statistically significant D The 95% Cl for the relative risk of moderate exacerbations (0.72-0.99) does not include EXACERBATIONS" DRUG'" (N = 745) PLACEBO (N = 745) Severe 0.1 1 - - - - - - - - - , - 0.12 Moderate 0.94 1.11 ----- the result is statistically significant RELATIVE RISK (95% Cl) 0.92 (0.61-1.~ I o.a5 {o.72-0.99) _ _ __, 'Mean rate, per patient per year "Roffumi/ast I l 95% Cl for severe exacerbation DOES include C'cross'1) one NOT STATISTICALLY SIGNIFICANT 0.75 1 1.25 does NOT include ("cross") one STAT!STICALLY SIGNIFICANT 0.72 1 - - - - - - - - - - - - - - - , 0.99 0.61 1 - - - - - - - + - - - - - i 1.29 0.5 95% Cl for moderate exacerbation 1.5 0.7 0.8 0.9 1.1 213 14 I BIOS TATIST ICS Confidence Intervals and Estimation (Extent and Variability in the Data) The goal of the majority of medical research is to use the study results to promote the procedure or drug for use in the general population of patients with the same medical condition. Clinicians need to understand how their patients would benefit. The CI includes the treatment effect and the range; both are helpful in estimating the effect on others. A CI can be written in slightly different formats. For example, a study comparing metoprolol to placebo finds a 12% absolute risk reduction (ARR) in heart failure progression, with a 95% CI range of 6 - 35%. This can be written as ARR 12% (95% CI 6% - 35%) or as decimals, with commas in the range, such as ARR 0.12 (0.95 CI 0.06, 0.35). The CI indicates that you are 95% confident that the true value of the ARR for the general (or true) population lies somewhere within the range of 6%35%, with some values as low as 6% and others as high as 35%. A narrow CI range implies high precision, and a wide CI range implies poor precision. If the reported CI range was 4% - 68%, the true value would still be within the range, but where? The range is wider, and therefore less precise. Cardiologists who interpret the results for their patients would not know whether to expect a result closer to 4% or 68%. A large range correlates to a large dispersion in the data. A narrower range is preferable. In some studies, specific patient types will cause a wider distribution in data. For example, fibrates are used to lower triglyceride levels; they cause a greater reduction in patients with higher triglycerides. The consideration of where the patient is likely to fall within the range will become part of the assessment of the individual's baseline risk. TYPE I AND TYPE II ERRORS Consider what would happen if a drug manufacturer developed and marketed a new drug as better for heart failure than the standard of care, when in fact the new, expensive drug has similar benefits to the old drug (it is not better at all) . The null hypothesis stated that the new drug and the old drug are equal. The statistical tests found a significant benefit with the new drug, and the null hypothesis was rejected when it should have been accepted. Type I Errors: False-Positives In the scenario described above, the conclusion was wrong and a type I error was made. The alternative hypothesis was accepted and the null hypothesis was rejected in error. The probability, or risk, of making a type I error is determined by alpha and it relates to the confidence interval. r 7 Cl- ,.- When alpha is 0.05 and a study result is reported with~ 0.05, it is statistically significant and the probability of a ~ I error (making the wrong conclusion) is < 5%. You are 95% confident (0.95 = 1- 0.05) that your result is correct and not due to chance. Type II Errors: False-Negatives The probability of a type II error, denoted as beta(~), occurs when the null hypothesis is accepted when it should have been rejected. Beta is set by the investigators during the design of a study. It is typically set at 0.1 or 0.2, meaning the risk of a type II error is 10% or 20%. The risk of a type II error increases if the sample size is too small. To decrease this risk, a power analysis is performed to determine the sample size needed to detect a true difference between groups. Study Power Power is the probability that a test will reject the null hypothesis correctly (i.e., the power to avoid a type II error) . Power = 1 - ~- As the power increases, the chance of a type II error decreases. Power is determined by the number of outcome values collected, the difference in outcome rates between the groups, and the significance (alpha) level. If beta is set at 0.2, the study has 80% power (there is a 20% chance of missing a true difference and making a type II error). If beta is set at 0.1, the study has 90% power. A larger sample size is needed to increase study power and decrease the risk of a type II error. HO ACCEPTED H0 is TRUE (There IS a difference between groups) _I Correct Conclusion (NO difference between groups) H0 is FALSE Type 11 Error Committed FALSE NEGATIVE 214 l · a (type I error) H 0 REJECTED Type I Error Committed FALSE POSITIVE Correct Conclusion RxPREP 2022 CO UR SE BOO K I Rx PR EP ©2 0 2 1, ©2 0 22 RISK In healthcare, risk refers to the probability of an event {how likely it is to occur) when an intervention, such as a drug, is given. The lack of intervention is measured as the effect in the placebo {or control) group. RELATIVE RISK (OR RISK RATIO) The relative risk (RR) is the ratio of risk in the exposed group {treatment) divided by risk in the control group. RR Formula __ N_u_m_b_er_o_f_s_ub _i_ec_t_s _in_g_r_ ou_p_w ~_ i~ t h=an_-_u=nf=a_ v-o~r_ab_l_ e _ev_e_n_t __ j Risk L Total number of subjects in group - ~-- F Risk in trea~m~ nt group ~ 7 in control group _ l J RR Calculation A placebo-controlled study was performed to evaluate whether metoprolol reduces disease progression in patients with heart failure (HF). A total of 10,lll patients were enrolled and followed for 12 months. What is the relative risk of HF progression in the metoprolol-treated group versus the placebo group? Calculate the risk of HF progression in each group. Then calculate RR. METOPROLOL CONTROL N = 5,123 N = 4,988 HF progression 823 Metoprolol Risk 823 5,123 1,397 "'0. 16 I_ I Control Risk 1,397 - - - - - =0.28 4,988 0.16 R R = - - - - = 0.57 0.28 X 100 = 57% Answer can be expressed as a decimal or a percentage; the exam question will specify with instructions RR Interpretation RR= 1 (or 100%) implies no difference in risk of the outcome between the groups. RR> 1 (or 100%) implies greater risk of the outcome in the treatment group. RR< 1 (or 100%) implies lower risk {reduced risk) of the outcome in the treatment group. In the metoprolol study, the RR of HF progression was 57%. Patients treated with metoprolol were 57% as likely to have progression of disease as placebo-treated patients. INTERPRETING THE RELATIVE RISK (RR) RR= 1 Equal risk between intervention (treatment) & control groups Intervention had no effect RR< 1 The treatment .J, the risk of the outcome (endpoint) (e.g., less HF progression in the treatment group) A RR of 0.5 indicates there is 50% (0.5 is 50% less than 1) risk in the treatment group as compared to the risk in the control group \ RR> 1 The treatment i the risk of the outcome (endpoint) (e.g., more HF progression in the treatment group) A RR of 1.5 indicates there is 50% (1.5 is 50% greater than 1) increased risk in the treatment group as compared to the risk in the control group [m ~l RxPrep 215 14 I BIO STATI STI CS RELATIVE RISK REDUCTION The RR calculation determines whether there is less risk (RR< 1) or more risk (RR> 1). The r elative risk r eduction (RRR) is calculated after the RR and indicates how much the risk is reduced in the treatment group compared to the control group. RRRFormula I (% risk in control group - % risk in treatment group) % risk in the control group ------- Decimals ar percentages may be used for risks I J 1- RR* or l J 'Must use decimal form of RR RRR Calculation Using the risks previously calculated for HF progression in the treatment and control groups (metoprolol: 16% and placebo: 28%), calculate the RRR of HF progression. (28% - 16%) RRR or 0.43 RRR 1 - 0.57 0.43 28% Answer can be expressed as a decimal or percentage; the exam question will specify with instructions RRR Interpretation The RRR is 43%. Metoprolol-treated patients were 43% less likely to have HF progression than placebo-treated patients. INTERPRETING THE RELATIVE RISK REDUCTION (RRR) RR 0.57 + RRR 0.43 = 1 RRR rnr,toprolr,I p,1twnts were 43% ~l!t.£J Y (than the control group) to suifer from HF - - progr,i~STon . ·· - RR RRR Therefore ·- ..___ AS likely (vs. the control) LESS likely (vs. the control) RR+ RRR = 100% _ _ _ __ __ _ _ _ _ _ ___, fll1 ©RxPrep ABSOLUTE RISK REDUCTION A clinician is listening to a presentation on a drug. The drug manufacturer representative reports that the drug causes 48% less nausea than the standard treatment. The result sounds great; the clinician asks the pharmaceutical representative: what is the absolute risk reduction (ARR)? The RR and RRR provide relative (proportional) differences in risk between the treatment group and the control group; they have no meaning in terms of absolute risk. Absolute risk reduction is more useful because it includes the reduction in risk and the incidence rate of the outcome. If the risk of nausea is reduced, but the risk was small to begin with (perhaps the drug caused very little nausea}, the large risk reduction has little practical benefit. It is best if a study reports both ARR and RRR, and for clinicians to understand how to interpret the risk for their patients. If the ARR is not reported, it is possible that the risk reduction, in terms of a decrease in absolute risk, is minimal. ARR Formula ARR 216 --------(% risk in control group) - (% risk in treatment group) 7 ) RxPREP 20 22 COUR SE BOOK I Rx PREP ©202 1, ©2 0 22 ARR Calculation Using the risks previously calculated for HF progression in the metoprolol study, calculate the ARR of HF progression. Metoprolol Risk 823 Control Risk 1,397 = 0.16 5,123 4,988 = 0.28 • ARR= 0.28 - 0.16 = 0.12 x 100 = 12% Answer can be expressed as a decimal or a percentage; the exam question will specify with instructions ARR Interpretation The ARR is 12%, meaning 12 out of every 100 patients benefit from the treatment. Said another way, for every 100 patients treated with metoprolol, 12 fewer patients will have HF progression. An additional benefit of calculating the ARR is to be able to use the inverse of the ARR to determine the number needed to treat (NNT) and number needed to harm (NNH). These concepts are discussed next. INTERPRETING THE ABSOLUTE RISK REDUCTION (ARR) Placebo risk minus the Treatment risk = ARR The absolute risk reduction is the true difference in risk between the treatment and the placebo groups. Said another way, the ARR is the net effect (benefit) beyond the effect obtained from a placebo. fffi © RxPrep NUMBER NEEDED TO TREAT OR HARM NNT and NNH help clinicians answer the question: how many patients need to receive the drug for one patient to get benefit (NNT) or harm (NNH)? This information, taken into consideration with the patient's individual risk, helps guide decisions. NUMBER NEEDED TO TREAT NNT is the number of patients who need to be treated for a certain period of time (e.g., one year) in order for one patient to benefit (e.g., avoid HF progression). NNTFormula r 1 NNT ,, - - - -- -- - or I __!__-l (risk in control group) - (risk in treatment group)* *Risk and ARR are expressed as decimals NNT Calculation The ARR in the metoprolol study was 12%. The duration of the study period was one year. Calculate the number of patients that need to be treated with metoprolol for one year in order to prevent one case of HF progression. NNT = 8.3, rounded up to 9* 0.12 *Numbers greater thon a whole number are rounded up NNT Interpretation For every 9 patients who receive metoprolol for one year, HF progression is prevented in one patient. 217

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