BROUGHT TO YOU BY Biostatistics 2 - Correlation and Risk Developed by Pfizer January 2018 This learning module is intended for UK healthcare professionals only. PP-GEP-GBR-0957 Date of preparation Jan 2018.
1 Introduction This learning module is intended for UK healthcare professionals only. Medical knowledge is constantly changing. As new information becomes available, changes in treatment, procedures, equipment and the use of drugs become necessary. The authors and editors have, as far as it is possible, taken care to ensure that the information given in this module is accurate and up to date at the time it was created. However, users are strongly advised to confirm that the information, especially with regard to drug usage, complies with current legislation and standards of practice.this learning module is intended for UK healthcare professionals only.
Introduction This course is designed to allow you to implement and understand the statistics used in many aspects of biology, from clinical trials to non-investigator lead research and even the more recent phenomenon classified as real life data. This course is split into three modules: Biostatistics 1, 2 and 3. To allow all readers to have a sound understanding we will start from the very basics, but feel free to skip the chapters if you feel they are unneeded or browse through for a refresh.
Learning objectives The module presents the second of three courses. It will help you to understand how to assess relationship between two variables and how to interpret risk measures.
2 Correlation This learning module is intended for UK healthcare professionals only.
Drug Serum Level (mcg/ml) Drug Serum Level (mcg/ml) Correlation The relationship that occurs between two variables when a change in one variable is associated with a change in the other variable Variable 1 Variable 1 Variable 2 Variable 2 100 60 0 20 40 60 80 100 120 Creatinine Clearance (ml/min) A positive correlation is the extent the variable increase or decrease in parallel A negative correlation indicates the extent to which one variable increases as the other decreases
Scatter Plot Scatter plots visually represent correlation between two variables Data plotted on a scatter plot give a visual representation of how strongly or weakly correlated one variable is to another. The more closely the data points line up, the stronger the correlation, and vice versa
Pearson Coefficient Pearson Coefficient (or Pearson Product- Moment Correlation) is indicated by r The strength of the correlation increased towards -1 or 1 r value range -1 0 +1 r = -1 r =.7 Perfect Correlation r = 0 Graph B r = -.7 Graph C r = 1 Perfect Correlation Graph D Graph E
Renal Function (ml/min) Pearson Coefficient Positive or Direct Correlation Two variables move in the same direction Negative or Indirect Correlation Two variables move in opposite directions 100 80 60 40 20 40 Negative Correlation r = -0.7 Age (years) 60 80 100
Pearson Coefficient No Relationship r = 0 indicates that there is no relationship between the variables
Pearson Coefficient r Value Chart rr General Interpretation 0.8 to 1 Very strong relationship 0.6 to 0.8 Strong relationship 0.4 to 0.6 Moderate relationship 0.2 to 0.4 Weak relationship 0.0 to 0.2 Weak or no relationship This table can be used as an easy way to interpret the value of r For example, if the correlation between two variables is 0.4, you can safely conclude that the relationship is weak to moderate However this is subjective thus, using this rule-of-thumb table is great for a quick assessment of r, but we will go onto explain a more precise method
Interpreting Correlation Coefficient of Determination: r 2 The percentage of variance in one variable that is accounted for by the variance in the other variable For example; r = 0.7 r 2 = 0.49 49% of the variance in blood pressure can be explained by the variance in dietary salt intake
Interpreting Correlation Coefficient of Determination: r 2 Even with a strong correlation of 0.7, the majority (51%) of the variance goes unexplained 51% Unexplained Variance 19% Unexplained Variance r = 0 r 2 = 0 r = +/- 0.7 r 2 = 0.49 r = +/- 0.9 r 2 =.81 Here, with r 2 equal to 0, the two variables have nothing in common and are totally unrelated When r 2 equals 0.49, both variables share 49% of the variance between themselves It follows that when r 2 equals 0.81, 81% of the variance is shared and relatively little variance (19%) goes unexplained
Blood Pressure (mmhg) Linear Regression A line of best fit is applied to the data points which measures the effect of a single independent variable Once the best fit line has been calculated, the regression analysis assesses how well the individual data points adhere to the line 180/120 160/110 140/100 130/90 Correlation r =.7 This allows the researcher to predict the change that will occur in one variable based on a change in a second variable 120/80 0 2 4 6 8 10 Salt Intake (grams)
Blood Pressure (mmhg) Linear Regression In the graph shown, you can predict that a dietary salt intake of 8g per day will correlate to a blood pressure reading of 160/110 mm Hg. The closer the fit of the data to the regression line, the higher the correlation coefficient, and the more accurate the prediction will be 180/120 160/110 140/100 Correlation r =.7 You have probably already surmised that if the correlation coefficient is +1 or -1, the prediction will be perfect, that is, from the value of the first variable you can predict the exact value of the second variable 130/90 120/80 0 2 4 6 8 10 Salt Intake (grams)
3 Risk This learning module is intended for UK healthcare professionals only.
Understanding Risk There are manly different types of risk described in statistic (listed below), throughout this chapter we will describe what each type of risk means and how it can be used Risk Terminology Absolute Risk (AR) Absolute Risk Reduction (ARR) Relative Risk (RR) Relative Risk Reduction (RRR) Odds Ratio Hazard Ratio
Absolute Risk Absolute Risk (AR) = Incidence or Occurrence Rate Absolute risk is another way of expressing the incidence, or occurrence rate, of an event. Drug A Drug B (Control) Example: in a clinical study, 6% of patients experienced nausea with Drug A. In the control group, 9% of patients experienced nausea on Drug B. We can now say that the absolute risk of nausea is 6% and 9% with Drug A and Drug B, respectively 6% AR = 6% 9% AR = 9%
Absolute Risk Reduction Absolute Risk Reduction (ARR) = Absolute Difference ARR = 3% (AR Drug B AR Drug A) Drug A Drug B (Control) The absolute difference, or ARR, with Drug A is 3%, simply by subtracting the proportion (or percentage) of patients 6% who experienced nausea with Drug A 9% from the proportion (or percentage) of AR = 6% patients who experienced nausea with Drug B 9% 6% = 3% ARR = 3% AR = 9%
Number Needed to Treat (NNT) Drug A Drug B (Control) The numbers needed to treat helps to establish clinical significance of the ARR. NNT = 1/ARR thus for the previous example 1/0.03 = 33 patients 6% 9% AR = 6% AR = 9% NNT = 1/.03 = 33 patients
Number Needed to Treat (NNT) Absolute difference (ARR) of 3% may, or may not be statistically significant, but we also want to determine the possibly clinically significance. To help to attribute a clinical aspect to the data, the numbers needed to treat (NNT) is calculated, the number of patients that the physician needs to treat so that one patient is likely to experience a benefit, in our case, no nausea. The NNT is calculated by using the formula 1/ARR. In our case NNT would be 1/0.03, or 33 patients. Thus, the physician would have to make a clinical judgment as to whether or not it is beneficial to treat 33 patients with Drug A so that one patient can avoid nausea. 6% Drug A Drug B (Control) 9% AR = 6% AR = 9% NNT = 1/0.03 = 33 patients
Number Needed to Harm (NNH) Although we can establish the benefit we also want to look at the possibility of harm. Instead of absolute risk reduction, we state the results in terms of absolute risk increase, or ARI In turn, number needed to treat becomes number needed to harm, or NNH Absolute Risk Increase (ARI) Number Needed to Harm (NNH) NNH = 1/ARI Drug A 6% AR = 6% ARI = 3% or.03 Drug B (Control) 9% AR = 9% NNH = 1/.03 = 33 patients
Absolute Risk Increase (ARI) Number Needed to Harm (NNH) NNH = 1/ARI Drug A Drug B (Control) Let s go back to our example: suppose that the treatment group (Drug A) was associated with an absolute risk of nausea of 9% and the control group (Drug B) was associated with a nausea risk of only 6%. In other words, we have reversed the incidence rates, or absolute risk. Using a similar formula to NNT, NNH becomes 1/ARI or again, 1/.03 or 33 patients. 6% AR = 6% ARI = 3% or.03 9% AR = 9% NNH = 1/.03 = 33 patients In this case, the physician would have to treat 33 patients with Drug A for one more patient to experience nausea than if they were taking Drug B
Relative Risk (RR) Incidence in Drug A/Incidence in Drug B Another way to express risk is as relative risk, that is, the risk of patients receiving Drug A developing nausea, relative to that among patients in the control group receiving Drug B Drug A Drug B (Control) Example: the risk of nausea with Drug A is 6% compared to that of Drug B, 9%. Mathematically, this would be expressed as the incidence of nausea in the treatment group divided by the incidence of nausea in the control group, or 0.06/0.09, which equals 0.67, or 67%. Thus, we can say that the relative risk of nausea with Drug A is 0.67 or 67% of that seen with Drug B 6% 9% AR = 6% AR = 9% RR = 0.06/0.09 = 0.67 or 67%
Hazard Ratio (HR) Another common term you are likely to see in the literature is hazard ratio Hazard ratio is a term used in the context of survival over time and basically indicates the increased speed in which one group is likely to experience an event, such as death So if the hazard ratio is 0.5, then the relative risk of dying in one group is half that of the second group Relative risk of death: 1/15 Relative risk of death: 3/15 Hazard ratio of coal miners: 3
Hazard Ratio (HR) A survival analysis produces a hazard ratio rather than an odds ratio or relative risk The hazard ratio is roughly equivalent to the relative risk of death For instance, if a risk factor, such as working in a coal mine, is associated with a fatal form of lung cancer and has a hazard ratio of 3, then we can say that a coal miner is likely to die of lung cancer at three times the rate of those who are not coal miners. Relative risk of death: 1/15 Relative risk of death: 3/15 Hazard ratio of coal miners: 3
Understanding Risk If either RR or OR is 1, there is no increase in risk, because the numerator and denominator are the same No Increased in risk 2-Pack Smokers 1-Pack Smokers 3% 3% OR =.03/.03 = 1
RRR and ARR Relative Risk Reduction (RRR) vs. Absolute Risk Reduction (ARR) : Differences It is important to appreciate and understand the distinct differences between relative risk reduction and absolute risk reduction More often than not, the medical literature will report the relative risk reduction rather than the absolute risk reduction. The reason, quite simply, is that RRR is often more impressive than ARR and, thus, reinforces and, in some cases magnifies the true differences between study groups Although RRR is more impressive, it s the ARR that is more clinically useful, as illustrated earlier in our discussion of NNT and NNH RRR More often reported Often more impressive Less clinically useful ARR Less often reported Often less impressive More clinically useful
RRR and ARR Example: ARR (Drug A) = 3%, RRR (Drug A) = 33%, Absolute Difference (ARR) =3%, NNT= 33 patients The absolute risk reduction in nausea with Drug A was 3% compared to Drug B, although the relative risk reduction was 33% If the authors of the study were to report a relative risk reduction of 33% in nausea with the new treatment, Drug A, one would be inclined to immediately stop using the control drug B and begin using Drug A, all other things being equal However, a closer look at the data revealed an absolute difference of only 3%. And again, the physician would have to treat 33 patients with the new drug in order for one less patient to experience nausea vs Drug B probably not clinically worthwhile, especially if there was a difference in cost (more expensive) or dosing frequency, and so on RRR More often reported Often more impressive Less clinically useful ARR Less often reported Often less impressive More clinically useful
4 Testing your knowledge This learning module is intended for UK healthcare professionals only.
Question 1 Looking at the diagram, what type of correlation is this an example of? A) Strong B) Weak
Question 2 Absolute Risk Reduction (ARR) = Absolute Difference True False
Question 3 Select three characteristics of relative risk reduction (RRR) in comparison to absolute risk reduction (ARR) Often reported less Often reported more Less clinically useful More clinically useful Often more impressive Often less impressive
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Contact Us For general inquiries or information about Pfizer medicines, you can contact Pfizer on 01304 616161. This learning module is intended for UK healthcare professionals only. PP-GEP-GBR-0957 Date of preparation Jan 2018.