1. Interpreting Basic Statistics
Beginners’ statistics for assessing the
effectiveness of an intervention
UH Bristol library service

2. Aim
To give you a greater understanding of how to interpret basic medical statistics.
Session outline:
Statistics which compare risks
Statistics which test confidence
Forest Plots

3. Objectives Use raw data to calculate simple statistics to compare risk
Interpret p-values and confidence intervals within the context of a study
Pick out key information from a forest plot
Understand the values and issues of using different statistical measures

4. Statistics Which Compare Risk

5. Randomised Control Trial
Experiment Event Group
Control Event Group

6. Experiment Event Group
Control Event Rate (CER)
= Risk of outcome event in
control group
Experimental Event Rate (EER)
experimental group
Control Event Group
Experiment Event Group

7. Example 1
Randomised Control Trial of a new drug tested on a population at risk of a heart attack.
90/100 of those not receiving the drug (control group) will have a heart attack.
60/100 of those receiving the drug (experimental group) will have a heart attack.

8. Experiment Event Group
Risk
Control event rate (CER)
number in the control group with event 90
total number in the control group 100
Risk in the control group is: 0.9 = 90% risk of event
Experimental event rate (EER)
number in the experimental group with event 60
total number in the experimental group 100
Risk in experiment group is: 0.6 = 60% risk of event
Control Event Group
Experiment Event Group
90/100 = 0.9x100 = 90%
60/100 = 0.6x100 = 60%
The intervention has lowered the risk of the event happening

9. Relative Risk (RR)
Compares the risk of having an event between two groups
RR = EER /CER = ÷
relative risk or risk ratio (RR) is the ratio of the probability of an event occurring (for example, developing a disease, being injured) in an exposed group to the probability of the event occurring in a comparison, non-exposed group. 
RR = event when exposed divided event when not exposed
0.6 ÷
0.9
0.67

10. Relative Risk What is our Outcome?
We are measuring the event, Is our outcome Adverse or Beneficial?, Our event is Heart Attack, Our outcome is adverse
When a treatment has an RR greater than 1, the event - or risk - is increased by the treatment; when the RR is less than 1, the event – or risk is decreased
Compares the risk of having an event between two groups
RR=1 the event is equally likely in both groups
RR<1 event is less likely to happen than not (i.e. the intervention reduces the chance of having the event)
RR>1 event is more likely to happen than not (i.e. the intervention increases the chances of having the event)

11. Example 2
2 RCTs of a new drug tested on two populations at risk of a heart attack over 10 years.
RCT1: High risk group (n=200)
90/100 of those not receiving the drug (control group) will have a heart attack.
60/100 of those receiving the drug (experimental group) will have a heart attack.
RCT 2: Low risk group (n=200)
3/100 of those not receiving the drug (control group) will have a heart attack.
2/100 of those receiving the drug (experimental group) will have a heart attack.

12. Experiment Event Group
High Risk Group
Control Event Rate (CER)=
number in the control group with event 90
total number in the control group
Risk in the control group is: 0.9 = 90% risk of event
Experimental Event Rate (EER)=
number in the experimental group with event 60
total number in the experimental group
Risk in experiment group is: 0.6 =60% risk of event
Control Event Group
The intervention has lowered the risk of the event happening
Experiment Event Group

13. Experiment Event Group
Low Risk Group
Control Event Rate (CER)=
number in the control group with event 3
total number in the control group
Risk in the control group is: = 3% risk of event
Experimental Event Rate (EER)=
number in the experimental group with event 2
total number in the experimental group
Risk in experiment group is: 0.02 = 2% risk of event
Control Event Group
The intervention has lowered the risk of the event happening
Experiment Event Group

14. Relative Risk (RR) RR = EER/CER =
Compares the risk of having an event between two groups
RR = EER/CER =
High Risk
0.6 ÷
0.9
0.67
Low Risk
0.02
0.03
The relative risk (RR) of an outcome in a group given intervention is a proportional measure estimating the size of the effect of a treatment compared with other interventions or no treatment at all.
It is the proportion of outcomes in the intervention group divided by the proportion of outcomes in the control group.

15. Relative Risk Reduction (RRR)
The reduction in the rate of the event in the treatment group relative to the control group
RRR = 1 – RR =
High Risk 1 -
0.67
Low risk =
0.33
= 33%
Relative risk reduction (RRR) tells you by how much the treatment reduced the risk of the event - in the experimental/intervention group - relative to the risk of the event in the control group - who did not have the treatment.

16. Absolute Risk Reduction (or Risk Difference)
Compares the risk of having an event between two groups
ARR = CER – EER =
High Risk
0.9 -
0.6 =
0.3
30%
Low Risk
0.03
0.02
0.01 1%
33%
RRR

17. Example
If you didn't take aspirin, your risk of having a heart attack was 2% over 5 years.
If you did take aspirin, your risk of having a heart attack was 1% over 5 years.
Lets say that a study shows that aspirin reduces of your risk of having a heart attach from 2% to 1% RRR would show this as a drop in the risk of the event by 50% which might consider to be a huge reduction but if we look at the figures from the perspective of the ARR we can see that it still just a drop of 1%
Relative Risk Reduction would say that aspirin reduces your chance of heart attack by 50%
Absolute Risk Reduction would say that aspirin reduced your chance of heart attack by 1%

18. Numbers Needed to Treat (NNT)
The number of people who must be treated to result in benefit in one person. It is the inverse of ARR.
NNT = 1/ARR =

19. Numbers Needed to Treat (NNT)
High Risk
CER
0.9 -
EER
0.6 =
0.3
30%
Low Risk
0.03
0.02
0.01 1%
ARR = CER – EER =
NNT = 1/ARR =

20. Odds Ratio
Expresses the odds of having an event compared with not having an event.

21. Odds Ratio OR = (A / B) ÷ (C / D) = ? 2 x 2 table Disease No Disease
Exposure
Positive A B
Negative C D
0.166
Online Calculator:

22. Odds Ratio Odds Ratio = (60/40) ÷ (90/10) = 0.166 2 x 2 table Disease
No Disease
Exposure
Positive A B
Negative C D
Online Calculator:

23. RE-CAP RR = EER / CER RRR = 1 – (EER/ CER) ARR = CER - EER
RR = EER / CER
RRR = 1 – (EER/ CER)
ARR = CER - EER
NNT = 1- ARR
OR = odds of EER / odds of CER
All the statistics and calculations that we have looked at based on the same raw data but presented in different ways.

24. Statistics Which Test Confidence

25. P-values P value Interpretation P<0.05
The probability (ranging from zero to one) that the results observed in a study could have occurred by chance.
Convention states we accept p-values of p<0.05 to be statistically significant
The P value is computed from the F ratio which is computed from the ANOVA table.
P value
Interpretation
P<0.05
The result is unlikely to be due to chance.
i.e. It s a statistically significant result.
P>0.05
The result is likely to be due to chance,
i.e. It is not a statistically significant result.
P= 0.05
The result is quite likely to be due to chance,

26. Confidence Intervals What is a confidence interval?
The range within which we can be 95% sure that the true value for the whole population lies
What can a confidence interval indicate?
Indication of precision
Strength of the evidence
Whether a result is statistically significant

27. Relative Risk / Odds Ratio RRR, ARR or mean difference
Interpreting CIs
Relative Risk / Odds Ratio
(binary outcome)
RRR, ARR or mean difference
(continuous outcome)
Measure of effect
Measure of effect
< 0
> 0
If the CI range crosses 1, then the difference between the two groups is not statistically significant
If the CI range crosses 0, then the difference between the two groups is not statistically significant

28. Trials to examine the effect of probiotics on the risk of antibiotic associated diarrhoea
Which study/studies show a significant result?
Which study demonstrated the strongest evidence?

29. Forest Plots

30. Forest Plots
“Effect of probiotics on the risk of antibiotic associated diarrhoea”

31. Exercise Do the studies favour group behaviour for smoking cessation?
Which study/studies show a significant result?
Which study demonstrated the strongest evidence?

32. Confidence interval graphic
A closer look at Significant Results
Confidence interval graphic
With "Non-Significant" Results - The difference between the perspective provided by the confidence interval and significance testing is particularly clear when considering non-significant results. The image shows two confidence intervals; neither of them is "statistically significant" using the criterion of P< 0.05, because both of them embrace the null (risk ratio = 1.0). However, one should view these two estimates differently. The estimate with the wide confidence interval was likely obtained with a small sample size and a lot of potential for random error. However, even though it is not statistically significant, the point estimate (i.e., the estimated risk ratio or odds ratio) was somewhere around four, raising the possibility of an important effect. In this case one might want to explore this further by repeating the study with a larger sample size. Repeating the study with a larger sample would certainly not guarantee a statistically significant result, but it would provide a more precise estimate. The other estimate that is depicted is also non-significant, but it is a much narrower, i.e., more precise estimate, and we are confident that the true value is likely to be close to the null value. Even if there were a difference between the groups, it is likely to be a very small difference that may have little if any clinical significance. So, in this case, one would not be inclined to repeat the study. For example, even if a huge study were undertaken that indicated a risk ratio of 1.03 with a 95% confidence interval of , this would indicate an increase in risk of only 2 - 4%. Even if this were true, it would not be important, and it might very well still be the result of biases or residual confounding. Consequently, the narrow confidence interval provides strong evidence that there is little or no association.
With "Significant" Results - The next figure illustrates two study results that are both statistically significant at P< 0.05, because both confidence intervals lie entirely above the null value (RR or OR = 1). The upper result has a point estimate of about two, and its confidence interval ranges from about 0.5 to 3.0, and the lower result shows a point estimate of about 6 with a confidence interval that ranges from 0.5 to about 12. The narrower, more precise estimate enables us to be confident that there is about a two-fold increase in risk among those who have the exposure of interest. In contrast, the study with the wide confidence interval is "statistically significant," but it leaves us uncertain about the magnitude of the effect. Is the increase in risk relatively modest or is it huge? We just don't know.

33. Library outreach service
The library
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Education Centre
Upper Maudlin St
Tel. ext .