Calculating and communicating risk Flashcards
If the numbers are negative you might have to..
If the numbers are negative, you might have to swap your EER and CER around depending on whether the trial is showing an increase or decrease in event rate for the intervention compared with control. Use common sense and the context of the trial to determine if a negative is a true result or an incorrect calculation.
If 75 women out of 2575 given letrozole have a recurrence of breast cancer, compared with 132 women out of 2582 given a placebo then,
- EER, ARR, RR, RRR, NNT =?
EER = 75/2575 = 0.029 or 2.9%, CER = 132/2582 = 0.051 or 5.1%
ARR or ARI = 0.051 - 0.029 = 0.022 or 5.1 - 2.9 = 2.2%
RR = 0.029/0.051 = 0.57 or 2.9/5.1 = 57%
RRR or RRI = (0.051 - 0.029)/0.051 = 0.43 or 43%
NNT = 1/0.022 or 100/2.2 = 46
Which acronym relates to the risk of an event or outcome in the experimental group divided by the risk in the control group?
RR = The relative risk is the EER/CER. The experimental rate compared with the control rate
Which acronym relates to the ratio of events over non-events in the experimental group, divided by the ratio of events over non-events in the control group?
OR = Odds Ratio
Which acronym relates to the difference in risk between the control and the experimental group?
ARR = Absolute risk reduction is EER-CER
In a randomised controlled trial of smoking cessation therapies (Aubin et al Thorax 2008; 63; 717-724), 746 smokers who had expressed a desire to quit were recruited into a trial of varenicline (experimental treatment: oral, 1mg/day for 12 weeks) compared with nicotine replacement therapy (control treatment, NRT: transdermal patch 7 mg/day for 10 weeks).
The outcome of interest is the number of people still not smoking a year later. A year after treatment, 97 of 376 participants in the varenicline group had remained abstinent compared with 73 of 370 participants in the NRT group.
What is the CER or control event rate, as a percentage?
Using the data from the question above, what is the EER or experimental event rate as a percentage?
Using the values for EER and CER, calculate how many more folk stay abstinent with varenicline vs NRT as a percentage of the whole. (The percentage increased risk of remaining abstinent with varenicline treatment compared with NRT).
2) Which of the following statements are correct in relation to the data from the smoking cessation trial (multiple answers can be selected):
a. The number needed to treat in order than one more varenicline-treated patient was abstinent than NRT-treated patients was 25
b. The proportion of patients remaining abstinent on NRT was only three-quarters that of the proportion abstinent after varenicline treatment
c. More people give up smoking permanently with varenicline than with NRT
d. The absolute risk difference between the varenicline and NRT groups was 6%
Q4.
Ans = the control event rate (event rate for NRT) = 73/370 = 0.197 or 19.7%
Q5.
Ans = the experimental event rate (event rate for varenicline) = 97/376 = 0.258 or 25.8%
Q6.
Ans = the relative risk increase is calculated as (0.258-0.197)/0.197 = 0.31 or (25.8 - 19.7)/19.7 = 31%
2)
b. The proportion of patients remaining abstinent on NRT was only three-quarters that of the proportion abstinent after varenicline treatment
d. The absolute risk difference between the varenicline and NRT groups was 6%
Incorrect answers:
a - this is not true. The NNT was 17. Calculation: 1/(0.258 - 0.197) = 16.39 rounded up to 17.
c - this statement is too much of an extrapolation. From the data given, we can only comment on abstinence after 1 year.
The Diabetes Control and Complications Trial (Ann Intern Med 1995; 122:561-8) evaluated the effect of intensive diabetes therapy vs. usual care on the development and progression of neuropathy (nerve damage) in patients with type 2 diabetes. The results showed that neuropathy occurred in 9.6% of patients randomised to usual care, and 2.8% of patients randomised to intensive therapy.
What is the reduction in absolute risk of neuropathy with intensive therapy vs. usual care?
Using your answer for the ARR from the DCCT trial above, calculate the number needed to treat to prevent one additional case of neuropathy with intensive treatment vs. usual care
2) Which of the following statements is not true about the results of the DCCT trial?
a. 7% fewer patients developed neuropathy with intensive treatment compared with usual care
b. Treating 15 patients with type 2 diabetes with intensive therapy instead of usual care will prevent one additional case of neuropathy
c. There was a 71% lower risk of developing neuropathy with intensive therapy vs. usual care
d. Intensive therapy prevents the development and progression of neuropathy
The ARR= 9.6 - 2.8 = 6.8
100/6.8 = 14.7, rounded up to 15 (The NNT is rounded up to give the most conservative estimate of the number needed to treat)
2)
c. Intensive therapy prevents the development and progression of neuropathy (This is the false answer in that it is too great an extrapolation from the data. All we know is that the risk of neuropathy appears lower with intensive therapy in these particular patients.)
A small RCT (Am J Gastroenterol. 2002 Oct;97(10):2536-9) compared two antibiotic-based triple therapy treatments for the eradication of helicobacter pylori infection in patients presenting with upper GI symptoms at a gastroenterology clinic. After confirmation of infection, 27 patients were randomised to a new azithromycin-based triple therapy (intervention: B-LAA), and 29 patients randomised to the control clarithromycin-based therapy (control: B-LAC). After eight weeks of treatment, patients were tested for eradication of the helicobacter pylori infection using endoscopy, rapid urease test and histopathology.
The results of the intention-to-treat analysis were that the eradication rates for B-LAC and B-LAA were 81% and 52%, respectively (p = 0.019) i.e. the infection was no longer present in 81% of patients treated with the B-LAC therapy and 52% of patients given the B-LAA therapy.
Using the information above, calculate the absolute risk difference between B-LAA and B-LAC
2) Based on your answer above, select one of the two options in the square brackets below to form a conclusion about the results of the trial.
The rate of eradication of h. pylori was [A] with the new treatment (B-LAA) than with usual therapy (B-LAC). This data suggests that the usual therapy is the [B] treatment, and [C] is not a suitable treatment for the eradication of h. pylori.
A. Higher or lower
B. More effective or less effective
C. B-LAA or B-LAC
-29. Carrying out the calculation as requested gives you a negative result: 52 - 81 = - 29% which shows that the new treatment showed no benefit
2)
The rate of eradication of h. pylori was [lower] with the new treatment (B-LAA) than with usual therapy (B-LAC). This data suggests that the usual therapy is the [more effective] treatment, and [B-LAA] is not a suitable treatment for the eradication of h. pylori.
A large placebo-controlled trial evaluated simvastatin treatment in participants at high risk for cardiovascular disease. The primary outcome was death from any cause. After five years of treatment, there were 1,328 deaths due to any cause in the group of 10,269 participants given simvastatin, compared with 1,507 deaths out of 10,267 participants given a placebo.
These next four questions about odds ratios use data from the simvastatin trial above:
What are the odds of dying from any cause in the group treated with simvastatin?
What are the odds of dying from any cause in the control group?
What are the odds of dying in the simvastatin group compared with the control group?
Q13. Ans = The odds are calculated as the ratio of people in the simvastatin-treated group who had the outcome (death in this case) divided by those who didn’t
= 1328/(10269-1328) = 1328/8941 = 0.148
Q14. Ans = The odds are calculated as the ratio of people in the control group who had the outcome (death in this case) divided by those who didn’t = 1507/(10267-1507) = 1507/8760 = 0.172
Q15. Ans = The odds ratio is calculated as 0.148/0.172 = 0.86
