statistics

Question 1

Define absolute risk reduction (ARR)?

Answer 1

Absolute risk reduction is difference in rate of events between the two groups ARR = risk of event in control group – risk of event in Rx group. If ARR = 0 there is no difference between the two groups (no treatment effect).

Question 2

Define relative risk reduction?

Answer 2

Tells us reduction in the rate of the outcome in the treatment group relative to control group.

Question 3

What is the relationship between absolute and relative risk reduction?

Answer 3

RRR = ARR/risk of outcome in control group OR RRR = 1 – RRExample: Death rate in control group: 15% or 0.15 Death rate in treatment group: 10% or 0.10 RRR = ARR/risk of outcome in control group = 0.05/0.15 = 0.33 or 33% Or RRR = 1 – RR = 1 – 0.67 = 33% or 0.33

Question 4

Do pharmaceutical companies tend to present data as absolute or relative risk reduction?

Answer 4

RRR - why? - because…‘You could take this extra tablet, dipyridamole, twice daily for the next year and you could reduce your risk of having a further event by up 20% compared to not taking it’. (Relative risk reduction 20%).‘You could take this extra tablet, dipyridamole, twice daily for the next year and at the end of the year you are 1% less likely to have had an event’. (Absolute risk reduction 1%)

Question 5

What is a Forest Plot?

Answer 5

Forest plots are used to explain the results of a meta-analysis. Results from each individual trial is presented, and then combined at the bottom.Forest plots are used to explain the results of a meta-analysis. Results from each individual trial is presented, and then combined at the bottom.

Question 6

What are hazard ratios?

Answer 6

Hazard ratios are a form of relative risk (see that section). A hazard ratio of greater than 1 means an event is more likely to happen in the treatment group than in the placebo group.

Question 7

Why are likelihood ratios useful?

Answer 7

They incorporate both sensitivity and specificity.

Question 8

Define mean, median, and interquartile range?

Answer 8

E.g., for the numbers: 65, 68, 72, 75, 78, 83, 108bpmMean: add all the results up and divide by the number of results you had (= 549/7 = 78.4).Median: line up all the numbers in order, and the median is the middle number (in this case the 4th number = 75).Interquartile range: the difference between the 25th quartile and 75th quartile of data (i.e. the middle 50% of data). In this case the 25th quartile is 68 and the 75th quartile is 83, so the interquartile range is 68–83). The interquartile range is important because although it can be similar to the median, it ignores outliers that may skew data (such as the person with the pulse of 108bpm who may well have AF).

Question 9

What are non-inferiority trials and why are they useful?

Answer 9

Most trials are superiority trials: is this new drug better than this other drug or this placebo? However, sometimes non-inferiority trials are run. This is often the case when it would be unethical to offer placebo, for example if someone has H. pylori, ethically you can’t really enrol them in a trial of new drug versus placebo. However, you could offer them a non-inferiority trial, testing out this new drug versus standard H. pylori eradication therapy.

Question 10

What can’t non-inferiority trials do?

Answer 10

Non-inferiority trials will tell you whether your new drug is no worse than the control treatment BUT it can’t tell you if it is any better (although you can run a non-inferiority trial that tests for non-inferiority but is also sufficiently powered to detect superiority!).There are several inherent weaknesses in non-inferiority trials, in particular that the margin for proving effect can be set nice and wide, making almost anything look effective. Also non-inferiority trials assume the standard control therapy is effective (it may not be!). In addition, intention-to-treat analysis (deemed good in superiority trials) may blur the effect for new and old treatments still further.

Question 11

What are numbers needed to treat/harm? Why are they useful? How to calculate?

Answer 11

NNTs tell us how many people have to be treated for 1 person to benefit. An ideal NNT is 1; everyone treated gets better, no one given the placebo group gets better. NNHs are numbers needed to harm. NNT/H should, but don’t always, quote a time frame.An NNT (or H) of 40 over 2 years means that 40 people have to be treated for one to get a benefit (or harm) over a 2-year period.NNTs are easy to calculate: NNT = 1/ARR (absolute risk reduction)If risk of event in treatment group: 4%, and risk of event in placebo group: 1% ARR is 4 – 1=3% NNT=1/ARR = 1/3 (x100) = 33

Question 12

What is an odds ratio?

Answer 12

An odds ratio is a way of expressing probability or relative risk – an odds ratio of greater than 1 means an event is more likely to happen in the treatment group than in the placebo group.

Question 13

What is positive and negative predictive value?

Answer 13

The positive predictive value of a symptom or test is the proportion of the people who test positive who actually have the disease.The negative predictive value of a symptom or test is the proportion of people told they don’t have the disease that really don’t have it.Positive predictive values (PPV) = TP/(TP + FP)Negative predictive value (NPV) = TN/(TN +FN)The higher the PPV of a symptom or test, the more likely the patient sitting in front of you really does have that disease.The higher the NPV of a test, the more likely it is that the patient who has tested negative, really doesn’t have the disease.A PPV of 10% means 10% of people with that symptom will, after investigations, actually have cancer. That means 90% of people with that symptom will not.In the Cancer chapter we discuss how low some PPVs are for classic ‘red flags’ for cancer and what this means in terms of our ability to detect cancers.(ADD TABLE!!)

Question 14

What is pre-test probability?

Answer 14

This is the probability of having the disease before a diagnostic test is done. For example a 56-year-old man who smokes comes to the surgery looking pale and clammy and complaining of a severe chest pain. The pre-test probability of him having an MI is quite high. ECGs and troponins will make this diagnosis more or less likely (change the pre-test probability).The pre-test probability can be calculated from a two by two table (as above) like this:Pre-test probability = (TP + FN) / (TP + FP + FN + TN)OrAll those with the disease divided by all patients with the symptoms (both those with and without the disease).

Question 15

What is rate ratio?

Answer 15

Rate ratio is simply the ratio of the rate of something in one population divided by the rate in another population. It is often used for comparing the incidence of a disease in a group of people exposed to a something compared to an unexposed population. For example, the rate of cancer in a population exposed to a carcinogen may be 10/hundred person years. The rate of cancer in an unexposed population might be 3/100 person years. The rate ratio would be 3.333, suggesting that those exposed to the carcinogen were 3x more likely to get cancer than the unexposed population.

Question 16

What is relative risk?

Answer 16

How many times more likely is it that an event will occur in the treatment group compared to control group? RR is risk in treatment group/risk in control group RR of 1 = no difference RR 1 means treatment increases risk of outcomeExample: Death rate in control group: 15% or 0.15 Death rate in treatment group: 10% or 0.10 RR is Risk in treatment group/risk in control group = 0.10/0.15 = 0.67

Question 17

What is the difference between sensitivity and specificity?

Answer 17

Sensitivity is the proportion of people with a disease who are detected by the test.Specificity is the people who don’t have the disease and don’t test positive (i.e. they test negative). Using the 2 x 2 chart from before:Sensitivity = TP/(TP + FN) E.g. you work out the proportion of cancers detected as a proportion of all the cancers. High sensitivity – good test for cancer.Specificity = TN/(TN + FP) E.g. you work out the proportion of the people who haven’t got cancer and test negative for cancer as a proportion of all those without cancer. High specificity = few false positives.

Question 18

What are the ideal characteristics of a screening test? In this context, what is the sensitivity and the specificity of a screening test?

Answer 18

Ideally, a screening test should identify as many people with the disease as possible. This is the “sensitivity” of the test. It should also give a low number of false alarms, or false positives - this is called the “specificity” of the test.

Question 19

A simple 2x2 table is used when measuring screening test performance-can you describe it?

Answer 19

Disease Present. Disease Absent
Positive
Test result. True positive (a). False positive (b).

Negative
Test result. False negative (c). True negative (d).

Question 20

Using the table on the (potentially) previous card, describing true positives as a, false positives as b, true negatives as c, and false negatives as d, what calculations reveal sensitivity, specificity, positive predictive value, and negative predictive value?

Answer 20

Sensitivity = a / (a+c) (I.e., true positives divided by true positives + false positives).
Specificity = d / (b+d) (I.e., true negatives divided by false positives + true negatives).
Positive predictive value = a/(a+b) (I.e., true positives divided by true positives + false positives).
Negative predictive value = d/(c+d) (I.e., true negatives divided by false negatives + true negatives).

Question 21

What, in words rather than numbers, is the meaning of positive and negative predictive value?

Answer 21

Positive predictive value is the chance that a person who tests positive for a disease has that disease.
Negative predictive value is a measure of how likely the person is not to have the disease if they test negative for it.

Question 22

Screening has benefits , but can also potentially cause harm. So the UKNSC have criteria that they apply to potential and current screening programs to see if they are worthwhile, or will do more harm than good.
Broadly, what are the domains they look at? (4)

Answer 22

1) The condition.
2) The test.
3) The treatment.
4) The screening program itself.

Question 23

When assessing the viability of a screening program, what factors regarding the condition must be true? (3)

Answer 23

1) The condition should be an important health problem.
2) The epidemiology or natural history of the condition should be understood, and there should be a detectable risk factor or early stage.
3) All primary prevention interventions should have been implemented.

Question 24

Regarding a new/existing screening program, what should be true of the test used in the screening program? (2)

Answer 24

1) There should be a simple, safe, validated, and precise screening test which is acceptable to the population.
2) There should be an agreed policy on the further investigation of an individual with a positive test result and on the options available to them.

Question 25

Regarding a new/existing screening program, what should be true of the treatment used in (or after) the screening program? (2)

Answer 25

1) There should be effective treatment for patients identified through the screening program, with evidence that early treatment leads to better outcomes.
2) There should be evidence-based policies covering which individuals should be offered treatment, and the appropriate treatment that should be offered.

Question 26

Regarding a new/existing screening program, what should be true of the screening program itself?(6)

Answer 26

1) There should be evidence from randomised control trials that the screening program is effective in reducing mortality and/or morbidity.
2) The screening program should be clinically, socially, and ethically acceptable to health professionals and to the public.
3) The benefit from the screening program should outweigh the harm.
4) The screening program should be cost effective, and a more cost-effective screening program should not exist.
5) Adequate staffing facilities for testing, diagnosis, treatment, and programme management should be available.
6) Evidence based information, explaining the consequences of testing, investigation, and treatment, should be made available to the potential participants to assist them in making an informed choice.