Fucking Statistics

Question 1

What is the number needed to treat (NNT)?

Answer 1

NNT = 1 / Absolute Risk Reduction

The number needed to treat (NNT) indicates how many patients need to be treated with an intervention to reduce the expected number of outcomes by one

Question 2

What is the absolute risk reduction?

Answer 2

The absolute risk reduction is the difference between the event rate (EER) in the treatment group and the event rate in the control group (CER)

e.g.

If 800 people receive a drug and 40 die: EER = 40/800 = 0.05

If 1200 are in the control group and 120 die: CER 120/1200 = 0.1

ARR therefore = 0.1 - 0.05 = 0.05

(for added bonus the NNT would be 1/0.05 = 20!)

Question 3

What is the relative risk?

Answer 3

Relative risk is defined as the ratio of risk in the experimental group (the experimental event rate, EER) to risk in the control group (control event rate, CER).

Relative Risk = EER / CER

Question 4

What is the negative predictive value?

Answer 4

Negative predictive value = TN / (TN + FN)

Question 5

What are funnel plots used for?

Answer 5

A funnel plot is primarily used to demonstrate the existence of publication bias in meta-analyses. Funnel plots are usually drawn with treatment effects on the horizontal axis and study size on the vertical axis.

Question 6

What does a symmetrical, inverted funnel plot indicate?

Answer 6

A symmetrical, inverted funnel shape indicates that publication bias is unlikely

Conversely, an asymmetrical funnel indicates a relationship between treatment effect and study size. This indicates either publication bias or a systematic difference between smaller and larger studies (‘small study effects’)

Question 7

What is the relative risk reduction?

Answer 7

Relative risk reduction (RRR) or relative risk increase (RRI) is calculated by dividing the absolute risk change by the control event rate

Using the above data, RRI = (EER - CER) / CER

Question 8

What is the difference between equivalence and non-inferiority studies?

Answer 8

equivalence: an equivalence margin is defined (-delta to +delta) on a specified outcome. If the confidence interval of the difference between the two drugs lies within the equivalence margin then the drugs may be assumed to have a similar effect

non-inferiority: similar to equivalence trials, but only the lower confidence interval needs to lie within the equivalence margin (i.e. -delta). Small sample sizes are needed for these trials. Once a drug has been shown to be non-inferior large studies may be performed to show superiority

Essentially you only pay attention to the lower confidence interval limit.

Question 9

What are the parametric and non-parametric tests for correlation?

Answer 9

parametric (normally distributed): Pearson’s coefficient
non-parametric: Spearman’s coefficient

Pearson’s coefficient measures the linear correlation between two sets of data such as BMI and systolic blood pressure in this case. It is a normalised measurement of the covariance so has a value between −1 and 1.

Question 10

What is the Mann-Whitney U test for?

Answer 10

Mann-Whitney U test

compares ordinal, interval, or ratio scales of unpaired data (non parametric)

Question 11

What is the Wilcoxon signed-rank test for?

Answer 11

Wilcoxon signed-rank test
compares two sets of observations on a single sample, e.g. a ‘before’ and ‘after’ test on the same population following an intervention (non parametric)

Question 12

What is the chi-squared test for?

Answer 12

chi-squared test
used to compare proportions or percentages e.g. compares the percentage of patients who improved following two different interventions (non parametric)

Question 13

What is the standard error of the mean?

Answer 13

Standard error of the mean = standard deviation / square root (number of patients)

Question 14

What is the likelihood ratio for a positive test result?

Answer 14

sensitivity / (1 - specificity)

1. Always set up the equation as sensitivity/specificity (alphabetically)
2. Then to decide where you put the ‘1-‘….
   If likelihood ratio for a Positive test - put the 1- with the P = sensitivity/1-specificity
   If likelihood ratio for a Negative test - put the 1- with the N = 1-sensitivity/specificity.

Question 15

What is the likelihood ratio for a negative test result?

Answer 15

(1 - sensitivity) / specificity

1. Always set up the equation as sensitivity/specificity (alphabetically)
2. Then to decide where you put the ‘1-‘….
   If likelihood ratio for a Positive test - put the 1- with the P = sensitivity/1-specificity
   If likelihood ratio for a Negative test - put the 1- with the N = 1-sensitivity/specificity.

Question 16

What is the action of secukinumab?

Answer 16

Interleukin-17A inhibitors include secukinumab. Under specialist use, this is also licensed for the treatment of ankylosing spondylitis

Question 17

What is the p-value?

Answer 17

The p value is the probability of obtaining a result by chance at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.

Question 18

What is a type I error?

Answer 18

Type I: the null hypothesis is rejected when it is true

i.e. Showing a difference between two groups when it doesn’t exist, a false positive.

This is determined against a preset significance level (termed alpha). As the significance level is determined in advance the chance of making a type I error is not affected by sample size. It is however increased if the number of end-points are increased. For example if a study has 20 end-points it is likely one of these will be reached, just by chance.

Question 19

What is a type II error?

Answer 19

type II: the null hypothesis is accepted when it is false -

i.e. Failing to spot a difference when one really exists, a false negative.

The probability of making a type II error is termed beta. It is determined by both sample size and alpha

Question 20

What is the power of a study?

Answer 20

The power of a study is the probability of (correctly) rejecting the null hypothesis when it is false, i.e. the probability of detecting a statistically significant difference

power = 1 - the probability of a type II error
power can be increased by increasing the sample size