Statistics - MRCPsych Mentor

Question 1

What does Cohen’s Kappa Coefficient measure

Answer 1

Inter-rater reliability (ranges from 0-1)

Question 2

What is a ratio scale?

Answer 2

A continuous scale with a true 0 and that ratios between values have meaning (i.e 200 is twice as hot as 100 on Kelvin scale of heat)

Interval scales (also numeric) do not have a true 0 - 0 on these is arbitrary. For temperature 0 is when water turns to ice (not the absence of heat), and 30 is not twice as hot as 15

Examples of ratio include kelvin (temperature), weight, height, pulse, concentration, reaction time, survival time

Question 3

What is a cost minimisation analysis?

Answer 3

Assess the difference in costs of an intervention (inputs) assumes the outputs are the sames

Costs can be
- Direct - costs of intervention (travel, childcare, drug costs, costs of social care intervention)
- Indirect - loss of productivity of the patient (loss of time in work, time spent for relatives to care for patient, reduced productivity of patient)
- Intangible - difficult to measure i.e pain or suffering

Question 4

How is an incremental cost-utility analysis conducted?

Answer 4

Cost of A - Cost of B / QALYs gained by A - QALYS gained by B

Cost-utility analyses use generic outcomes therefore allow comparisons of interventions for different conditions
QALY is calculated by number of years left for a patient and attributing a score to each.

Question 5

How is incremental cost-effectiveness analysis calculated?

Answer 5

Cost of A - cost of B / Effects of A - effects of B

Question 6

How is the positive likelihood ratio calculated?

Answer 6

True positive rate / false positive rate
= sensitivity / (1-specificity)

LR+ is the probability of a positive test in person with the disease divided probability of a positive test in a person without the disease

> 1 positive result more likely in person with disease
< 1 positive result less likely in person with disease than person without disease

Question 7

How is a negative likelihood ratio calculated?

Answer 7

False negative rate / True negative rate
= (1 - sensitivity) / specificity

A LR- > 1 means that a negative test is more likely to occur in people with the disease than in people without the disease.

A LR- < 1 means that a negative test is less likely to occur in people with the disease compared to people without the disease.

Question 8

What is the difference between background and foreground questions?

Answer 8

Foreground questions are direct and relate to care - query specialised and distinct knowledge necessary for specific and relevant clinical questions

Background questions - general questions about illnesses, patterns of disease and pathophysiology

Question 9

Outline the difference between cumulative incidence and incidence?

Answer 9

Cumulative incidence rate: number of new cases of disease that develop during follow up / number of disease free individuals at the start of the follow up

Incidence rate: number of new cases of disease that develop during follow up / total number of disease free years (includes non-diseased individuals and disease individuals before they develop disease)

Question 10

When is hazard ratio used?

Answer 10

When risk is not constant to time

Question 11

What is the formula for the standard error of the mean?

Answer 11

SEM = SD / (square root of n)

SEM is a measure for how acurate the sample mean is to the population mean

As sample size gets bigger SEM gets smaller

Question 12

What are the axis on funnel plots measure?

Answer 12

x - risk or odds ratio (some measure of effect)
y - often standard error of mean (may be reversed 0 near the top)

Therefore larger studies often near top - large sample small standard error

Symmetric distribution - no publication error
Asymmetric distribution - publication bias - relationship between study size and effect or study effects

Question 13

Spearman’s rank correlation may be used over Pearson if?

Answer 13

Data is not continuous or if one variable is ordinal (ranked)

Question 14

How is relative risk reduction calculated?

Answer 14

Absolute risk reduction / control event rate
= control event rate - experimental event rate / control event rate

Question 15

What is the formula for sensitivity?

Answer 15

True positives / true positives + false negatives

Question 16

What is case-mix bias?

Answer 16

A form of selection bias where due to the range of disease severity/subtype in the sample this may lead to an association being identified between exposure and outcome (or absence of an association)

Also known as disease spectrum bias

Question 17

What was the Delphi method originally devised for?

Answer 17

The development of questionnaires

Question 18

Bracketing is a method of qualitative analysis used in what type of studies?

Answer 18

Phenomenology

Here the researcher “brackets” any preconcieved notion he or she may have of the participants experience to look objectively at the data in the search of patterns and themes

Question 19

Name some methods of checking validity of data in qualitative studies

Answer 19

Triangulation - comparing data collected two or more different sets/methods

Bracketing

Reflexivity - awareness of the ways the researchers through their assumptions and approaches have impacted on the data that is collected.

Member checking or respondent validation - checking a researchers narrative to that of a participant

Question 20

What is Berkson’s bias?

Answer 20

A form of selection bias that arises when the participants are sampled not from the general population but from a subsample

Question 21

In bayesian statistics what are pre-test probability?

Answer 21

Prevalence (can point or period)

This is then multiplied by post-test probability = post test odds / (1 + post test odds). Post-test probability is the proportion of patients with that particular test result that have the disease

Question 22

Incidence density is another term for….

Answer 22

Incidence rate

Question 23

What type of tests is summarised by the F statistic?

Answer 23

ANOVA

Question 24

What type of scale is pH?

Answer 24

Interval - no true 0 (0 does not mean no acid or no alkaline)

Question 25

What is the formula for the absolute risk reduction?

Answer 25

EER - CER

Question 26

What is the formula for the relative risk reduction?

Answer 26

CER / ARR

Question 27

Superiority or non-inferiority trials

Answer 27

Superiority trials require larger confidence intervals

Equivalence trials - for a specified outcome equivalence is set from -delta to +delta effect size. To show equivalence the confidence interval for the difference between groups on the outcome variable needs to be within the equivalence margin

Non-inferiority trials require small confidence intervals (here only the lower confidence interval needs to lie within the equivalence margin)

Question 28

What are likelihood ratios?

Answer 28

The likelihood of a particular result in someone with disease compared to a well person

Positive likelihood ratio is the likelihood of a positive result in a person with the disease compared the likelihood of a positive result in a person without the disease (true positive / false positive): sensitivity / 1 - specificity

Negative likelihood ratio is the likelihood of a negative result in a person with the disease compared to the likelihood of a negative result in a normal person (false negative / true negative): 1 - sensitivity / specificity

Likelihood ratios are not affected by prevalence (unlike predictive values)

Question 29

What does a positive likelihood ratio of 14 mean

Answer 29

That a positive test is 14 x more likely to occur in a person with disease than without

LR+ < 1 means that a positive result is more likely to occur in those without the disease than with the disease (not helpful!)

Question 30

What does a negative likelihood ratio of 2 mean?

Answer 30

Then a negative result is twice as likely to occur in individuals with the disease than without the disease (not good!)

LR- < 1 means individuals with the disease are less likely to get a negative test result than individuals with the disease (good!)

Question 31

How is pre-test odds calculated?

Answer 31

Pre-test probability / 1 - pre-test probability
n.b the pre-test probability is the prevalence

(The pre-test odds are the odds of having the disease before the test is done)

Question 32

How do you calculate the post-test odds from the pre-test odds?

Answer 32

pre-test odds x LR

(Post-test odds are the odds of having the disease with a specific test result)

Question 33

post-test odds / 1 - post test odds is the formula for?

Answer 33

Post test probability?

Question 34

What is the equation for standard error of the mean?

Answer 34

Standard deviation / Square root of n

Question 35

Outline the differences between population attributable risk, attributable risk and attributable proportion

Answer 35

Population attributable risk - proportion of cases in the population due to the exposure and thus can be eliminated by eliminating the exposure

Attributable risk - difference in risk between exposed and unexposed groups

Attributable proportion - the proportion of cases in exposed group that is due to to the exposure (measure of exposed group and not entire population)

Question 36

How is systematic sampling conducted?

Answer 36

Systematic sampling is conducted by selected every Xth from a list (it is prone to bias due to differing frequencies of events)

Question 37

The probability of correctly rejecting the null hypothesis is known as?

Answer 37

The power of the test

Question 38

What value can relative risk take?

Answer 38

0 - 1

It is a proportion
Calculated from absolute risk in experimental group / absolute risk in control group (absolute risk is the incident rate)
Relative risk cannot be used in case control trials (here odds ratio is used)

Question 39

How is the relative risk reduction calculated?

Answer 39

ARR / CER

It is the proportion which the intervention reduces the event rate

Question 40

How is post-test probability calculated?

Answer 40

Post-test odds / 1 + post-test odds

Question 41

What is a parameter?

Answer 41

A numerical quantity that describes a certain population statistic - within a population the value of a parameter does not change

an estimate of a parameter based on the sample of a population is known as a statistic

Question 42

Describe some tests of normality

Answer 42

Kolmogorov-Smirnov test
Jarque-Bera test
Wilk-Shapiro test
P-plot
Q-plot