statistics

Question 1

How do you calculate incidence percentage? How do you calculate incidence per N

Answer 1

Usually reported over a time period
– E.g. 1% per year or 1 in 100 per year
– 2 per 100,000 per year = 0.002% per year
* (new cases / population)*100 = %age
* (new cases / population) *n = rate per n
– E.g. (new cases / population) *100,000 = rate
per 100,000

Question 2

Prevalence
-What is this
-How do you calculate prevalence at one point in time
-How do you calculate prevalence over an interval of time

Answer 2

Proportion of population with a disease:
– at a point in time (point prevalence)
– over an interval of time (period prevalence)
* Calculation of point prevalence
– (all cases/population)100 = %age
* Calculation of period prevalence
– (all cases during a give time / population over
that period)100 = %age

Relationship

prevalence = incidence * duration of condition
in chronic diseases the prevalence is much greater than the incidence
in acute diseases the prevalence and incidence are similar. For conditions such as the common cold the incidence may be greater than the prevalence

Question 3

P values
-What does a P value of 0.1 mean?
-What does a p value of 0.01 mean?

Answer 3

• P = 0.1 = 1 in 10 probability due to chance
• P = 0.01 = 1 in 100 due to chance
  – “highly statistically significant”
• P = 0.05 = 1 in 20 due to chance
  – often arbitrarily set as statistically significant
• P = 0.001 = 1 in 1000 due to chance
  – “very highly statistically significant”
• P value does not tell us ANYTHING about
  CLINICAL significance

Question 4

What is null hypothesis? when is this rejected? when is this accepted?

Answer 4

Null Hypothesis – H0
* Null hypothesis – that there is no
difference between groups
* If p value statistically significant, we
REJECT the null hypothesis and accept
the finding as genuine
* If p value is NOT statistically significant,
we ACCEPT the null hypothesis

Question 5

What is type 1 error vs type 2 error

Answer 5

Type 1 error is a false positive
– Positive result actually due to chance
– False rejection of null hypothesis
* Type 2 error is a false negative
– Negative result actually due to error
– False acceptance of null hypothesis

Question 6

What is a confidence interval?

Answer 6

Give us an idea where the TRUE
population value lies rather than the
observed value
* Expressed as a range
* Usually interested in 95% CI
* This means that there is a 95% chance the
TRUE value falls within this range
* As sample size increases, 95% CI range
decreases

Question 7

What are properties of normal distribution?

Answer 7

Properties of the Normal distribution

symmetrical i.e. Mean = mode = median
68.3% of values lie within 1 SD of the mean
95.4% of values lie within 2 SD of the mean
99.7% of values lie within 3 SD of the mean
this is often reversed, so that within 1.96 SD of the mean lie 95% of the sample values
the range of the mean - (1.96 *SD) to the mean + (1.96 * SD) is called the 95% confidence interval, i.e. If a repeat sample of 100 observations are taken from the same group 95 of them would be expected to lie in that range

Standard deviation

the standard deviation (SD) is a measure of how much dispersion exists from the mean
SD = square root (variance)

Question 8

How do you calculate sensitivity?

Answer 8

Sensitivity
TP / (TP + FN ) Proportion of patients with the condition who have a positive test result

Question 9

How do you calculate specificity?

Answer 9

Specificity
TN / (TN + FP) Proportion of patients without the condition who have a negative test result

Question 10

what is a positive predictive value?

Answer 10

Positive predictive value
TP / (TP + FP)
The chance that the patient has the condition if the diagnostic test is positive

Question 11

What is a negative predictive value?

Answer 11

Negative predictive value
TN / (TN + FN)
The chance that the patient does not have the condition if the diagnostic test is negative

Question 12

How do you calculate likelihood ratio for positive test result?

Answer 12

Likelihood ratio for a positive test result sensitivity / (1 - specificity)
How much the odds of the disease increase when a test is positive

Question 13

How do you calculate Likelihood ratio for a negative test result?

Answer 13

Likelihood ratio for a negative test result (1 - sensitivity) / specificity How much the odds of the disease decrease when a test is negative

Question 14

Describe the 4 phases of a study

Answer 14

Phase 1

small studies (e.g. 100) on healthy volunteers
used to assess pharmacodynamics and pharmacokinetics

Phase 2

small studies (e.g. 100-300) on actual patients
examines efficacy, adverse effects

Phase 3

larger studies (e.g. 500-5,000 patients)
examines efficacy, adverse effects
may compare drug with existing treatments
studies of special groups e.g. renal, elderly

If drug shown to be safe and effective then drugs may be approved for marketing

Phase 4

post-marketing surveillance

Question 15

What is the hawthorne effect?

Answer 15

Hawthorne effect - describes a group changing it’s behaviour due to the knowledge that it is being studied

Question 16

What is selection bias?

Answer 16

Error in assigning individuals to groups leading to differences which may influence the outcome. Subtypes include sampling bias where the subjects are not representative of the population. This may be due to volunteer bias. An example of volunteer bias would be a study looking at the prevalence of Chlamydia in the student population. Students who are at risk of Chlamydia may be more, or less, likely to participate in the study. A similar concept is non-responder bias. If a survey on dietary habits was sent out in the post to random households it is likely that the people who didn’t respond would have poorer diets than those who did.

Other examples include

loss to follow up bias
prevalence/incidence bias (Neyman bias): when a study is investigating a condition that is characterised by early fatalities or silent cases. It results from missed cases being omitted from calculations
admission bias (Berkson's bias): cases and controls in a hospital case control study are systematically different from one another because the combination of exposure to risk and occurrence of disease increases the likelihood of being admitted to the hospital
healthy worker effect

Question 17

What is recall bias?

Answer 17

Difference in the accuracy of the recollections retrieved by study participants, possibly due to whether they have disorder or not. E.g. a patient with lung cancer may search their memories more thoroughly for a history of asbestos exposure than someone in the control group. A particular problem in case-control studies.

Question 18

What is publication bias?

Answer 18

Failure to publish results from valid studies, often as they showed a negative or uninteresting result. Important in meta-analyses where studies showing negative results may be excluded.

Question 19

What is work-up / verification bias?

Answer 19

In studies which compare new diagnostic tests with gold standard tests, work-up bias can be an issue. Sometimes clinicians may be reluctant to order the gold standard test unless the new test is positive, as the gold standard test may be invasive (e.g. tissue biopsy). This approach can seriously distort the results of a study, and alter values such as specificity and sensitivity. Sometimes work-up bias cannot be avoided, in these cases it must be adjusted for by the researchers.

Question 20

What is expectation bias? pygmalion bias?

Answer 20

Only a problem in non-blinded trials. Observers may subconsciously measure or report data in a way that favours the expected study outcome.

Question 21

What is late look bias?

Answer 21

Gathering information at an inappropriate time e.g. studying a fatal disease many years later when some of the patients may have died already

Question 22

What is procedure bias?

Answer 22

Occurs when subjects in different groups receive different treatment

Question 23

Lead-time bias

Answer 23

Occurs when two tests for a disease are compared, the new test diagnoses the disease earlier, but there is no effect on the outcome of the disease

Question 24

How do you calculate standard error of the mean? how do you calculate upper limit and lower limit of a 95% confidence interval?

Answer 24

The standard error of the mean (SEM) is a measure of the spread expected for the mean of the observations - i.e. how ‘accurate’ the calculated sample mean is from the true population mean

Key point

SEM = SD / square root (n)
where SD = standard deviation and n = sample size
therefore the SEM gets smaller as the sample size (n) increases

A 95% confidence interval:

lower limit = mean - (1.96 * SEM)
upper limit = mean + (1.96 * SEM)

Question 25

What is the power of a study?

Answer 25

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

Question 26

what may limit use of a randomised control trial?

Answer 26

practical or ethical problems

Question 27

what is the usual outcome of a cohort study?

Answer 27

relative risk

Question 28

what is the usual outcome of a case-control study?

Answer 28

odds ratio

Question 29

Cross-sectional surveys - AKA, what does this provide?

Answer 29

Provide a ‘snapshot’, sometimes called prevalence studies

Provide weak evidence of cause and effect