Calculations and definitions

Question 1

Prevalence

Answer 1

the proportion (or %) with the disease at a particular point in time

Prevalence = (number with the disease at a particular time)/(total number in population at that time)

Question 2

Risk/Cumulative incidence

Answer 2

the proportion (or %) of new cases of disease occurring in a specified time period

Risk = (number of new cases of disease in period)/(total number disease-free at outset)

Question 3

Incidence rate (incidence)

Answer 3

rate at which new cases are occurring

Incidence (rate) = (number of new cases of disease)/(total number disease free at outset x time interval)

‘per’ whatever 1 unit of time input e.g. 1 year if time interval is 5 years

Question 4

Reference range

Answer 4

e.g. 95% reference range: 95% of data lies within the 95% reference range

Only for a normally distributed population

95% Reference Range = (X ̅-1.96xSD) to (X ̅+1.96xSD)

X ̅ = mean
SD = SD of X ̅
i.e. 95% reference range = mean ± 1.96xSD

Question 5

95% CI

Answer 5

the range of values within which we can be 95% confident the true value lies

Question 6

What do reference range and SD measure?

Answer 6

how much variation there is between the individual observations in the sample

Question 7

What do confidence intervals and SE measure?

Answer 7

how precise an estimate the sample mean is of the true population mean, given the sample size

Question 8

Risk ratio (relative risk) (RR)

Answer 8

the risk of disease in exposed individuals compared to unexposed

RR>1: increased risk
RR<1: reduced risk

Risk ratio = (risk in exposed individuals)/(risk in unexposed individuals) = (d1/n1)/(d0/n0)

D = number with disease
H = healthy
So d + h = n (total number of individuals)

Question 9

Where are risk ratios used?

Answer 9

• RCTs

- cohort studies

Question 10

Risk difference (RD)

Answer 10

this is simply the difference in risk between exposed and non-exposed groups

Risk difference = risk in exposed – risk in unexposed = d1/n1 - d0/n0

Question 11

NNTB or NNTH

Answer 11

• Number needed to treat to benefit (NNTB) – how many patients need to be treated to prevent 1 event or whatever
• Number needed to treat to harm (NNTH) – how many patients need to be treated for 1 complication to occur

the inverse of the RD (1/RD) but using the POSITIVE value of the RD (so if it is a negative just use the positive)

NNTB is rounded up to nearest integer, NNTH is rounded down

Question 12

Odds of disease

Answer 12

probability of an event/disease sort of versus probability of it not occurring (whereas risk is just probability of it occurring)

Odds of disease = (number with disease)/(number without disease)= (number of cases)/(number of controls)= d/h

so compares number with to number WITHOUT rather than to total

Question 13

What are odds ratios used?

Answer 13

case control studies

Question 14

When are the odds of disease approximately the same as the risk of disease?

Answer 14

when a disease is so rare that the number of individuals without disease is approx. equal to the total number of individuals (i.e. h approx same as n)

Question 15

Odds ratio (cross-product ratio)

Answer 15

Odds ratio = (odds of disease in exposed individuals)/(odds of disease in unexposed individuals)= (d1/h1)/(d0/h0 )

Question 16

Sensitivity

Answer 16

probability of a positive test in people with the disease i.e. the proportion of people with disease (true positives) correctly identified

sensitivity = true positives/total positives (with disease)

Question 17

Specificity

Answer 17

probability of a negative test result in people without the disease i.e. the proportion of people without the disease (true negatives) identified as not having it

specificity = true negatives/total negatives (without disease)

Question 18

Positive likelihood ratio

Answer 18

how much more often does a positive test occur in people with disease compared to those without disease

+ve LR = sensitivity/1-specificity

Question 19

Negative likelihood ratio

Answer 19

how much less likely is a negative test result in people with the disease compared to those without the disease

-ve LR = 1 - sensitivity/specificity

Question 20

What does a likelihood ratio close to 1 indicate?

Answer 20

no better than random

Question 21

Incremental cost-effectiveness ratio (ICER)

Answer 21

gives a valuation PER incremental effect of new treatment e.g. £ per QUALY

Incremental cost-effectiveness ratio (ICER) = (difference in cost)/(difference in effect)

Question 22

Positive predictive value

Answer 22

the probability of having disease if you test positive

PPV=(true positive)/(true positive+false positive)

Question 23

Negative predictive value

Answer 23

the probability of being disease free if the test result is negative

NPV=(true negative)/(true negative +false negative)

Question 24

What is a type I error?

Answer 24

false positive - reject the null hypothesis when there is not a genuine effect

Question 25

What is a type II error?

Answer 25

false negative - fail to reject the null hypothesis when there is a genuine effect