Sample Size

Question 1

Why do we need sample size caluclations in RCTs?

Answer 1

we test the research population on only a sample of the population. a good sample size allows us to make inferences about that population

Question 2

what things restrict the size of the sample?

Answer 2

• ethical reasons - ensures researchers can maintain adequate care for the subjects. too big a sample might limit this.
• cost, collecting data is expensive - limiting sample size reduces costs
• time considerations - time taken to collect data e.g., condcuct interviews, administer tests, recruit n. limiting sample size reduces time required to collect data

Question 3

what makes the perfect sample size

Answer 3

not too small that it cant detect important effects. Not too big that its a waste of tim, money and resources.

Ideal sample size is realistic and worthwhile

Question 4

two main things sample size calculations tell us

Answer 4

1: the forward “patients|need” appproach - how many n you need to get per group

1: the backwards “patients you can get” approach. determins the statistical power or significance that can be achieved with a sample size you can get

Question 5

what are the components of a sample size calculation

Answer 5

> objective of the study or research quesion
study design
type of primary outcome

Question 6

for a sample size calculation we need to know the objective of the study or reserach question, what does this mean?

Answer 6

we need to know if it seeks to determine superiorirty, non inferiority or equivelance

Question 7

for a sample size calculation we need to know the study design, what like?

Answer 7

basically just the way the research design is structured

• parallel or crossover
• cluster trial
• number of arms

Question 8

for a sample size calcualtion we need to know the type of the primary outcome, what kind of things could the primary outcome variable be for: continuous, binary or time-to-event outcomes

Answer 8

> continuous
- means in each group or the difference in means between groups
- anticipated standard deviation

> binary
- anticipated event rate in each group

> time to event
- anticipated survival time in each group
- anticipated survival proportion at a given time point in each group
- recruitment period
- follow up period

Question 9

for a sample size calcualtion we need to know the type of the primary outcome, what kind of things could the primary outcome variable be for: continuous, binary or time-to-event outcomes

Answer 9

> continuous
- means in each group or the difference in means between groups
- anticipated standard deviation

> binary
- anticipated event rate in each group

> time to event
- anticipated survival time in each group
- anticipated survival proportion at a given time point in each group
- recruitment period
- follow up period

Question 10

things to consider in a sample size calculation for a supriority trial

Answer 10

> type 1 error (alpha)
type 2 error (beta)
power
clinically important difference or effect size

other things:
> attrition rate
> multiple comparisons
> multiple primary outcomes
> sample size per treatment group (allocation ratio)

Question 11

what is a type 1 and 2 error

Answer 11

type one error - false positive. could lead to introducing an ineffective treatment - this works! when it doesnt

type 2 error - rejecting a true effect - end up rejecting an effective therapy - this doesnt work! when it does

Question 12

what does the sample size need to do to minimise the occurence of a type 1 or type 2 error

Answer 12

specify a type 1 or 2 error that would be acceptable for the trial - this should be small

type 1 error (Alpha) usually fixed at 0.05 (i.e. 5% chance of making a false positive

type 2 error (beta) - conventionally set at .10 or .20 (10-20% chance of a false negative conclusion). we accept a 10% probability of getting a false negative

Question 13

what does power signify. how do we calcualte power in the study and what is the conventional power that is used

Answer 13

the ablity to detect an effect that is present based on the sampel size calculation

statistical power - 1-beta i.e. 1-0.20 - 0.80 or 80%

conventionally power is chosen at 80% or 90%

Question 14

what is an effect size and what effect size is chosen for clinical trials?

Answer 14

the smallest difference between the two groups that is regarded as important to be able to detect

the minimum value that would change clinical practice (MCID)

Question 15

how do we determine the effect size we want to get?

Answer 15

> look to existing studies that have investigated similar primary outcomes

• results form meta-analyses
• pilot studies
• experts, policy makers, patient opinons

mixture of evidence + common sense

Question 16

what is the critical value (Zstatistic) for different alpha levels: 0.05 and 0.01

Answer 16

two-Tailed Test

α Z

0.20 1.282

0.10 1.645

0.05 1.960

0.010 2.576

Question 17

what is the formula for calculating the sample size for continuous outcome?

Answer 17

𝑛(𝑝𝑒𝑟 𝑔𝑟𝑜𝑢𝑝) =2 × 𝑓 (𝛼, 𝛽) × (𝜎2)
/
(𝜇1 − 𝜇2)

Question 18

in the sample size calculation what is f(a, 𝛽)?

Answer 18

ALPHA: the multiplier for a certain alpha value for a two-sided test (i.e. the critical value/z score) , then the multiplier for a certain beta value and its corresponding power (i.e. the critical value/z score)

𝑓 (𝛼, 𝛽) = (𝑧α/2 + 𝑧β)2

Question 19

what is the z score for the most common power values used?

Answer 19

β=0.80 = 0.84
- beta 0.20, power = 80%
β=0.90 = 1.28
- beta 0.10, power = 90%

Question 20

sampsi 125 140, p(0.7) r(1) sd1(20) sd2(20)

in stata, what is going on here?

Answer 20

sample size calcualtion for a study with treatment group mean 125, placebo group mean 140, with 70% power, a 1:1 allocation , sd for the treatment and sd for placebo groups

gives us the sample size needed in each group

Question 21

smple size formula for binary outcome

Answer 21

𝑛(𝑝𝑒𝑟 𝑔𝑟𝑜𝑢𝑝) =𝑃1 (1 − 𝑃1) + 𝑃2(1 − 𝑃2)
/
(𝑃1 − 𝑃2)2

then times this by

𝑓(𝛼, 𝛽)

where:
p1 Proportion of individuals with event in group 1
p2 Proportion of individuals with event in group 2
𝑓 𝛼, 𝛽 = (𝑧α/2 + 𝑧β)2

Question 22

. sampsi 0.3 0.2, power(0.8) a(0.05) r(1.0)

whats happening here?

Answer 22

sample size calcualteion for binary outcome with set number of porportions in each group

alpha = 0.05, power = 80%
p1 = 0.30 , p2 = 0.20, 0.15, 0.10

Question 23

other considerations for sample size calucaltions: Adjusting for attrition

Answer 23

need to take into account n dropping out

divide calculated sample size (N) by 1-Attrition rate

N’ = N / 1-A

example: with N = 100 and an expected frop out rate of 20%

n’ = 100 / (1-0.2) = 125

Question 24

other considerations for sample size calucaltions: Adjusting for multiple comparisons

Answer 24

adjusting for multiple comparisons is a statistical technique applied when computing multiple statistical tests. controls the risk of generating a false positive (type 1 error)

if the researchers already decided which groups will be compared e.g., group a and B vs a placebo (A vs P and B vs P) then the sample size calculation will handle this additional test.

Its only when additional tests are included after the trial onset then we need to adjust for multiple comparisons. if another comparison is introduced the type 1 error needs to be adjusted to ensure that the false positive rate isnt inflated

Question 25

how can we adjust for multiple comparisons?

Answer 25

use bonferroni correction. This adjusts thte significance level to a/K (k being the number of comparisons)