sample size determination session 6...learning objectives by the end of session, students will be...

Sample Size Determination

Learning Objectives

By the end of session, students will be able to:

Describe the Importance of sample size calculation

Explain basic assumptions in sample size determination

Calculate Sample size for one sample mean and proportion using formula

Calculate sample size for descriptive and analytical studies using Open Epi software (Tutorial)


2

Why do we need to calculate sample

size?

Get information from large populations with:

Reduced costs

Reduced field time

Increased accuracy

Enhanced methods


3

Sample Size for Descriptive Studies

(Estimation Studies)


4

Assumptions-

What's needed for Estimation

Studies

1. Identification of major study variables

2. Decision about confidence level

3. Decision about closeness of expected mean/prevalence to the actual mean/prevalence (Bound on the error )

4. Expectation about possible variation for the data

5. Population size (if known)

Note: Decisions about confidence level and Bound on the error are not statistical but practical


5

Formula for estimation of one

Sample mean

For the estimation of population mean

n = (Zα/2)2 σ2

B2

Where

Zα/2 is the value of Z at the selected level of significance

σ2 is the expected variance of the selected variable (taken from previous literature)

B is the bound of error

n is the minimum sample size required


6

Example

Suppose we want to estimate the average birth weight of children born to non smoking women in community within 0.2 of its actual value with 95% confidence. Assume the standard deviation of birth weight is 0.5 kg. find the required sample size.

n= (1.96)2 (0.50)2

(0.20)2

A sample size of at least 25 is required to estimate the average birth weight of children born to non smoking women in community


7

Formula for estimation of one

sample Proportion

no= (Zα/2)2 (pq)

B2

Where

• p is the anticipated (expected) probability of event happening (taken from previous literature)

• q is the anticipated (expected) probability of event not happening

• B is the bound of error (the minimum absolute difference between actual and anticipated proportion)

If p or the probability of success is unknown then we use p=0.5 or 50%


8

Example

An investigator is interested in estimating the prevalence of respiratory illness among carpenters, using 95% confidence level (Zα/2=1.96)and a half bound on the error of 5%. Previous studies suggest that the prevalence is somewhere between 7% and 20%. Calculate the sample size

n= (Zα/2)2 (pq)

B2

n= (1.96)2 (0.2*0.8)= 0.6144/0.0025= 246

(0.05)2

n= (1.96)2 (0.07*0.93)= 0.249/0.0025= 100

(0.05)2

A sample size of at least 246 is required to estimate the prevalence of

respiratory illness among carpenters


9

Sample Size Relationships

1. n is directly proportional to confidence level e.g.

Zα/2 at 95% confidence is 1.96 and at 99% 95%

confidence is 2.58

2. n is directly proportional to variation i-e Ó or pq

3. n is inversely proportional to Bound on error (Less

the error, greater the sample size)


10

Sample size for Analytical Studies:

HYPOTHESIS TESTING


11

Assumptions-

What's needed for Hypothesis

Testing

Determine whether one sided or two

sided hypothesis

Values of type 1 error (α) and type 2

error (β)

Critical difference D= μ1 – μ2 or p1-p2


12

Type 1 and 2 errors

α: Finding a difference when it does not exist

β: Not finding a difference when it actually exist

13

Power

Power=1- β

Power of 80 percent to detect a difference of a specified size means that if the study were to be conducted repeatedly, a statistically significant result would be obtained four times out of five if the true difference existed


14

Tutorial

Calculating Sample

Size Using Open EPI


15

Practice Question 1

A health awareness campaign was organized to educate people for improvement in uptake of vaccination. After 6 months vaccination surveys were carried out in the intervention Tehsil and a control Tehsil which had similar socio-demographics. It was expected that the intervention will increase the vaccination coverage from 50% to 70% as indicated by literature from previous studies.

a) What sample size will be required for intervention and control area to conduct this study at 95% confidence level and 80% power?

b) What will be the sample size at 90% power?


16

Practice Question 2

A case control study was planned to see the relationship

between high stroke and cholesterol intake. Overall prevalence

of high cholesterol intake in general population has previously

been reported to be 40%. A study conducted in India reported

an odds ratio of 1.5 between stroke and cholesterol intake.

a) What sample size will be required for cases and controls to

conduct this study at 95% confidence level and 80% power?

b) What will be the sample size if reference odds ratio 1.3?

What will be the sample size if reference odds ratio is 1.8?


17

Practice Question 3

An investigator is interested in estimating the prevalence of

respiratory illness among carpenters, using 95% confidence

level and a bound on the error of 5%. Previous studies suggest

that the prevalence is somewhere between 25% and 35%.

Calculate the sample size?

a) What will be the sample size if 90% confidence level is

used?


18

Practice Question 4

A study in Karachi aimed at comparing mean BMI scores of public and private schools. A similar study in Lahore reported mean BMI of 23.5 ± 3.6 in public sectors schools and 26.61 ± 4.1 in private schools.

a) What sample size will be required for public and private schools to conduct this study at 95% confidence level and 80% power?

b) What will be the sample size if mean BMI in private schools was 25.1 ± 4.1?

c) What will be the sample size if SD in public schools was 5.6 and private schools was 5.5?


19

THANKS


20

sample size determination session 6...learning objectives by the end of session, students will be...

Documents