What is Pre-requisites for calculation of sample size ? and Cross-Sectional Observational Study.

Sample Size for Cross-Sectional Observational Studies in Medical Research: A Complete Guide

What is Pre-requisites for calculation of sample size?

In medical research, it is very important to enroll sufficient number of samples in a study. For a study samples should not be smaller or larger.  Results become invalid if study done on smaller size than required. Un-necessary large sample size should be avoided. So sample size should be calculated using appropriate formula. For calculation of sample size following Pre-requisites is essential. 

Pre-requisites for calculation of sample size: 

1. Study Type: 

 First rquirement for calculation of sample size is study type. Study type me be observational study, Clinical Trial, Case Control Study & Cohort Study etc.

2. Information on Variable: 

Information on outcome variable is reuired i.e. Propotions, Mean & Standard deviation, Propotion of exposed and unexposed cases etc.

3. α error, and Confidence Level : 

α error (Alpha error ): α  is Significance level of a test. It is probability of rejecting a true    null hypothesis known as “Type-I Error”. Commonly accepted level of alpha error is:  0.05 or 0.10   =   5% or 10%. 

         Confidence Level: The probability of correctly accepting Null Hypothesis. 

           Denoted by 1- α or (100 x 1- α)

           When α is decided, Confidence Level is automatically fixed.

4. ß error, and Power of Test: 

 Beta (ß) : The probability of rejecting a true alternate hypothesis. It is also called “Type-II Error”.  Commonly accepted levels of Beta error are: 0.05, 0.1 & 0.2. In terms of % : 5%, 10% & 20%

Power of a Test: The probability correctly accepting an alternate hypothesis.

                  It is denoted by 1- ß . In terms of % it is 100 x (1- ß).

                  When ß is selected, Power of Test is automatically fixed.

5. Z values: 

         z 1- α /2 and  z z 1- α are the functions of the confidence level, 

      While z 1- ß is the function of the power of the test.

        Two sided test: z 1- α /2 = 1.96   (95 % Confidence)

One Sided test: z 1- α    = 1.65   (95 % Confidence)

Two sided test: z 1- α/2  = 1.65   (90 % Confidence)

One sided test: z 1- α    = 1.28   (90 % Confidence)

                                        z 1- ß    = 1.28   (90 % Power )   

                                      z 1- ß    = 0.84   (80 % Power)    

6. Precision: 

Measure of how close are the estimates to the parameter. Expressed in absolute terms or relative points.

How to Find sample size for Cross Sectional Observational Studies in Medical Research.

One of the most popular research designs in public health and medicine is the cross-sectional observational study. They offer a rapid and effective means of determining illness prevalence, evaluating risk factors, characterizing health-related behaviors, and analyzing correlations all at once. However, sample size is one of the most important factors that influences the validity and reliability of such investigations. Inaccurate conclusions, insufficient statistical power, and resource loss might result from a poorly determined sample size.

What Is a Cross-Sectional Observational Study?

A cross-sectional study observes a population or a subset of it at a single point in time. Researchers measure the exposure and outcome simultaneously without any follow-up period. These studies are frequently utilized for:

• Estimating prevalence

• Assessing knowledge, attitudes, and practices (KAP)

• Determining the risk variables

• Surveys conducted in community or hospital environments

Compared to longitudinal investigations, these snapshot-based studies are quicker, less expensive, and simpler to carry out.

1: How to find sample size based on Prevalence/ Incidence of a Disease. 

For calculation of sample size in medical related studies wide number of software are available on internet. Using these open source/ paid softwares we can find sample size for a study based on Type of study (study design) and other Pre-requisites for calculation of sample size.

For Cross sectional Observational study design sample size can be calculated. 

I] Prevalence/ Incidence of a disease.
II] Based on mean and Standard Deviation of parameter. 

I] Based on Prevalence/ Incidence of a disease: 

The sample size is calculated using following Formula 

Source: Lwanga SK, Lameshaw S. Sample size determaination in health studies. WHO, Geneava, 1991.

Where:

         n = sample size.

    

         Z2 =  value for the selected alpha level (1.96 at 95% confidence level)

         d =  desired level of precision.

         p = prevalence or incidence os a disease.

         q = 1-p

Example 1: Suppose in an Observational study, we want to estimate Prevalence of Diabetic Mellitus disease. So how much population to be included in sample?

A. Estimated Prevalence(P) of  Diabetic Mellitus in India is  : 10%

P=0.10, q= 1-p = 1-0.10 = 0.90

B. Confidence: 95%, so z =1.96

C. Absolute Precision: d=  3%

The sample size is calculated using following Formula 

So required sample size for study is 384 samples.

Note: Sample size can be decrease by increasing precision of a study. Precision can consider up to prevalance or incidence. 

2. How to find sample size for Observational Study based on Based on mean and Standard Deviation of variable: 

If variable is measured on Ratio Scale.

II] Based on mean and Standard Deviation of Variable: If variable is measured on Ratio Scale.

The sample size is calculated using following Formula 

Source: Lwanga SK, Lameshaw S. Sample size determaination in health studies. WHO, Geneava, 1991.

Where:

     n= sample size.

     Z= value for the selected alpha level (1.96 at 95% confidence level)

     d= desired level of precision (Should not be more than Standard Deviation)

     S= Standard Deviation of a variable 

  

For Example: If you want to estimate hemoglobin level of under five childrens. So pilot study or published previous study shows that mean hemoglobin level of under five children was 10.0 gm% with Standard deviation of 4.00gm%.

A. Mean hemoglobin level of under five children was 10.0gm% with  Standard deviation of 4.00gm%

S= 4.00gm%.

B. Confidence: 95%, so z =1.96

C. Absolute Precision: d= 0.5  (Should not be more than Standard Deviation)

The sample size is calculated using following Formula 

  So required sample size for study is 246 samples.

Note: Sample size can be decrease by increasing precision of a study. Precision can be consider up to Standard deviation