Sample size finding is one of the cardinal dogmas of medical research. If the sample size is unequal, so the survey will neglect to observe a existent difference between the effects of two clinical attacks. On the contrary, if the sample size is larger than what is needed, the survey will go cumbrous and ethically prohibitory. Apart from this, the survey will go expensive, clip consuming and will hold no added advantages. A survey which needs a big sample size to turn out any important difference in two interventions must guarantee the appropriate sample size. It is better to end such a survey when the needed sample size can non be attained so that the financess and work force can be conserved. When covering with multiple sub-groups in a population the sample size should be increased the equal degree for each sub-group. To guarantee the dependability of concluding comparing of the consequence, the important degree and power must be fixed before the sample size finding. Sample size finding is really of import and ever a hard procedure to manage. It requires the coaction of a specializer who has good scientific cognition in the art and pattern of medical statistics. A few suggestions are made in this paper sing the methods to find an optimal sample size in descriptive and analytical surveies.

## Key Wordss

Sample size, Power analysis, Medical research

## Background

In Medical research, it is of import to find a sample size sufficient plenty to guarantee dependable decisions. If the survey is good designed with a coveted sample size so the criterion mistake will be less and the power and preciseness will be good. All statistical processs become valid in this context. Every research worker must endeavor for the proper sample size and the protocol should incorporate its inside informations.

Inferential statistics has two parts: appraisal of population parametric quantity and testing of hypothesis. Harmonizing to the type of medical research, any one of them can be adopted. The appraisal method is used in prevalence / descriptive surveies and the testing of hypothesis is used for cohort/case control/ clinical tests.

Using appraisal method, the best estimations for population features such as prevalence, incidence, mean, standard divergence, etc. can be found out.

By proving the hypothesis, rightness of whatever values or any relationship or association between variables derived from appraisal can be verified.

These are the two demands for the analysis of informations in medical research. Before the testing of the hypothesis, one must corroborate the type of normalcy of the informations so that the type of the trial ( parametric or non parametric ) could be decided. Misdemeanor of this regulation will ensue in incorrect decision. Once the right trial is selected, the following of import measure is to find the sample size. If proper attending is non given to the finding of the sample size, a existent difference will go statistically undistinguished. Therefore, the survey has to be repeated on a larger sample so that the existent difference can be statistically proved. A indiscriminately decided sample will ask for non trying mistakes in the survey. An under sized sample will non give right information and that will go waste of clip and resource. An over sized sample will stop up with loss of resources with regard to money, adult male power and clip. Finally both mistakes will imply even unethical results.

Therefore, sample size finding is an of import issue in medical research but handiness of literature in this subject is bare. On a recent study a few of them could be located.1-23

Mentioning to the available literature and from the personal experience in this of import subject, the writers would wish to propose a few methods for the finding of relevant sample size in assorted state of affairss in medical research. The writers believe that this brief discourse will be of aid to all forces involved in medical research.

## Sample size finding

Choosing a sample size is to be done by combination of logistical and matter-of-fact considerations which include:

( a ) the figure of topics who can be recruited in the given clip period within available resources, and

( B ) the concluding figure calculated must stand for the minimal figure of topics required to secure a dependable reply to the research inquiry.

## Factors that affect the sample size

## Power of the survey

The power of a survey is the chance of observing a existent difference. In other words, it is same as the chance of doing a positive diagnosing when the disease is present. For a good survey one should hold to take at least 80 % power.

An addition in the sample size or a greater difference between the control and the trial groups lead to an addition in the power of the trial, while an increasing standard divergence of the characteristic and an addition in significance degree lead to a autumn in the power of the survey.

## Degree of significance

Degree of significance is the chance of rejecting void hypothesis when it is true. In another words observing a important difference when it is absent. This is the most of import factor in finding of sample size. Therefore, the degree of significance must be fixed before the testing of hypothesis, appraisal and sample size computation. In a standard state of affairs, the chance can be taken as 0.05 or 0.01. Recently, research workers are utilizing the chance up to 0.2 ( 20 % ) .

3. Event rate

If an event studied occurs more normally among the survey population, of course, the power can be expected to be higher. Even though the expected event rate can be found out from old surveies, there is a possibility that the event rate can be estimated wrongly because of the background, of the referred survey, like differences in topographic point, clip, population etc. If the overall event rate falls to an out of the blue low degree so the sample size must be re-estimated by following the new ( presently observed ) event rate.

## 4. Consequence of conformity

Conformity is another factor that straight affects the sample size. So it should be calculated right. The conformity accommodation expression is as follows:

Adjusted sample size n1 per group peers

Where N is the original sample size, and c1, c2 are the mean conformity rates per group.

In add-on to the above factors, other factors that affect the sample size include consideration for unequal allotment, consequence of of import clinical intervention, etc.

One of the most of import determinations to do before ciphering a sample size is to specify the consequence of of import clinical intervention, i?¤ ( delta ) , which should non be confused with a statistical significance of the intervention consequence – neither one implies the other and the differentiation between them is of import.

## Table 1- Typical values for significance degree and power

## Significance degree

## Power

## 5 %

## 1 %

## 0.1 %

## 80 %

## 85 %

## 90 %

## 95 %

## 1.96

## 2.58

## 3.29

## 0.84

## 1.04

## 1.29

## 1.64

## Descriptive Study

Descriptive surveies are designed to depict happening of disease by clip, topographic point and individual. Descriptive survey is the 1 that deals with appraisal of population parametric quantity. Two normally used parametric quantities are the mean ( step of cardinal inclination ) and the proportion.

## Sample size computation, when mean is the parametric quantity of survey

The assurance interval contains an estimation, above or below a border of mistake. The border of mistake for a 95 % assurance interval is 1.96 times the standard mistake. It shows the truth of the conjecture and is based on the variableness of the estimation.

Let E denote the border of mistake. Then

Similarly for 99 % assurance,

eg. The average pulse rate of a population is believed to be 70 per minute with a standard divergence of 8 beats. Calculate the minimal sample size required to verify this if allowable mistake is 1 round at 1 % hazard.

n = 426

## Sample Size computation, when proportion is the parametric quantity of survey

For 95 % assurance

For 99 % assurance

Where P is the population proportion and Q= 1 – Phosphorus

If E is given as a per centum, so it is to be taken as a per centum of P.

eg. Hookworm prevalence rate was 30 % before the specific intervention and acceptance of other steps. Find out the size of sample required to happen the prevalence rate now if available mistake is 10 % at 5 % hazard.

n = 896

## Calculate sample size for a sensitiveness of a Trial

eg. Sensitivity ( P ) =75 % , Q= 100- P = 100-75 =25 % , Precision ( E ) = 10 % , Formula is

n=72

## Analytical survey

Analytic surveies are designed to analyze etiology and causal associations. Testing of hypothesis is the statistical method in analytical survey. Analytic surveies can be divided into two chief types: viz Observational Studies, Experimental surveies -Clinical tests.

## Experimental Surveies

## Calculating sample size for a case-control survey: binary exposure

Use difference in proportions formula

n = Sample size in the instance group

R =ratio of controls to instances

= A step of variableness ( similar to standard divergence )

= Represents the coveted power ( typically 0.84 for 80 % power ) .

= Represents the coveted degree of statistical significance ( typically 1.96 ) .

= Effect Size ( the difference in proportions )

## =

e.g. For 80 % power, you want to observe an odds ratio ( OR ) of 2.0 or greater, Zb=0.84, for 0.05 significance degree, Za=1.96, r=1 ( equal figure of instances and controls ) , the proportion exposed in the control group is 20 % , to acquire proportion of instances exposed:

=.33

Average proportion exposed = ( .33+.20 ) /2=0.265

Therefore, n=362 ( 181 instances, 181 controls ) .

## Calculating sample size for a case-control survey: uninterrupted exposure

Use difference in agencies formula

n = Sample size in the instance group

R =ratio of controls to instances

= Standard divergence of the result variable

= Represents the coveted power ( typically.84 for 80 % power ) .

= Represents the coveted degree of statistical significance ( typically 1.96 ) .

= Effect Size ( the difference in agencies )

e.g. For 80 % power, Zb=.84, For 0.05 significance degree, Za=1.96, r=1 ( equal figure of instances and controls ) , s=10.0, Difference = 5.0.

Therefore, n=126 ( 63 instances, 63 controls )

## Sample size for independent cohort surveies

This map gives the minimal figure of instance topics required to observe a true comparative hazard or experimental event rate with power and two sided type I error chance alpha. This sample size is besides given as a continuity-corrected value intended for usage with corrected chi-square and Fisher ‘s exact trials.

Information required

Power

alpha

p0: chance of event in controls ( can be estimated as the population prevalence of the event under probe )

p1: chance of event in experimental topics

RR: comparative hazard of events between experimental topics and controls

input either P1 or RR, where RR=P1/P0

m: figure of control topics per experimental topic

Practical issues

Usual values for power are 80 % , 85 % and 90 % ; seek several in order to explore/scope.

5 % is the usual pick for alpha.

p0 can be estimated as the population prevalence of the event under probe.

If possible, take a scope of comparative hazards that you want have the statistical power to observe.

Technical proof

The estimated sample size N is calculated as:

Where,

where ? = alpha, ? = 1 – power, North Carolina is the continuity corrected sample size. n is rounded up to the closest whole number.

## Experimental surveies

## Simplified expression for difference in proportion

= Sample size in each group ( assumes equal sized groups )

= A step of variableness ( similar to standard divergence )

= Represents the coveted power ( typically.84 for 80 % power ) .

= Represents the coveted degree of statistical significance ( typically 1.96 ) .

= Effect Size ( the difference in proportions )

## =

## Simplified expression for difference in agencies

= Sample size in each group ( assumes equal sized groups )

= Standard divergence of the result variable

= Represents the coveted power ( typically.84 for 80 % power ) .

= Represents the coveted degree of statistical significance ( typically 1.96 ) .

= Effect Size ( the difference in agencies )

## If unequal Numberss in each group

Ratio of instances to controls

Use if want ? patients randomized to the placebo arm for every patient randomized to the intervention arm

Take no more than 4-5 controls/case

controls for every instance

## K:1 Sample Size Shortcut

Use equal discrepancy sample size expression: entire sample size additions by a factor of

Entire sample size for two equal groups = 26 ; want 2:1 ratio

26* ( 2+1 ) 2/ ( 4*2 ) = 26*9/8 = 29.25 ? 30

20 in one group and 10 in the other

## Unequal Numberss in Each Group:

## Fixed figure of Cases

Case-Control Survey

Merely so many new devices

Sample size computation says n=13 instances and controls are needed

Merely have 11 instances!

Want the same preciseness

n0 = 11 instances

kn0 = figure of controls

= 13 / 9 = 1.44

kn0 = 1.44*11 ? 16 controls ( and 11 instances ) this will give the same preciseness as 13 controls and 13 instances

## If figure of events are of import

Cohort of exposed and unexposed people

Relative Risk = R

Prevalence in the unexposed population = ?1

n1 = figure of events in unexposed group

= figure of events in exposed group

n1 and n2 are the figure of events in the two groups required to observe a comparative hazard of R with power 1-?

N = figure of topics per group.

## Number of Covariates and figure of Subjects

At least 10 topics for every variable investigated

In logistic arrested development

No general justification

This is stableness, non power

Principle constituent analysis ( PCA ) N?10m+50 or even N ? m2 + 50

## One-sample t-test and Paired t-test

For proving the hypothesis:

H0: m = K vs. H1: m ? K

With a two-tailed trial, the expression is:

= Represents the coveted power ( typically.84 for 80 % power ) .

= Represents the coveted degree of statistical significance ( typically 1.96 ) .

Note: this expression is used even though the trial statistic could be a t-test.

## Lehr ‘s expression

Lehr ‘s expression can be used for finding the sample size for the surveies expected to be verified by mated or odd t-tests or Chi-squared trial.

It is a really simple expression. In a criterion survey where the power is 80 % and a reversible significance degree of 0.05, the needed sample size in each group will be:

If the standardised difference is little, this overestimates the sample size. So we have to get the better of this by utilizing a numerator of 21 ( alternatively of 16 ) relates to a power of 90 % .

Unpaired t-test is to be applied in a research when both or one samples size will be less than 30 so Standardized difference is ? /? and N/2 observation in each group ? the smallest difference in agencies that is clinically of import. The false equal criterion divergence ( ? ) of the observations in each of the two groups. You can gauge it utilizing consequences from a similar survey conducted antecedently or from published information. Alternatively, you could execute a pilot survey to gauge it. Another attack is to show ? as a multiple of the standard divergence ( e.g. the ability to observe a difference of two standard divergences ) .

If the test is to carry on a before and after intervention comparing survey ( e.g. efficaciousness of drug, surgery etc. ) in same topics so you should utilize Paired t-test. In this instance Standardized difference is 2?/? and N braces of observations. ? is the smallest difference in agencies that is clinically of import. ? is the standard divergence of the differences in response, normally estimated from a pilot survey.

To happen out the relationship or association between exposure variable and outcome variable, one should utilize Chi-squared trial ( e.g. Smoking [ exposure variable ] and Cancer [ outcome variable ] ) . In this instance Standardized difference is p1-p2/ ( ( 1- ) and N/2 observation in each group. p1-p2 the smallest difference in the proportions of ‘success ‘ in the two groups that is clinically of import. One of these proportions is frequently known, and the relevant difference evaluated by sing what value the other proportion must take in order to represent a notable alteration.

= ( p1+p2 ) /2.

## Cluster Randomised Trial

Our research support, manpower, clip etc. are less at the same clip disease is concentrated in peculiar country so we will travel for bunch randomised test. We want to happen out the sample size in bunch randomised test. Notations are given below

k- Number of bunchs ( bunchs – small towns, communities, families, schools, category suites etc. )

m – Size of the bunch ( 5 members HH )

– Discrepancy among the bunchs ;

– Within bunch variableness

– Interstate commerce commission ( Intracluster correlativity coefficient )

d – preciseness ; i – intercession groups

( one = 1 intervention and I = 2 control )

To take history of the clustered nature of the informations, the entire overall sample size to observe a given difference, or gauge a measure with a given preciseness, will necessitate to be multiplied by and amount known as the ‘design factor ‘ which is calculated as:

## Design consequence = 1 + ( ( Number per bunch -1 ) x ICC )

where ICC is the intraclass correlativity. This expression assumes a changeless figure per bunch, if this is variable so an norm can be taken.

## Appraisal ( Prevalence Study )

## Continuous result:

s – standard divergence of the result

Where,

Equivalently, the figure of bunchs required is given by

## Binary result:

p – prevalence ( per centum or proportion )

where,

Equivalently, the figure of bunchs required is given by

## Testing of Hypothesis ( RCT )

Comparison of agencies:

Equal bunch size:

The figure of topics required per intercession group to prove the hypothesis H0: M1 = M2 is given by

m1- mean in the intercession group

m2 – mean in the control group

Note: For unequal bunch size, replace m by

or more cautiously mmax.

## Suggestion

If the consequence of a clinical intervention is non marked when compared to a placebo, or power of the survey is low, or a lower significance degree ( lower ‘p ‘ value ) is expected so the sample size should be increased.

If the measurings are extremely changing so utilize the norm of perennial measurings.

Determine the scientifically acceptable power and degree of significance.

Estimate the event rate signifier similar population.

In research protocols, statistically determined sample size, power of the survey, significance degree, event rate, continuance of the survey, and conformity should be mentioned.

The sample size should be increased to adequate degree for each sub-group when covering with multiple sub-groups in a population.

Always aim for a cost effectual sample size.

In little negative tests, meta analysis can be tried.

When a survey requires really big sample size cyberspace working with other research workers engaged in similar undertakings and Multi-centre tests will be good.

A survey which needs a big sample size to turn out any important difference in two interventions must guarantee the needed sample size. Otherwise such surveies may non supply much information by any method and are better terminated so that the money and clip are at least saved.

## Decision

Carefully and good planned Medical researches will stop up in a relevant and socially utile consequence. Planning has several parts, such as good defined relevant research hypothesis, aims, topics must be selected from appropriate population, and instruments should be dependable, carefully undergone through best possible processs ect. Sample size finding is really of import and ever hard procedure to manage. It requires the coaction of a specializer who has a good scientific cognition in the art and pattern of medical statistics.

## Conflict of Interests

The writers do non hold any struggle of involvement originating from the survey.