Estimation and Comparison of Immunization Coverage under Different Sampling Methods for Health Surveys

Immunization currently averts an estimated 2-3 million deaths every year in all age groups. Hepatitis B is a major public health problem worldwide. In this study, the estimates of hepatitis B vaccine coverage are compared among three sampling plans namely, 30 × 30 sampling and 30 × 7 sampling method under cluster sampling and systematic random sampling schemes. The data has been taken from the survey “Comparison of Two Survey Methodologies to Estimate Total Vaccination Coverage” sponsored by Indian Council of Medical Research, New Delhi. It is observed that the estimations of proportions of this vaccination coverage are significantly not different at 5% level of probability. Both 30 × 30 sampling and 30 × 7 sampling will be preferred to systematic sampling in estimation of hepatitis B vaccine coverage for this study population because of quick estimation and lesser cost. The 30 × 7 cluster sampling is the most recommended method for such immunization coverage especially in a developing country.


Introduction
World Health Organization states that trends related to global vaccination coverage (global estimates for 2008) continue to be positive [1].Immunization has been one of the greatest public health successes.As many emerging and reemerging diseases are now the significant contributor to childhood morbidity and mortality, hepatitis B is one of them [2].Hepatitis B is a liver disease caused by the hepatitis B virus [3].It is a disease with high prevalence, severe morbidity, and premature mortality.It is highly infectious and can spread rapidly in the population through asymptomatic carriers [4].About 78% of global pool of hepatitis B virus infection is from the Asian countries, particularly the developing countries of Asia-Pacific region [5].Medical and public health experts strongly support universal vaccination against the hepatitis B virus, but many parents still do not think that their children need to be vaccinated.The hepatitis B virus is 100 times more infectious than the HIV virus [6].The carrier rate of hepatitis B in India is different in the different regions of the country.The overall carrier rate is often quoted as being 4.7% [7].Thus, India is an intermediate to high endemicity country [4].
Since 1982, hepatitis B vaccine has been available to prevent hepatitis B virus infection [8].Hepatitis B vaccine was given within 12 hours of birth, then at 6 weeks and at 14 weeks [9].This is to be noted that the children of Assam in the North-East Region of India have consistently evidenced low rates for routine childhood immunizations.Lack of information among the parents was one of the major causes of dropout of vaccinations [10].
In the late 1980s, the World Health Organization (WHO) developed the Expanded Program on Immunization (EPI) survey methodology also known as a two-stage (30 × 30) cluster sampling (recommended by WHO), which has been widely used ever since to assess vaccination coverage.Immunization status of children was evaluated using WHO-30 cluster methodology [11][12][13][14].In this study, the estimates of hepatitis B (at birth) vaccine coverage are compared by using two-stage cluster and systematic random sampling method.The main objective of the study is to make a comparative study of hepatitis B (at birth) vaccine coverage between (i) two-stage cluster (30 × 30) and systematic random sampling and (ii) two-stage cluster (30 × 7) and systematic random 2 International Journal of Population Research sampling.Also costs of surveys of these three methodologies have been compared.

Methods
The data for this study has been taken from a survey (conducted in 2011) "Comparison of Two Survey Methodologies to Estimate Total Vaccination Coverage" sponsored by Indian Council of Medical Research (ICMR), New Delhi.The data has been collected during the period from January to October, 2011.
2.1.30 × 30 Cluster Sampling Method.In this method, the population needs to be divided into a complete set of nonoverlapping subpopulations, usually defined by geographic or political boundaries.These subpopulations are called clusters.In the first stage, 30 of these clusters are sampled with probability proportionate to the size (PPS) of the population in the cluster.Sampling with probability proportionate to size allows the larger clusters to have a greater chance of being selected.The clusters are sampled without replacement.In the second stage of sampling, 30 subjects are selected within each cluster.Although the sampling unit is the individual subject, the sampling is conducted on the household level.

30 × 7
Cluster Sampling Method.The 30 × 7 cluster sample was developed by WHO in 1978.The goal of this sampling design was to estimate immunization coverage within ±10 percentage points of the true proportion, with 95% confidence.It is also a two-stage cluster sampling where in the first stage 30 clusters are selected and thereafter in the second stage 7 units are selected within each cluster [15].

Systematic Random
Sampling.Systematic sampling is a random method of sampling in which only the first unit is selected with the help of random numbers and the rest get selected automatically according to some predesigned pattern.If the population size  = , where  is the sample size and  is an integer, and a random number less than or equal to  be selected and every th unit thereafter.This procedure is linear systematic sampling.When  ̸ = , then every th unit should be included in a circular manner till the whole list is exhausted; which is known as circular systematic sampling.
The questionnaire has been developed to collect information of household details like type of family, source of drinking water, purification of drinking water, toilet facility in the household, fuel used for cooking, number of household members, number of eligible members (the children of age from 6 months to 5 years), number of earning members in the household, and approximate monthly household income; information of the eligible members regarding record of vaccine and place of vaccination is collected.The vaccination coverage of hepatitis B at birth is considered.
The survey is conducted in Guwahati, the capital city of Assam.To get the idea of geographical location of Guwahati city, the ward map of the city has been collected and a listing of its wards from Guwahati Municipal Corporation (GMC) gives a lot of idea about the proper location of different wards of the city.And the listing of its wards gives the information about the number of assesses per ward.The city is comprised of a total of 60 wards.Out of 60, 30 wards are selected where selections are being made with the help of random number table (Table 1).
With the two-stage (30 × 30) cluster sampling method in the first stage 30 wards are selected and in the second stage 30 units from each ward are selected.For the selection of second stage units, a selected ward is divided into numbers of blocks such that the sizes of blocks are more or less of equal size.Also they are divided in such a way that the sizes of blocks are sufficient to draw the required numbers of sample.Then, one block is selected randomly and from that selected block we have collected the required number of sampling units (here it is 30 numbers of sampling units).Then, to select these 30 units, only the first household is randomly selected in a centrally located area of the block.After the first household is visited, the surveyor moves to the "next" household, which is defined as the one whose front door is closest to the one just visited.Where there are bylane in a particular lane survey procedure is carried out in that place according to the serial household number in that bylane.This process continues until all 30 eligible subjects are found.The subjects are chosen by selecting a household and for more than one eligible subject (children from 6 months to 5 years of age) in a household all are selected.This resembles random permuted block where the position of each unit is equally likely.
After completing the 1st sampling method (i.e., two-stage (30 × 30) cluster sampling) in a ward, 2nd sampling method (systematic random sampling) is carried out in same ward.In this sampling technique, a random number is selected from random number table on the basis of the number of households in a lane where the survey was carried out in case of two-stage (30 × 30) cluster sampling and this became the first sampling unit (household) of the systematic random sampling.After that, each household is selected at an interval of 10 households continuing the process until the 30 sampling units are not completed.Here, the interval of household is taken as 10 so that the interval is neither too small nor too large.If we take the interval too small, then we should get so many repetitions of the samples from two-stage (30 × 30) cluster sampling which results in the same sampling unit in the 2nd sampling method (systematic sampling) and if we take the interval too large, then there should not be any relation between the two methodologies as the larger interval will cover larger area and both of the sampling techniques should take different places.

Statistical Analysis
Here, we estimate hepatitis B (at birth) vaccine coverage, demographic characteristics, and other health outcomes under both sampling methods.Chi-square test has been used to compare the results obtained from the two sampling methodologies.Tests for equality of two population proportions and 95% confidence intervals have been used to compare estimates under the two methodologies for hepatitis B (at birth) vaccine coverage.The -statistic and 95% confidence interval for the difference of proportion are given as follows.The null hypothesis is , there is no significant difference between the proportions of the number of children undergoing hepatitis B (at birth) vaccine of two methodologies) against the alternative The test statistic is given by , where p1 and p2 are proportions of number of children undergoing hepatitis B (at birth) vaccine of cluster and systematic sampling, respectively.If || > 1.96, we reject our null hypothesis.The 95% confidence interval for  1 −  2 is given by (2)  there is a significant difference between two-stage cluster and systematic sampling in case of respondents religion ( = 0.02), source of drinking water ( = 0.01), purification of water ( = 0.00), and toilet facility ( = 0.04).On the other hand, there is no significant differences between twostage cluster and systematic sampling under 30 × 7 sampling scheme.

Result and Discussion
The family related information of the respondents under the two sampling schemes (Table 3) shows that more than 90% are living in nuclear family; that is, people prefer to live in nuclear type of family rather than joint family.Family related information has not shown any significant differences between two-stage cluster and systematic sampling under both (30 × 30 and 30 × 7) sampling schemes except for the age of mother ( = 0.02) and the age of father ( = 0.00) under 30 × 30 sampling scheme.
Immunization related information of the respondents under the two sampling schemes (Table 4) shows that coverage of hepatitis B (at birth) vaccine is 58.4% and 55.8%, respectively, in 30 × 30 sampling scheme under cluster sampling and systematic sampling.On the other hand, it is 55.7% and 52.9% in 30 × 7 sampling scheme under two-stage cluster and systematic sampling, respectively.
From the result, it is clear that people prefer private health sector as nearly about 60% prefer private health sector.
Considering vaccination (hepatitis B at birth) of children by background characteristics of the respondents under the two sampling schemes (Table 5), it is observed that there is no significant difference between genders of children in both sampling schemes regarding their immunization of hepatitis B (at birth) vaccine.As the level of mother's education increases, the percentage of vaccination (hepatitis B at birth) coverage also increases.
Religion-wise, people belonging to others category (Christian, Jain) are 100% vaccinated whereas the remaining people are more or less 50% vaccinated against the vaccine ( = 0.01 under 30 × 30 sampling scheme).There is no such difference of estimates of hepatitis B (at birth) vaccine coverage under the two methodologies considering the category of the study population.It is seen that children belonging to higher income families are more vaccinated (more than 90%) and coverage of hepatitis B (at birth) vaccine in lower income families is very low (4.5-12% only).
Table 6 representing place of vaccination (hepatitis B at birth) of children by background characteristics of the respondents under the 30 × 30 sampling scheme shows that highly educated mothers prefer private health sector.Significant results are only in case of mother's education ( = 0.00), religion ( = 0.01), and monthly household income ( = 0.01) for subdivisional civil hospital under 30 × 30 sampling scheme.Same result is seen in case of income of families as higher income families like to go to private health sector.Considering religion and caste of people, it is seen that more people prefer private health sectors.Compared with Table 7 representing place of vaccination (hepatitis B at birth) of children by background characteristics of the respondents under the 30 × 7 sampling scheme, it shows the same characteristics as Table 6.
Calculating estimates of proportion of number of children undergoing hepatitis B vaccine, it is seen that ward number 11 has the highest coverage (93% in two-stage (30 × 30)   cluster and 83% in systematic sampling).Ward number 2 shows the lowest coverage (17% in 30 × 30 cluster and 13% in systematic sampling).
Values of -statistic with confidence interval under 30 × 30 sampling scheme are given in Table 8.All -values are less than 1.96, except for ward number 37.
Again, estimates of proportion of number of children undergoing hepatitis B vaccine in case of 30 × 7 sampling are given in Table 9.It is seen that the highest coverage is 86% (ward number 11) and the lowest coverage is 0% in ward number 24.Values of -statistic with confidence interval under 30 × 7 sampling scheme show that except ward number 55 all other ||-values are less than 1.96.
Similarly, estimates of proportion of number of children undergoing hepatitis B vaccine (Table 10) in case of 30 × 30 cluster and 30 × 7 cluster sampling show that there is no significant difference between these two methodologies.
Comparison of larger systematic (30 × 30) and smaller systematic (30 × 7) sampling (Table 11) also shows the same result (only ward number 35 has a significant value).

Time and Cost Factor
To determine a better methodology, time and cost also play an important role.A comparison of time and cost factor between two-stage cluster and systematic sampling is given here.In case of 30 × 30 sampling scheme, it is seen that on average 148 households in each ward have been covered under cluster sampling and 459 households have been covered under systematic random sampling (Table 12).As the figure shows that more household has been covered in systematic random sampling so also the time required for collecting the data is also higher and it is near about three times (on the basis of average figure) that the time spent in case of two stage cluster sampling.
As the time required is more, the cost incurred is definitely high in case of systematic sampling.Again, in case of 30 × 7 sampling scheme, the number of households covered (on average) in each ward is 38 (in two-stage cluster sampling) while, in case of systematic random sampling, it is 114 numbers which is three times more than that of the figure of the two-stage cluster sampling.It means that on average the required time is three times more in systematic sampling than in two-stage cluster sampling so cost incurred is higher in systematic sampling.Thus, we can say that, in both sampling schemes, systematic sampling is more time-consuming than the two-stage cluster sampling and hence the cost is higher in systematic random sampling in compared to that of two stage cluster sampling.

Conclusion
It is found that there is no significant difference between the estimates of hepatitis B (at birth) vaccine coverage under the three methodologies in demographic and health practices, family related information, and immunization related information of the respondents of the study population.Mother's education plays an important role in case of vaccination coverage and selecting the place of vaccination.30 × 7 sampling method failed to capture hepatitis B (at birth) vaccine coverage only in ward number 24.It is observed that both sampling schemes provide estimation of proportion of hepatitis B (at birth) vaccine coverage which is significantly not different at 5% level of probability indicating that it is insignificant and we have no evidence to reject the null hypothesis that there is no significant difference between the proportions of number of children undergoing hepatitis B (at birth) vaccine of two methodologies, namely, 30 × 30 cluster and systematic and 30 × 7 cluster and systematic sampling.On average, only 53-58% of children are vaccinated against hepatitis B. Coverage of hepatitis B (at birth) vaccine is moderate in this urban society of North-East India indicating poor child health scenario.It may be concluded that methodology-wise 30 × 7 sampling scheme (two-stage cluster sampling) will be preferred to 30 × 30 and systematic sampling because of quick estimation and lesser cost.But it is also to be noted that 30 × 30 sampling scheme will be more reliable than 30 × 7 sampling scheme as the sample size is larger in case of 30 × 30 sampling scheme than the later one.

Table 1 :
Selected wards with area and total assesses.
Ward number 9 (Kamakhya Railway Station) is rejected as the ward list shows that the ward has only a total of 44 assesses.

Table 2
presenting the demographic and health practices of the respondents shows that under 30 × 30 sampling scheme International Journal of Population Research

Table 2 :
The demographic and health practices of the respondents under the two sampling schemes (figures in %).

Table 3 :
The family related information of the respondents under the two sampling schemes (figures in %).

Table 4 :
Immunization related information of the respondents under the two sampling schemes (figures in %).

Table 5 :
Vaccination (hepatitis B at birth) of children by background characteristics of the respondents under the two sampling schemes (figures in %).

Table 6 :
Place of vaccination (hepatitis B at birth) of children by background characteristics of the respondents under the 30 × 30 sampling scheme (figures in %).

Table 7 :
Place of vaccination (hepatitis B at birth) of children by background characteristics of the respondents under the 30 × 7 sampling scheme (figures in %).

Table 8 :
Estimates of proportion of number of children undergoing hepatitis B (at birth) vaccine and values of -statistic with confidence interval under 30 × 30 sampling scheme.

Table 9 :
Estimates of proportion of number of children undergoing hepatitis B (at birth) vaccine and values of -statistic with confidence interval under 30 × 7 sampling scheme.

Table 11 :
Estimates of proportion of number of children undergoing hepatitis B (at birth) vaccine and values of -statistic with confidence interval for larger and smaller systematic sampling.