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Background: Immunization averts a large number of children in each year. The burden of vaccine preventable diseases remains high in developing countries compared to developed countries. To overcome from this burden different types of immunization programs have been implemented. For better immunization coverage in developing countries, considerable progress is to be made to improve the knowledge and awareness regarding importance of vaccines. In this study a compara-tive study of immunization coverage under two sampling methods has been performed. Methods: In this study variance and design effect of proportion of children vaccinated against different types of vaccines (BCG, OPV, DPT, Hepatitis B, Hib, Measles and MMR) are estimated under two stage (30 × 30) cluster and systematic sampling for comparison of these two survey sampling methods. Also the homogeneity of clusters has been tested by using chi-square test. Results: It is observed that BCG, OPV and DPT vaccination coverage is more than 90% whereas Hepatitis B, Measles, Hib and MMR vaccination coverage is between 50% - 64% only. Here systematic random sampling is more complicated than two stage (30 × 30) cluster sampling. Also the result shows that the clusters are homogeneous with respect to proportion of children vaccinated. Conclusion: There is no significant difference between the two survey methodologies regarding the point estimation of vaccination coverage but estimation of variances of vaccination coverage is less in two stage (30 × 30) cluster sampling than that of the systematic sampling. Also the clusters are homogeneous. Very less improvement has been observed in case of fully vaccination coverage than the previous study. From the study it can be said that two stage (30 × 30) cluster sampling will be preferred to systematic sampling and simple random sampling method.

World Health Organization (WHO) recommends that all children should receive one dose of Bacillis Calmette- Guerin Vaccine (BCG), three doses of diphtheria-tetanus-pertusis vaccine (DPT), three doses of either oral polio vaccine (OPV) or inactivated polio vaccine (IPV), three doses of hepatitis B vaccine, and one dose of a measles virus-containing vaccine (MVCV), either anti-measles alone or in combination with other antigens. It also recommends three doses of vaccine against infection with Haemophilus influenza type b (Hib). To boost immunity at older ages, additional immunizations are recommended for healthcare workers, travelers, high-risk groups and people in areas where the risk of specific vaccine-preventable diseases is high [

In this study estimates of vaccination coverage have been compared using design effect and variance of estimated proportion of children vaccinated against BCG, OPV, DPT, Hepatitis B, Hib, Measles and MMR (measles mumps rubella) vaccines under two stage (30 × 30) cluster sampling and systematic random sampling.

The data that has been used in this study is taken from a survey “Comparison of Two Survey Methodologies to Estimate Total Vaccination Coverage” sponsored by Indian Council of Medical Research (ICMR), New Delhi. It has been collected during the period from January to October, 2011 using following sampling techniques.

Two stage (30 × 30) cluster sampling: In this method the population needs to be divided into a complete set of non-overlapping 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, thirty subjects are selected within each cluster. Although the sampling unit is the individual subject, the sampling is conducted on the household level. Cluster sampling is often a practical approach to surveys because it samples by groups (clusters) of elements rather than by individual elements. It simplifies the task of constructing sampling frames, and it reduces the survey costs [

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 pre-designed pattern. If the population size N = nk, where n is the sample size and k is an integer, and a random number less than or equal to k be selected and every k^{th} unit thereafter. This procedure is linear systematic sampling. When N ≠ nk then every k^{th} unit be included in a circular manner till the whole list is exhausted, it is called circular systematic sampling. Systematic sampling is commonly used as an alternative to simple random sampling (SRS) because of its simplicity. It selects every k^{th} element after a random start (between 1 and k). Its procedural tasks are simple, and the process can easily be checked, whereas it is difficult to verify SRS by examining the results. It is often used in the final stage of multistage sampling when the fieldworker is instructed to select a predetermined proportion of units from the listing of dwellings in a street block. The systematic sampling procedure assigns each element in a population the same probability of being selected [

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 in a selected ward only the first household is randomly selected. 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.

After completing the 1^{st} sampling method (that is two stage (30 × 30) cluster sampling) in a ward, 2^{nd} 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 household 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 household and 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 same sampling unit in the 2^{nd} sampling method (systematic sampling) and if we take the interval too large then there should not be any similarity between the two sampling methodologies as the larger interval will cover larger area and both the sampling techniques would take different places.

Analysis has been carried out in the following two sections.

Here, variance of proportion of vaccination coverage and design effect of the same has been estimated.

Let, P = proportion of children who are vaccinated

Since same number of children has sampled per cluster, estimate of P

where ^{th} cluster

n = the number of clusters

Then approximate estimated variance of

Again the estimated variance of

An approximate 95% confidence interval on P can be obtained by using

The design effect may be estimated as

where

is the estimated variance under simple random sampling [

Also the design effect for cluster sampling vs systematic sampling is obtained as

In this section homogeneity of clusters have been tested by using chi-square test. That is to test equality of proportion of children vaccinated in each clusters. The test procedure is carried out taking Hepatitis B (at birth) vaccine (two stage (30 × 30) cluster sampling).

The null hypothesis is that there are no significant differences among the proportions of children vaccinated against Hepatitis B (at birth) in each clusters.

H_{0}:

Against the alternative that all the proportions are not equal.

H_{1}: Not all P_{j}’s are equal (where

The test statistic is

where

f_{o} = observed frequency in a particular cell of a 2 × 30 contingency table

f_{e} = expected frequency in a particular cell if the null hypothesis is true

If the null hypothesis is true the proportions are all equal across the population. And rejecting the null hypothesis only allows to reach the conclusion that all proportions are not equal. But the test statistics does not give any information about proportions that differ. To identify the differences between proportions we will rely on a multiple comparison procedure. The Marascuilo procedure [

where α = level of significance, k = number of clusters

To compare each of test statistics with the corresponding critical value a specific pair is significantly different if the absolute difference in the sample proportion

Estimated variance of proportion of vaccination coverage is given in

Vaccine | Two stage cluster (30 × 30) | Systematic sampling | |||
---|---|---|---|---|---|

Coverage estimate | 95% CI | Coverage estimate | 95% CI | ||

BCG | 0.99 | (0.98, 0.99) | 0.99 | (0.98, 0.99) | |

OPV | OPV1 | 0.99 | (0.98, 0.99) | 0.99 | (0.98,0.99) |

OPV2 | 0.98 | (0.97, 0.98) | 0.99 | (0.98,0.99) | |

OPV3 | 0.98 | (0.97, 0.98) | 0.99 | (0.98,0.99) | |

OPV4 | 0.97 | (0.96, 0.97) | 0.99 | (0.98,0.99) | |

OPV5 | 0.90 | (0.89, 0.90) | 0.89 | (0.86,0.91) | |

OPV6 | 0.54 | (0.53, 0.54) | 0.54 | (0.50,0.57) | |

DPT | DPT1 | 0.98 | (0.97, 0.98) | 0.99 | (0.98,0.99) |

DPT2 | 0.98 | (0.97, 0.98) | 0.99 | (0.98,0.99) | |

DPT3 | 0.97 | (0.96, 0.97) | 0.98 | (0.98,0.99) | |

DPT4 | 0.90 | (0.89, 0.90) | 0.90 | (0.88,0.91) | |

DPT5 | 0.52 | (0.51, 0.52) | 0.51 | (0.47,0.54) | |

Hepatitis B | HepB1 | 0.58 | (0.57, 0.58) | 0.56 | (0.52,0.59) |

HepB2 | 0.59 | (0.58, 0.59) | 0.56 | (0.52,0.59) | |

Hib | Hib1 | 0.57 | (0.56, 0.57) | 0.55 | (0.51,0.58) |

Hib2 | 0.57 | (0.56, 0.57) | 0.55 | (0.51,0.58) | |

Hib3 | 0.57 | (0.50, 0.64) | 0.55 | (0.51,0.58) | |

Measles | 0.64 | (0.63, 0.64) | 0.64 | (0.60, 0.67) | |

MMR | 0.52 | (0.51, 0.52) | 0.50 | (0.46, 0.53) |

Vaccines | Methodology | ||
---|---|---|---|

Two stage cluster (30 × 30) | Systematic sampling | ||

BCG | 9.2009 × 10^{−09} | 2.44173 × 10^{−06} | |

OPV | OPV1 | 1.1947 × 10^{−08} | 4.87257 × 10^{−06} |

OPV2 | 3.2958 × 10^{−08} | 9.70164 × 10^{−06} | |

OPV3 | 3.2134 × 10^{−08} | 1.32949 × 10^{−05} | |

OPV4 | 1.2785 × 10^{−07} | 1.56768 × 10^{−05} | |

OPV5 | 5.4684 × 10^{−06} | 2.29435 × 10^{−04} | |

OPV6 | 6.0007 × 10^{−07} | 1.06516 × 10^{−04} | |

OPV7 | 9.5874 × 10^{−07} | 2.73425 × 10^{−04} | |

DPT | DPT1 | 3.2958 × 10^{−08} | 9.70164 × 10^{−06} |

DPT2 | 6.4818 × 10^{−08} | 1.20999 × 10^{−05} | |

DPT3 | 9.4344 × 10^{−08} | 1.32949 × 10^{−05} | |

DPT4 | 6.4134 × 10^{−07} | 1.03118 × 10^{−04} | |

DPT5 | 9.8328 × 10^{−07} | 2.75069 × 10^{−04} | |

Hepatitis B | HepB1 | 1.1741 × 10^{−06} | 2.7177 × 10^{−04} |

HepB2 | 1.1741 × 10^{−06} | 2.71907 × 10^{−04} | |

Hib | Hib1 | 1.2841 × 10^{−06} | 2.72553 × 10^{−04} |

Hib2 | 1.2814 × 10^{−06} | 2.72303 × 10^{−04} | |

Hib3 | 1.305 × 10^{−06} | 2.72429 × 10^{−04} | |

Measles | 1.6381 × 10^{−06} | 2.53068 × 10^{−04} | |

MMR | 1.702 × 10^{−06} | 2.75305 × 10^{−04} |

To study the homogeneity of clusters chi-square test has been performed. Here calculated value of

Vaccine | Design effect | |||
---|---|---|---|---|

Cluster vs SRS | Systematic vs SRS | Cluster vs systematic | ||

BCG | 0.000835516 | 0.221728395 | 0.003768 | |

OPV | OPV1 | 0.001084923 | 0.442469136 | 0.002452 |

OPV2 | 0.001511716 | 0.880987654 | 0.003397 | |

OPV3 | 0.0014739 | 1.207284 | 0.002417 | |

OPV4 | 0.003949769 | 1.423580247 | 0.008155 | |

OPV5 | 0.022256 | 0.933037 | 0.023834 | |

OPV6 | 0.005094 | 0.831239 | 0.005634 | |

OPV7 | 0.001308 | 0.411678 | 0.003506 | |

DPT | DPT1 | 0.001511716 | 0.880987654 | 0.003397 |

DPT2 | 0.002973041 | 1.098765432 | 0.005357 | |

DPT3 | 0.002914598 | 1.207283951 | 0.007096 | |

DPT4 | 0.0054443 | 0.87535464 | 0.00622 | |

DPT5 | 0.00133547 | 0.41166791 | 0.003575 | |

Hepatitis B | HepB1 | 0.004333 | 0.991563 | 0.00432 |

HepB2 | 0.004364 | 0.992063 | 0.004318 | |

Hib | Hib1 | 0.004710096 | 0.99 | 0.004712 |

Hib2 | 0.0047 | 0.989091 | 0.004706 | |

Hib3 | 0.0047867 | 0.9895506 | 0.00479 | |

Measles | 0.0059581 | 0.9380207 | 0.006473 | |

MMR | 0.0052098 | 0.8413334 | 0.006182 |

Sl. No. | Ward No. | Estimated proportions | |
---|---|---|---|

1 | 2 | 0.17 | |

2 | 4 | 0.70 | |

3 | 5 | 0.23 | |

4 | 11 | 0.93 | |

5 | 12 | 0.53 | |

6 | 15 | 0.60 | |

7 | 17 | 0.47 | |

8 | 18 | 0.70 | |

9 | 24 | 0.17 |

10 | 25 | 0.67 | |
---|---|---|---|

11 | 26 | 0.63 | |

12 | 33 | 0.73 | |

13 | 35 | 0.40 | |

14 | 36 | 0.63 | |

15 | 37 | 0.63 | |

16 | 38 | 0.43 | |

17 | 40 | 0.53 | |

18 | 42 | 0.73 | |

19 | 43 | 0.67 | |

20 | 46 | 0.53 | |

21 | 47 | 0.57 | |

22 | 48 | 0.60 | |

23 | 50 | 0.80 | |

24 | 51 | 0.63 | |

25 | 53 | 0.67 | |

26 | 54 | 0.63 | |

27 | 55 | 0.37 | |

28 | 57 | 0.70 | |

29 | 59 | 0.57 | |

30 | 60 | 0.83 |

It is seen that Hepatitis B (at birth) vaccine coverage is higher for ward number 11 (p_{4} = 0.93) than all other wards. After that

Results are significant only for proportion of Hepatitis B (at birth) vaccine coverage for ward number 1 vs ward number 4 (

Estimates of variances and design effect have been used by Milligan et al. [