In study there was used two stage cluster sampling technique. First stage, 16 clusters is selected from 100 clusters using PPS. Clusters are heterogeneous in size. In second stage, 12 households are selected from each 16 clusters using random walk technique. From each selected households one children aged 6-59 months are tested for anemia (hemoglobin level <11.0 g/dl= anemic, other wise non-anemic). If I want calculate prevalence of anemia, then I need to adjust sampling weight. Which type of sampling weight I can use?
I'm sorry to say: it is not possible to create proper sampling weights for this design. The calculation of a sampling weight requires calculation of the probability of selection at each stage of the sample: 1) selection of cluster; 2) selection of household; 3) selection of child. However the probability of household selection cannot be calculated with a random walk design, also known as the EPI (Expanded Program on Immunization) method.
The random walk and like-methods are designed to reduce bias from conscious choice in selection, but (DHS III Manual, page 5) "they fail to meet the requirement that the sample be selected in such a way as to give a known and nonzero probability to every potential respondent." For more, see: Luman et al., 2007; Milligan & Bennet (2004); Turner et al. 1996; Multiple Indicator Cluster Survey Manual; 2005. The Demographic and Health Survey; DHS III Sampling Manual, page 5.
The customary analysis with the random walk design is to ignore the weights, However in your case, the probabilities of selecting a child at the final stage will not be equal : If there were $k$ eligible children in a HH, the probability that the respondent child is selected is $1/k$ at that stage. You may therefore choose to give each respondent child a weight of $k$. It the resulting prevalence estimate is not much different from the unweighted estimate, I would use the unweighted version.
Luman, Elizabeth T, Alemayehu Worku, Yemane Berhane, Rebecca Martin, and Lisa Cairns. 2007. Comparison of two survey methodologies to assess vaccination coverage. International journal of epidemiology 36, no. 3: 633-641.
Milligan, Paul, and Steve Bennett. 2004. Comparison of two cluster sampling methods for health surveys in developing countries. International Journal of Epidemiology 33, no. 3: 469-476. http://ije.oxfordjournals.org/content/33/3/469.long
Turner, A., R. Magnani, and M. Shuaib. 1996. A Not Quite as Quick but Much Cleaner Alternative to the Expanded Programme on Immunization (EPI) Cluster Survey Design. International Journal of Epidemiology 25(1).
Division of Policy and Planning United Nations Children's Fund (2005) Monitoring he Situation of Children and Women, Multiple Indicator Cluster Survey Manual 2005 http://www.childinfo.org/files/Multiple_Indicator_Cluster_Survey_Manual_2005.pdf
Demographic and Health Survey III Sampling Manual http://pdf.usaid.gov/pdf_docs/pnabz765.pdf