Family planning (FP) indicators measure demand for and use of contraceptive methods. Indicators include the proportion of women who use a contraceptive method, broken down into traditional and modern methods. National and subnational estimates of FP indicators are produced by the Family planning estimation model (FPEM), which is a Bayesian model that is fitted to FP data from various sources. The main source of FP data is self-reported use as collected in surveys. Small-scale studies on the accuracy of self-reporting in such surveys suggest that misclassification is present. However, the findings from these studies cannot be generalized to population-periods without such studies. This dissertation focuses on data processing, modeling, and model validation for the use of compositional data that may be subject to misclassification error, as motivated by the data used for estimating FP indicators. In chapter 1, we propose a minimal modeling approach to provide a more accurate assessment of uncertainty for low-prevalence subgroups and groups with less-than-optimum data, along with a corresponding module to the R package for the processing of family planning survey data. In chapter 2, we propose a new data model leveraging normal-Laplace distribution to specify the relationship between the true proportion and observed data to better account for potential misclassification. In chapter 3, we propose a approximation approach for posterior predictive distribution to carry out model validation for Bayesian models that are fitted using the normal-Laplace data model as proposed in chapter 2.