In most surveys, sampling the entire population is unrealistic due to restrictions on time, cost, and computing power. A subset of the population may be studied instead, and inferences made regarding this sample are used to characterize the entire population. This involves the use of estimators, which are statistics used to estimate a population parameter based on information from a sample. Ideally, an estimator would yield an accurate estimation of the parameter in question. Many popular methods today rely on the Central Limit Theorem, but their performance is often dependent on the size of a sample. This may lead researchers to seek other methods of estimation, especially when studying smaller populations, or when faced with nonresponse in surveys.

Multiple paradigms for parameter estimation have been developed over the past several decades, differing in various aspects. Some of their differences include the importance of the chosen sampling method, the intended source of variation or ‘randomness,’ and whether they intend to predict a fixed or random value. The accuracy and precision of such methods of estimation may set them apart as well, and one may have to decide on which of these attributes to prioritize.

A comparison between design- and model-based methods of estimation was explored, including how each framework was developed, as well as their benefits and drawbacks, is presented.  This comparison was supported by a simulation using data generated based on a coronary heart disease dataset. An estimator was developed based on each of the two frameworks: the design-based estimator was the sample proportion, and the model-based estimator was a weighted average based on a logistic regression model fitted to the data. These are used to estimate the population proportion of patients who have this disease. The sample proportion yielded more accurate results than the weighted average, while the latter was more precise.

This work presents the undergraduate project completed in Fall 2022 for the first author’s 4^th year project, under the supervision of the second author.S