Design and analysis of a dynamic IGG seropositivity study for Covid-19 using MIP bayesian inference

Abstract

This thesis will solve the problem that arises when trying to analyze the presence of a binary variable in a population given different factors and solving a MIP that sought to achieve the biggest representative sample possible. In this particular case, the problem presented was understanding the presence of antibodies for SARS-CoV-2 in the population of Chile, taking into consideration different biological and non-biological parameters. The implementation of the models involved testing for IgG; having a positive result that would indicate the presence of antibodies in the subject, helping in both lowering the probability of contracting SARS-CoV-2 as well as lessening the severity of it if contracted. The first model we present seeks to achieve the maximum representative sample of the population for urban centers in Chile, using census zones as a geographical parameter to measure geographical representativeness, as well as other factors such as age and comorbidities. Results from the first model show that it was possible to obtain a much larger representative sample. As an example, Gran Santiago showed a theoretical usage of 84% of the results (12957 out of 15404 samples) as of July 13th, an important improvement considering the prior time frame had a usable data of 15% (1182 out of 7902) Future implementations of a model of this kind should seek as much flexibility as possible in the reallocation of sites to collect samples, as this factor proved to be the biggest limitation at closing the gap between the implementation and the theoretical model, hence improving it would greatly increase the possibility to adapt to the collected data and get a larger representative sample. The second model presented in the thesis seeks to analyze the sample collected, in order to estimate the probability to detect the presence of IgG assuming a perfect test. It used biological variables such as age and comorbidity, as well as non-biological variables such as method of transportation and frequency of transportation. It combines these factors as a logistic regression to estimate the probability described. Using a bayesian approach and Marcov Chain Monte Carlo algorithm to fit the model. Our results show a notable difference in the expected presence of IgG between vaccinated and not vaccinated individuals, as well as a considerable difference between vaccines, where BNT162b12 shows higher seroprevalence. Future implementations of a model of this kind should seek to optimize both the code and hardware used, aiming to refine results and lower the algorithm's time complexity.