This dissertation addresses complex biostatistical challenges through the application of nature-inspired metaheuristics. As the name suggests these algorithms are often motivated by animals' behavior and natural processes. A salient feature of nature-inspired metaheuristic algorithm is that they provide flexible and robust strategies for solving tackling all types of optimization problems and can solve optimization problems that traditional methods cannot. Interestingly, they rarely come with rigorous proofs of convergence to the global optimum, but they frequently do so or get close to the optimum in practice. Codes for these algorithms are widely available in different format and platforms, and they are easy to implement and use. Consequently, nature-inspired metaheuristic algorithms are popular and are increasingly used across disciplines. There are many such algorithms, and to fix ideas, we focus on two such algorithms, Particle Swarm Optimization (PSO) and Competitive Swarm Optimizer with Mutated Agents (CSO-MA), and demonstrate their utility and effectiveness for tackling several types of biostatistical applications.

The primary contribution of this research is the development and applications of these algorithms to solve a range of biostatistical problems. They include solving challenging optimization problems to improve accuracy in statistical inference for single-cell RNA sequencing data analysis (Chapter 2), parametric and non-parametric statistical estimation (Chapter 3), and finding more efficient and realistic experimental designs in toxicology (Chapter 5 and Chapter 6). In addition, the dissertation introduces an innovative semi-parametric Bayesian model (DPMIV) for interval-censored and doubly-censored data (Chapter 4).

The applications and results showcased in the dissertation not only highlight the adaptability of metaheuristics to tackle a diverse set of biostatistical problems but also open up new avenues for future research in statistical methodology and its applications in biomedicine.