Local instrumental variables and latent variable models for identifying and bounding treatment effects

An experimental design is a systematic process that allows researchers to evaluate the relationship between dependent and independent variables. There are three widely used types of experimental design - pre-experimental design, true experimental design, and quasi-experimental design. In pre-experimental design, the researcher compares the data before and after some interventions or treatments. The true-experimental design has more than one purposefully created group, a commonly measured...

Biostatistics plays a crucial role in understanding and analyzing data in healthcare and biology. Biostatisticians conduct experiments, gather evidence, and draw meaningful conclusions using statistical methods and techniques. Different variables form the foundation of biostatistical analysis, allowing researchers to understand and interpret data effectively. These variables are classified into different types, each serving a specific purpose in statistical analysis.
Discrete variables are...

Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
The range is a simple measure of variability, indicating the difference between the highest and...

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

Optimizing growth media enhances microbial proliferation and maximizes product yield. Statistical experimental design methodologies provide structured and reproducible approaches, offering progressively higher levels of robustness and efficiency.The One-Factor-at-a-Time (OFAT) MethodThe One-Factor-at-a-Time (OFAT) method involves adjusting a single variable while keeping all others constant. However, it cannot detect interactions between variables, often leading to suboptimal outcomes when...