Analyzing longitudinal orthodontic data. Part 1: multilevel linear and curvilinear models

Longitudinal studies are also widely used in other medical and social science fields. For instance, in cardiovascular research, they can monitor patients' health over decades to identify risk factors for heart disease, such as high cholesterol or smoking, and evaluate the long-term effectiveness of preventive measures. Similarly, in mental health studies, researchers might follow individuals from adolescence into adulthood to understand the development and progression of conditions like...

Sometimes we want to see how people change over time, as in studies of human development and lifespan. When we test the same group of individuals repeatedly over an extended period of time, we are conducting longitudinal research. Longitudinal research is a research design in which data-gathering is administered repeatedly over an extended period of time. For example, we may survey a group of individuals about their dietary habits at age 20, retest them a decade later at age 30, and then again...

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...

Survival analysis is a statistical method used to study time-to-event data, where the "event" might represent outcomes like death, disease relapse, system failure, or recovery. A unique feature of survival data is censoring, which occurs when the event of interest has not been observed for some individuals during the study period. This requires specialized techniques to handle incomplete data effectively.
The primary goal of survival analysis is to estimate survival time—the time until a...

Drug disposition in the body is a complex process and can be studied using two major approaches: the model and the model-independent approaches.
The model approach uses mathematical models to describe changes in drug concentration over time. Pharmacokinetic models help characterize drug behavior in patients, predict drug concentration in the body fluids, calculate optimum dosage regimens, and evaluate the risk of toxicity. However, ensuring that the model fits the experimental data accurately...