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...

The actuarial approach, a statistical method originally developed for life insurance risk assessment, is widely used to calculate survival rates in clinical and population studies. This method accounts for participants lost to follow-up or those who die from causes unrelated to the study, ensuring a more accurate representation of survival probabilities.
Consider the example of a high-risk surgical procedure with significant early-stage mortality. A two-year clinical study is conducted,...

When a fluid flows through a pipe, it experiences energy losses due to frictional resistance along the pipe walls, known as major losses. These energy losses result in a pressure drop, which varies based on the flow conditions — whether laminar or turbulent — and the specific physical properties of the fluid and pipe.
Fluid flow can be classified as laminar or turbulent, primarily based on the Reynolds number. This dimensionless number reflects the relative influence of inertial to...

Truncation in survival analysis refers to the exclusion of individuals or events from the dataset based on specific criteria related to the time of the event. This exclusion can happen in two primary forms: left truncation and right truncation.
Left truncation occurs when individuals who experienced the event of interest before a certain time are not included in the study. This is often due to a "delayed entry" into the study where only those who survive until a certain entry point are...

Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...

Survival models analyze the time until one or more events occur, such as death in biological organisms or failure in mechanical systems. These models are widely used across fields like medicine, biology, engineering, and public health to study time-to-event phenomena. To ensure accurate results, survival analysis relies on key assumptions and careful study design.