Mendelian randomisation and vitamin D: the importance of model assumptions - Authors' reply

An experiment is a planned activity carried out under controlled conditions. The purpose of an experiment is to investigate the relationship between two variables. When one variable causes change in another, we call the first variable the explanatory or independent variable. The affected variable is called the response or dependent variable. In a randomized experiment, the researcher manipulates values of the explanatory variable and measures the resulting changes in the response variable. The...

Diploid organisms have two alleles of each gene, one from each parent, in their somatic cells. Therefore, each individual contributes two alleles to the gene pool of the population. The gene pool of a population is the sum of every allele of all genes within that population and has some degree of variation. Genetic variation is typically expressed as a relative frequency, which is the percentage of the total population that has a given allele, genotype or phenotype.

Epidemiological study designs are fundamental tools for investigating the distribution, determinants, and control of health conditions in populations. They help researchers understand the relationships between exposures and outcomes, and they broadly fall into two categories: "observational" and "experimental" studies.
Observational studies are those where the researcher does not intervene but rather observes natural variations. They include cross-sectional, cohort, and...

The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
Simple...

The skin plays a crucial role in the synthesis of vitamin D, a vital nutrient for various physiological processes in the body. Vitamin D is unique because it can be synthesized in the skin through a series of chemical reactions triggered by exposure to ultraviolet B (UVB) radiation from sunlight.
The solar UV B rays (290-315 nm) are absorbed by the skin, and 7-dehydrocholesterol (provitamin D3) photolyzes it to previtamin D3, which undergoes a rapid transformation to vitamin...

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...