Inverse probability weighting with time-varying confounding and nonpositivity

Confounding is a critical issue in epidemiological studies, often leading to misleading conclusions about associations between exposures and outcomes. It occurs when the relationship between the exposure and the outcome is mixed with the effects of other factors that influence the outcome. Given that, addressing confounding is of high importance for drawing accurate inferences in research.
Confounding can be addressed at both the design phase of a study and through analytical methods after data...

Confounding in statistical epidemiology represents a pivotal challenge, referring to the distortion in the perceived relationship between an exposure and an outcome due to the presence of a third variable, known as a confounder. This variable is associated with both the exposure and the outcome but is not a direct link in their causal chain. Its presence can lead to erroneous interpretations of the exposure's effect, either exaggerating or underestimating the true association. This phenomenon...

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...

Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF), which...

Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...