The impaction difference between image of random variable and clinical practice in clinical trial

Question

In the clinical trial design, we often make assumptions about clinical endpoints. For example, we may assume the blood pressure followed a normal distribution, such as $ X \sim N(\theta, \sigma^2)$, $X \in (-\infty, +\infty)$.

From the perspective of clinical practice, a negative value of blood pressure is impossible or a very large positive value is also impossible. In such opinion, $P(X<a) =0 \ or \ P(X>b)=0$ or a very small probability, when $X \in [a, b]$, we assume the $X$ follows a probability distribution.

According to the statistical files submitted to FDA or EMA, we did not see any adjustments like the above.

My question is :

• 1, why we should not do such adjustments from a clinical practice perspective
• 2, when we use multiple imputation to deal with missing data, an unplausible value was generated in the process, such as a negative blood pressure, what should we do?

Answer 1

The questions you are asking are legitimate: we should do these adjustments; unplausible values in MI might indeed be generated, affecting the quality of the results, mostly the variance.

Most regulatory bodies have a tendency to make their procedures as simple and accessible to the public as possible.

Adding the requirement of specifying assumptions, distributions, etc is desirable but could complicate the administrative procedures. Imagine, for example, legal ramifications.

But gradually, as the overall education level of the public and clinicians improves, these procedures will tend to improve their rigour. It takes time.

The basic assumptions they are making by using normal distribution instead, for example, of lognormal/gamma distribution can be inferred by using the relationship among distributions, for example, see here: https://doi.org/10.1198/000313008X270448 ; http://www.math.wm.edu/~leemis/chart/UDR/UDR.html ; https://en.wikipedia.org/wiki/Relationships_among_probability_distributions .

Hope it helps.