A system of 13 ordinary differential equations with 42 parameters is presented to model hormonal regulation of the menstrual cycle. For an excellent fit to clinical data, the model requires a 36 h time delay for the effect of inhibin on the synthesis of follicle stimulating hormone. Biological and mathematical reasons for this delay are discussed. Bifurcations with respect to changes in three important parameters are examined. One parameter represents the level of estradiol adequate for significant synthesis of luteinizing hormone. Bifurcation diagrams with respect to this parameter reveal an interval of parameter values for which a unique stable periodic solution exists and this solution represents a menstrual cycle during which ovulation occurs. The second parameter measures mass transfer between the first two stages of ovarian development and is indicative of healthy follicular growth. The third parameter is the time delay. Changes in the second parameter and the time delay affect the size of the uniqueness interval defined with respect to the first parameter. Saddle-node, transcritical and degenerate Hopf bifurcations are studied.

Effective visual communication is a core competency for pharmacometricians, statisticians, and, more generally, any quantitative scientist. It is essential in every step of a quantitative workflow, from scoping to execution and communicating results and conclusions. With this competency, we can better understand data and influence decisions toward appropriate actions. Without it, we can fool ourselves and others and pave the way to wrong conclusions and actions. The goal of this tutorial is to convey this competency. We posit three laws of effective visual communication for the quantitative scientist: have a clear purpose, show the data clearly, and make the message obvious. A concise "Cheat Sheet," available on https ://graph icspr incip les.github.io, distills more granular recommendations for everyday practical use. Finally, these laws and recommendations are illustrated in four case studies.

A system of 16 non-linear, delay differential equations with 66 parameters is developed to model hormonal regulation of the menstrual cycle of a woman from age 20 to 51. This mechanistic model predicts changes in follicle numbers and reproductive hormones that naturally occur over that time span. In particular, the model illustrates the decline in the pool of primordial follicles from age 20 to menopause as reported in the biological literature. Also, model simulations exhibit a decrease in antimüllerian hormone (AMH) and inhibin B and an increase in FSH with age corresponding to the experimental data. Model simulations using the administration of exogenous AMH show that the transfer of non-growing primordial follicles to the active state can be slowed enough to provide more follicles for development later in life and to cause a delay in the onset of menopause as measured by the number of primordial follicles remaining in the ovaries. Other effects of AMH agonists and antagonists are investigated in the setting of this model.

Graphics are at the core of exploring and understanding data, communicating results and conclusions, and supporting decision‐making. Increasing our graphical expertise can significantly strengthen our impact as professional statisticians and quantitative scientists. In this article, we present a concerted effort to improve the way we create graphics at Novartis. We provide our vision and guiding principles, before describing seven work packages in more detail. The actions, principles, and experiences laid out in this paper are applicable generally, also beyond drug development, which is our field of work. The purpose of this article is to share our experiences and help foster the use of good graphs in pharmaceutical statistics and beyond. A Graphics Principles “Cheat Sheet” is available online at https://graphicsprinciples.github.io/.

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