Schedule Saturday Workshops The schedule for the Saturday workshops is described in the course overview. Wednesday concludes with a complex pharmacokinetic data set, done as a class, with multiple covariates. If attendees did not bring their own data to analyze, then Wednesday's homework is running examples in their area of interest. Monday full day : Model building with NONMEM, including advanced pharmacodynamic models, variance models, covariate models, simulation, and model diagnostics. The afternoon is devoted to users working with the examples or modeling their own data, with the instructors providing personal guidance.

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These are provided without restriction to promote research and education. Unlicensed copies may not be distributed. They have made enormous contributions to the sciences of clinical pharmacology and drug development. They have also trained many post-doctoral students, and have patiently tutored the world community of scientists studying drug behavior. We also wish to acknowledge the frequently unheralded contributions of Alison Boeckmann.

We acknowledge the many contributions to this document from the participants of previous workshops. With each workshop, comments are solicited and incorporated into the workshop and documentation. We also acknowledge the many helpful suggestions made by Nancy Sambol, PhD, in reviewing this text. Stuart Beal passed away in , at a similar age. Stuart and Lewis will be deeply missed by their many friends, and by the scientific community. Both were also close personal friends of ours.

This workshop is dedicated to the memory of their lifetime dedication to teaching and discovery. A common question is, what is the right test for these data? Most common statistical tests arose to meet specific experimental needs. Thus, investigators associate given study designs with statistical tests appropriate for that study design.

The underlying perspective is that experimental data arose from some underlying process, which is unknowable or known only to God, depending on your religious views. We can, however, develop a reasonably useful mathematical representation model of this underlying process using several building blocks. NONMEM is a tool for building this model, which includes that the ability to test it, to see if it is in some sense optimum.

The basic equations of Newtonian physics, thermodynamics, biology, and pharmacology are examples of structural models. The second building block describes random stuff that happens, resulting in noise in our measurements. Fixed Effects The structural model contains descriptors of a process e. The known, observable properties of individuals that cause the descriptors to vary across the population are called fixed effects.

For example, if we know that clearance is proportional to weight, then we simply express clearance in the model as a scalar times weight. Weight has a fixed effect on clearance. Random Effects The second type of effects are the random effects. These are random in that they can t be predicted in advance. If they could be predicted in advance, then they would become part of the fixed effects, like the influence of weight on clearance in the example above. In general, there are two sources of random variability when dealing with biological data.

The first source of variability is that one individual is different from another individual. This is called interindividual or between-subject variability. It is important to realize that this is not noise or error.

It is simply biology. Look around the room at the other course participants. The interindividual variability is obvious! In medicine, it is as important to understand the variability between individuals as it is to understand the characteristics of a typical individual. This is the difference between the prediction of the model for the individual, and the measured observation. This is also called intraindividual or within-subject variability.

This includes the error in the assay, errors in drug dose, errors in the time of measurement, etc. Getting back to the notion of using NONMEM to build a model to describe your experiment, we really have three building blocks: a structural model, and then two variance models, the intersubject variance model, and the intrasubject variance model.

The two variance models are built using random variables. The term random variables may be a new term for you, but the concept is one you are very familiar with. Let s say you go into a store and stand on 10 different scales. The scales will not give identical answers.

Instead, let s say that the scales read How much do you weigh? You have a true weight, but it is unknowable. All you have are these 10 measurements of the true, but unknowable, number. You would probably guess that these numbers are all clustered around the true number. Most people would say that the average of these numbers was a good approximation of their true weight. The average of these numbers is 70 kg, so you would probably guess that your true weight is What you intuitively have understood is that your measured weight is your true weight plus or minus some error.

Now, after standing on the scale the first time, and reading However, after standing on 10 scales, you know that the true value is about What do you know about the error.

The average error, of course, is zero, because positive errors cancel negative errors. However, the important thing is the range of errors, which are usually quantified as the standard deviation.

Let s say that you and 9 close friends decide to compare weights. What is the average weight of you and your friends? Now, let s say that you and your 10 friends are bored. For example, assume you are all stuck in a workshop at the Hotel Nikko in San Francisco, in a poorly air-conditioned room with a clueless instructor. Desperate for any entertainment, you decide to skip the afternoon lecture, and go to the local scale store. There you find 10 scales. Each of you gets on all 10 scales, and records your weight.

You obtain the following results, except for the second column, which is your true weight and thus unknowable. That is the intraindividual variability. That is the interindividual variability. You and your friends may be bored, and are entertaining yourselves by standing on scales, but you are still geeks, so you decide to construct a formal model of your experiment in the scale store.

The structural model is easy: you are measuring weight, so the only structural parameter is weight. However, you need to account for two sources of variability: the differences in weight between each of your friends, and the errors from each measurement of weight.

What we want to know, of course, is 1 what is the typical weight? Let s turn from our example with weights to a pharmacokinetic example. What are the sources of variability that make the observation different from the expectation?

Let s say I give a subject a drug, and then measure a concentration. There are two reasons for this: 1 The model describes the typical or most representative individual, not anyone in particular. This particular subject s volumes and clearances are. There are two reasons for this: 1 There is always measurement error. In other words, the subject isn t a set of tanks connected by tubes, but is a complex physiological system that is only crudely approximated by a compartmental model.

In other words, the statement above even if the subject happened to be exactly like the typical individual is illogical biology can t be reduced to a few simple equations.

This misspecification in the model is considered part of the error, and gets lumped, together with assay error, as residual error. If this makes you vaguely uncomfortable, it should. Classifying model misspecification as residual error glibly passes over what can be a significant problem, but that s what NONMEM does. To summarize, we have two reasons the concentration measured isn t precisely the concentration predicted: 1 The difference between the subject and the model, interindividual variability, and 2 the difference between the prediction of the subjects true model i.

Let s say that P is a parameter of a pharmacokinetic model. It might be a clearance value, a volume value, or maybe a lag time. Often times we like to think that the residual variability in some parameter is a constant fraction of the average parameter. However, in biological settings, most parameters follow a log normal distribution rather than a normal distribution. A quick reality check is to ask. If they can t and most biological parameters can t go negative then a log normal distribution is probably a good choice.

NONMEM only deals with normally distributed random variables, but log normally distributed random variables can be easily generated from normallydistributed random variables as follows. How do we interpret omega squared in this setting? Omega is approximately the same as the coefficient of variation in the standard domain. The three most common error structures are additive, constant coefficient of variation, and log normal. The constant coefficient of variation model is also called the constant CV model, or the proportional error model.

In this model, errors are normally distributed, but are proportional to the magnitude of the prediction. The additive error model almost always works OK. In situations where the data cover a large range i. As the errors get bigger, however, the distributions diverge. The reason is that the constant coefficient of variation model can go negative, while the log normal model cannot go negative.

Put another way, an error of - will give a value of - with a constant coefficient of variation model, but a value of 0 with a log normal model, since Exp - is 0.

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These are provided without restriction to promote research and education. Unlicensed copies may not be distributed. They have made enormous contributions to the sciences of clinical pharmacology and drug development. They have also trained many post-doctoral students, and have patiently tutored the world community of scientists studying drug behavior. We also wish to acknowledge the frequently unheralded contributions of Alison Boeckmann.

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