Stuart Beal, Ph.D
Univ. of California at San Francisco
Population methodology is all about distinguishing between inter-subject and intra-subject random variabilty. Initially, population methodology was applied to the analysis of data where intra-subject random variability can be modeled by a fairly symmetric continuous probability distribution. This is the most common scenario to this day. Of course, with a transformation of the data, such as a log transformation, the requirement that the distribution be fairly symmetric is not very restrictive. (Note, assumptions that the intra-subject or inter- subject random distributions be Gaussian, were never a part of the NONMEM methodology, published descriptions to the contrary notwithstanding).
With clinical outcome data especially, the intra-subject distribution is “odd”, i.e. it is not symmetric continuous. Consider, for example, simple “yes-no” outcome data. The distribution must be discrete; either the datum is “yes” or it is “no”. Other examples of odd data types are: (i) outcomes that take values in a number of discrete categories that may be greater than just 2, i.e. categorical data, (ii) outcomes that are counts of the number of events of a given type in a given volume of time (e.g. numbers of episodes per week), i.e. count data, (iii) outcomes that are the times till certain defined events occur (e.g. remission times), i.e. time-to-event data. Categorical data may be ordered categorical data. That is, the categories may be representable on an ordinal scale. Count data may sometimes be adequately modeled by a continuous distribution when the number of possible values a count can assume is large, perhaps even by a symmetric continuous distribution. Similarly, time-to-event data may also be so modeled. More often, though, a symmetric continuous distribution does not serve adequately.
Often, odd type data are transformed to another odd type, with loss of information. For example: the number of episodes is transformed to being either less than 11 or greater than 10 (count data are transformed into yes-no data). Or: remission times are reexpressed simply as the number of such times. This strategy is usually not needed, but our discussion does not preclude it.
With odd type data, one may still observe repeated measurements on the subjects sampled. E.g. the number of episodes per week, for each of 5 weeks. Population methods may still be used to advantage with such data. Although the intra-subject distribution is odd, the inter-subject distribution on inter-subject random effects is usually assumed at least to be continuous (or richly discrete).
This talk will describe examples of population models for all of the odd types of data listed above. Examples of actual data analyses having used such models, using NONMEM, will be briefly described.
The NONMEM program, especially version V, can be easily used for these types of analyses. At PAGE 96, I described the use of the program for simulating simple yes-no type data. Indeed, with NONMEM, one can simulate any of the types of data one can analyze. However, with this talk, analysis is the focal point, and in this regard, one must pay attention to “goodness of fit”. Goodness of fit for odd type data gives rise to issues that are not confronted with goodness of fit with “standard” data, and with odd type population data there are additional issues. This talk will describe some of these, illustrating some computations and plots which can be easily implemented using NONMEM to help assess goodness of fit.
Reference: PAGE 6 (1997) Abstr 589 [www.page-meeting.org/?abstract=589]
Poster: oral presentation