Categorical data ordered

The mean uses the most information from the sample, relying as it does on the actual numerical values. It is the most commonly used measure of location and therefore can be misused. For example, we have noted that it is inappropriate to use it for ordered categorical data such as 0 = absent, 1 = mild, 2 = moderate, 3 = severe since in taking an average the implicit assumption is being made that a change from absent to mild is identical to a... 

Categorical data is becoming increasingly common in population PK/PD analysis, especially ordered categorical data. Examples of such data are adverse events and efficacy measurements such as pain scales (16) or sedation scores (17). This section focuses on graphical methods for categorical type data. 

Figures 7.20 and 7.21 display the same information but in different ways. The main beneht of the latter is it compactness. The possibility to see patterns, on the other hand, is hampered by the fact the there are no fixed reference points (except for the categories with the lowest number). This can be remedied by adding lines that connect the cumulative probabilities of each category (Figure 7.22). Apart from making it easier to see trends, this is also informative from the perspective of the model. A logistic model for ordered categorical data is usually defined in terms of the cumulative probabilities (score ), that is, exactly what this graph is visualizing.

U. Wahlby, K. Matolcsi, M. O. Karlsson, and E. N. Jonsson, Evaluation of type I error rates when modeling ordered categorical data in NONMEM. J Pharmacokinet Pharmacodyn 31 61-74 (2004). 

OTHER METHODS FOR ANALYZING ORDERED CATEGORICAL DATA... 

Jonsson (25) showed from a simulation study that the use of the standard mixed effects modeling approach may produce biased parameter estimates when ordered categorical data with a skewed distribution are analyzed using the Laplacian method. Increasing interindividual variability and skewness in the distribution of the data increase the bias associated with the estimation of those parameters. The conse-... 

A. Agresti, Modelling ordered categorical data recent advances and future challenges. Stat Med 18 2191-2207 (1999). 

M. C. KjeUsson, S. Jonsson, and M. O. Karlson, The back-step method for obtaining unbiased population parameter estimates for ordered categorical data. AAPS I 6(3) El-ElO (2004). 

The hybrid model proposed by Zingmark et al. (26) is a straightforward way of incorporating Markov elements in an analysis of ordered categorical data. An inappropriate model—a bad descriptive model or a model with a bad predictive performance (see Ette et al. (34) Chapter 8 of this text)—would result if the correlated nature of the data is ignored and a proportional odds model is used to characterize the concentration-adverse effect relationship. Readers are referred to the article by Zingmark et al. (26) for a detailed description of the hybrid model. They also provide a NONMEM data set and control file for the implementation of the model. 

Koch GG, Tangen CM, Jung JW, Amara lA (1998) Issues for covariance analysis of dichotomous and ordered categorical data from randomized clinical trials and non-parametric strategies for addressing them. Statistics in Medicine 17 1863-1892. 

Cohen A, Sackrowitz HB, Sackrowitz M (2000) Testing whether treatment is better than control with ordered categorical data an evaluation of new methodology. Statistics in Medicine 19 2699-2712. 

Ivanova A, Berger VW (2001) Drawbacks to integer scoring for ordered categorical data. Biometrics 57 567-570. 

Bondesson A, Hellstrom L, Eriksson T, Hoglund P (2009) A structured questionnaire to asses patient compliance and beliefs about medicines taken account of the ordered categorical structure of data. J Eval Clin Pract (in press)... 

The simplest form of qualitative data is binary data in which there are only two possible values, for example, death/survival or success/failure each of which needs to be defined within a specified time interval has pain relief been achieved within two hours of treatment, success - or not, failure. This form of data is extremely common in medical research and yet it ignores the possibility of gradation, success may not be total but only partial and yet not be total failure. These considerations lead naturally to the concept of ordered categorical or ordinal data. 

The name ordinal reflects the fact that the various outcomes form an ordered sequence going from one extreme to its opposite. Such data are sometimes referred to as ordered categorical . In this case the data are usually discontinuous, individual cases being scored as — 1, +2 etc., with no fractional values. 

The structure of this book is based upon the different data types. Chapters 2—14 all deal with the handling of continuous measurement data, with Chapters 15 and 16 focusing on categorical data, and then Chapter 17 covers ordered data. 

Throughout this chapter we use two example data sets. The first is a real data set from a PK study in 73 individuals with an average of ten observations per individual. Each individual was studied on one to seven occasions. The second example is a simulated data set with an ordered categorical response variable and is described in greater detail in Section 7.4.7. 

Population Pharmacokinetic/ Pharmacodynamic Modeiing of Ordered Categorical Longitudinal Data... 

POPULATION PK/PD MODELING OF ORDERED CATEGORICAL LONGITUDINAL DATA... 

In the sections that follow, terminologies and functions used to characterize survival data are first explained, followed by the application of nonlinear mixed effects modeling to the analysis of nonrandomly censored ordered categorical longitudinal data with application to analgesic trials. 

NONLINEAR MIXED EFFECTS MODELING APPROACH TO THE ANALYSIS OF NONRANDOMLY CENSORED ORDERED CATEGORICAL LONGITUDINAL DATA FROM ANALGESIC TRIALS... 

L. B. Sheiner, S. L. Beal, and A. Dunne, Analysis of nonrandomly censored ordered categorical longitudinal data from analgesic trials. J Am Slot Assoc 92 1235-1255 (1997). 

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