Letter to the Editor
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0092-8615/2000 Copyright 0 2000 Drug Information Association Inc.
LETTER TO THE EDITOR GEERTVERBEKE AND STEFFEN FIEUWS Biostatistical Centre, Catholic University of Leuven, Leuven, Belgium
WE RECENTLY READ the paper “A mixed effects model for gastric ulcer data” by Donghui Zhang, published in the Drug I f o r mation Journal (1997 Vol. 31, pp. 12491254). The paper discusses an important class of models for the analysis of continuous longitudinal data, which has many applications in applied sciences, and more specifically, in medical sciences. The author also illustrates the fitting of such models using the SAS procedure MIXED. This might be helpful for the practicing statistician confronted with similar data structures. Unfortunately, we believe that this implementation in SAS suffers from some severe misconceptions and errors. First, we refitted model (3) in the paper, using the program provided by the author on page 1251. Our results are summarized in Table 1 of this letter, and they are clearly different from the results reported by Zhang in Tables 2 and 4. A very similar value for minus twice the log-likelihood is obtained, while different estimates and standard errors are found for the fixed effects PI and pZ. Surprisingly, the estimates as reported in the paper were obtained from fitting the modified model proc mixed data = sample; class subject trt; model y = trt * time / s; random int time / type=un( 1) subject=subject group=trt s; run;
which implicitly assumes common average intercepts for both groups, that is, a,= Q. Minus twice the log-likelihood value for this latter model equals -2h = 265.239. Second, in contrast to what has been stated in the paper, different models are fitted when the option ‘type=un( 1)’ is used in the random statement, rather than the option ‘type=un.’ The first option requires fitting of a linear mixed model with uncorrelated random intercepts and slopes, while the second option allows the intercepts T ~to , be correlated with the slopes yki.We refitted model (3), specifying ‘type=un’ in the random statement. The results are shown in our Table 2, which are different from the results previously obtained using the option ‘type-un(1)’ (see Table l), but also different from the results reported in the paper. Note also that the difference in -2h equals 6.275, which is significant ( p = 0.043) when compared to the chi-squared distribution with two degrees of freedom (two degrees of freedom because we are estimating a supplementary parameter in each group). This even suggests that the model used in the paper was over-simplistic. Third, using the program provided in the paper, the F-test for the interaction frr*rirne is summarized as: Tests of Fixed Effects Source NDF DDFType 111 F P r > F TIME*TRT 2 12 18.04 0.0002
Reprint address: Geert Verbeke. Biostatistical Centre, Catholic University of Leuven. U.Z. St.-Rafael, Kapucijnenvoer 35, B-3000 Leuven, Belgium. E-mail: geert. [email protected].
Clearly, this is not the result reported in Zhang’s paper (Table 3). The hypothesis
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