 |
 |
|
Home |
Current Issue |
Past Issues |
In the Clinic |
ACP Journal Club |
CME |
Collections |
Audio/Video |
Mobile |
Subscribe |
Tools |
Help |
ACP Online
|
Rapid Responses to:
|
|
Electronic letters published:
![[Read Rapid Response]](/icons/misc/sectionDOWN.gif){kind=icon}
Population-Average vs. Cluster-Specific Estimates
|
|
|||
|
Maren K Olsen, PhD Duke University Medical Center, John S. Preisser, UNC School of Public Health
Send rapid response to journal:
maren.olsen{at}duke.edu Maren K Olsen, et al.
|
To the Editor: Panageas and colleagues [1] analyzed volume-outcome trends using three different methods: standard logistic regression, a logistic model with confidence intervals adjusted for clustering using the generalized estimating equations (GEE) method, and a random-effects logistic model. Tables 1, 2, and 3 present a side-by-side comparison of results from these three methods whereby the importance of adjusting for clustering is illustrated. From a methodological standpoint, the reported results from the random-effects models are surprising. The odds ratio from the GEE method represents a population-average (PA) estimate; the odds ratio from the random-effects models represents a cluster-specific (CS) estimate (e.g., see Localio et al [2]). When there is clustering, the estimates from a random-effects model are expected to be larger (i.e., farther from the null value) than GEE estimates; the discrepancy is dependent on the variance of the random effect (sc2). For a logistic model, the PA effect is related to the CS effect using the following formula [3, p. 136]: bPA ~= bcs(1 + 0.346sc2)-1/2 In Table 2, however, the estimates from the random effects models are smaller than the estimates from GEE (1.46 vs. 1.58 and 1.88 vs. 2.32). Similarly, in Table 3, the random-effects model estimate for the abdominoperineal resection outcome is smaller than the GEE estimate (1.09 vs. 1.21). It is not clear why the random-effects model estimates are smaller than the GEE estimates. One possibility is computational error. The authors used gllamm6 in Stata to fit the random-effects models. Given the evolving state of computational methods, the authors may want to consider other procedures (e.g., gllamm in Stata Version 8 or proc nlmixed in SAS) to verify the random-effects model results. It would also have been helpful if an estimate of sc2 or the ICC had been included. In the discussion section, the authors note the “disconcertingly large differences in the results” and further state that, “both statistical methods endeavor to estimate the same effect, the odds ratio of volume on outcome, and the discrepancies in estimates must reflect their different technical formulations.” These methods do not estimate the same effect, and this affects the interpretation of the estimates [2]. The random-effects model is a conditional method, and the estimated odds ratio is conditional upon cluster (e.g., surgeon). In contrast, GEE is an unconditional method, and the estimated odds ratio is the overall effect averaged across clusters. As an illustrative paper, the authors should have drawn more careful distinctions between these estimates and their interpretations. Maren K. Olsen, PhD Duke University Medical Center Durham, NC 27705 John S. Preisser, PhD University of North Carolina, School of Public Health Chapel Hill, NC 27599 References 1. Panageas KS, Schrag D, Riedel E, Bach PB, Begg CB. The effect of clustering on the association of procedure volume and surgical outcomes. Ann Intern Med 2003;139(8):648-665. 2. Localio AR, Berlin JA, Ten Have TR, Kimmel SE. Adjustments for center in multicenter studies: an overview. Ann Intern Med. 2001;135:112- 23. 3. Diggle PG, Heagerty P, Liang KY, Zeger SL. 2002. Analysis of Longitudinal Data, 2nd edition. Oxford University Press, New York. Conflict of Interest:None declared |
|||
