Arthritis & Rheumatism, Volume 60,
October 2009 Abstract Supplement

The 2009 ACR/ARHP Annual Scientific Meeting
Philadelphia October 16-21, 2009.

Analysis of Correlated Ordinal Data in a Self-Matched Study with Applications to Knee Pain Severity

Zhu1,  Yanyan, Cabral2,  Howard, McCulloch3,  Charles E., Felson4,  David T., Nevitt3,  Michael C., Zhang1,  Yuqing

BUSM, Boston, MA
BUSPH, Boston, MA
Boston University School of Medicine, Boston, MA


In longitudinal studies, pain severity is often measured on an ordinal scale. To minimize confounding from person-level factors we have proposed a self-matched study in which comparisons are made within a knee over time and one knee per person is studied. To date, no statistical method is available to analyze such ordinal data when persons provide data for two knees. We adapted amalgamating conditional logistic regression (ACLR) for self-matched studies and tested 4 modifications to account for the correlation between knees.


We used 4 methods to account for between-knee correlation while applying ACLR: 1. Clustered: treat a person (cluster) as a stratum; 2. Pooled: obtain point estimates assuming independence but calculate proper robust variance estimates; 3. WEE: apply weighted estimating equations (WEE), the weighted version of the estimating equations used in the pooled method. Each knee was weighted by the inverse of the number of knees a person provided; 4. WCR: perform within-cluster resampling (WCR). Each time a knee was randomly selected from each person with replacement. We evaluated the performance of these methods by simulation and applied them to assess effusion in relation to knee pain severity in the Multicenter Osteoarthritis Study (MOST). Both simulated data and real data included 1349 persons. 188 persons had data for both knees, while the remainder contributed a single knee. Of the knees, 119 had observations from 3 time points and the rest had 2. A random-intercept proportional odds model was used in simulation. The simulated data (500 replicates) had a 4-level ordinal outcome variable and two covariates, one continuous from a N(0,1) distribution and the other binary (p=0.2). The regression coefficients were set at b1=0.5 and b2=1.0.


The effect estimates from all methods were close to true value with bias less than 1% except for the clustered method, and the average model-based standard errors (SE) were close to the true SE (SD) (Table 1A). When these methods were used on the MOST data, all results suggested that increased severity of effusion was associated with higher severity of knee pain, but the magnitude from clustered method differed from others (Table 1B).

1A. Simulation
Est: mean estimated betas
SD: standard deviation of the estimated betas
SE: average of estimated standard errors
1B. Effusion and Knee Pain Severity
Effusion Score1 vs 02–3 vs 0
MethodOR1 (95% CI)OR2 (95% CI)
Clustered1.30 (0.88, 1.91)3.72 (2.32, 5.94)
Pooled1.11 (0.72, 1.71)2.70 (1.55, 4.70)
WEE1.06 (0.68, 1.65)2.52 (1.43, 4.43)
WCR1.06 (0.69, 1.65)2.52 (1.43, 4.43)


Pooled data, WEE and WCR methods generated very consistent results when the proportion of persons with data for two knees was small (18%). Further studies are required to assess the performance of these approaches when proportion of persons with data for two knees is relatively large.

To cite this abstract, please use the following information:
Zhu, Yanyan, Cabral, Howard, McCulloch, Charles E., Felson, David T., Nevitt, Michael C., Zhang, Yuqing; Analysis of Correlated Ordinal Data in a Self-Matched Study with Applications to Knee Pain Severity [abstract]. Arthritis Rheum 2009;60 Suppl 10 :1129
DOI: 10.1002/art.26204

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