Mixed model analysis of ordinal response data with two nested levels of clustering: An application involving a clinical trial

Sadia Mahmud, Ursula Chohan, Gauhar Afshan, M. Qamar-ul-Hoda

Research output: Contribution to journalArticlepeer-review


In this paper we present analysis of ordinal response data, from a clinical trial, with two nested levels of clustering using the generalized linear mixed model approach. We present a generalization of the continuation ratio model with two nested random effects. The model was fitted using maximum marginal likelihood estimation, assuming the nested random effects are independent and normally distributed. The clinical trial recruited high risk patients coming for unilateral lower limb surgeries. All patients were given unilateral spinal anaesthesia that intends to anesthetize only the leg that has to be operated; motor level was the ordinal response in the trial, measured repeatedly over time for both legs. The objective of the analysis was to evaluate the difference in the severity of motor level paralysis between the operated and the non-operated leg, and also to assess the effect of time on progression of motor level to higher degrees of paralysis. There was a significant interaction between the covariates time and leg; at baseline progression rate to higher degrees of paralysis was more rapid for the operated relative to the nonoperated leg. The progression rate levelled off by the end of the study, at 30 minutes, more prominently for the non-operated leg. The continuation ratio method, that makes a series of comparison of all lower categories on a scale to the next succeeding one, intricately models the progression of motor level paralysis with time to higher degrees, and gives insight into the mechanism of progression.

Original languageEnglish
Pages (from-to)31-46
Number of pages16
JournalPakistan Journal of Statistics
Issue number1
Publication statusPublished - Jan 2011


  • Continuation ratio model
  • Maximum marginal likelihood estimation
  • Nested random effects
  • Three-level data


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