Browsing by Author "Singh, Gurbakhshash"

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    Binary and Ordinal Outcomes: Considerations for the Generalized Linear Model with the Log Link and with the Identity Link
    (2017) Singh, Gurbakhshash; Fick, Gordon; Kopciuk, Karen; Sajobi, Tolulope; Lu, Xuewen; Horrocks, Julie
    There are gaps in the current literature on Generalized Linear Models (GLM) for binary outcomes with the log link. This dissertation explores a number of these gaps and presents specific results: (1) Uniqueness considerations for the Maximum Likelihood Estimate (MLE) are established from the conditions for the strict concavity of the log-likelihood. The full column rank of certain subsets of the covariate matrix is shown to be a condition for the strict concavity of the loglikelihood. (2) Conditions are established for the finiteness of components of the MLE. A method is proposed to address the possibility of non-finite components for the MLE, and it is based on determining directions of recession of the log-likelihood. In addition, it is established when the MLE will be in the interior of the parameter space and when the MLE will possibly be on a boundary of the parameter space. (3) Examples are presented of closed form expressions for the MLE. For a number of models with indicator variables and measured variables, closed form expressions for the MLE are presented. (4) There are considerations for the construction of confidence intervals when the MLE is close to a boundary of the parameter space. A new metric, called the “fraction within the parameter space”, is introduced for assessing intervals for MLEs close to a boundary. A simulation study is provided that offers support for Bootstrap Percentile Intervals having larger fractions when compared to Relative Likelihood Intervals and Normal Confidence Intervals. This dissertation continues by developing a proportional probability model using the log link for ordinal outcomes. For this model, similar results are presented for topics (1) and (3) above. In addition, there is the introduction of a score test to assess proportionality. The dissertation concludes with a discussion of future work. In particular, this discussion includes some preliminary work with the identity link GLM for binary and ordinal outcomes. Throughout this dissertation, there are many practical considerations and illustrations presented. The use of the log link and the identity link for binary and ordinal outcomes should now become a viable modeling option for researchers.
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    Minimal sufficient balance randomization for sequential randomized controlled trial designs: results from the ESCAPE trial
    (2017-11-02) Sajobi, Tolulope T; Singh, Gurbakhshash; Lowerison, Mark W; Engbers, Jordan; Menon, Bijoy K; Demchuk, Andrew M; Goyal, Mayank; Hill, Michael D
    Abstract Background We describe the implementation of minimal sufficient balance randomization, a covariate-adaptive randomization technique, used for the “Endovascular treatment for Small Core and Anterior circulation Proximal occlusion with Emphasis on minimizing CT to recanalization times” (ESCAPE) trial. Methods The ESCAPE trial is a prospective, multicenter, randomized clinical trial that enrolled subjects with the following main inclusion criteria: less than 12 h from symptom onset, age 18 years or older, baseline NIHSS score > 5, ASPECTS score > 5 and computed tomography angiography (CTA) evidence of carotid T/L or M1-segment middle cerebral artery (MCA) occlusion, and at least moderate collaterals by CTA. Patients were randomized using a real-time, dynamic, Internet-based, minimal sufficient balance randomization method that balanced the study arms with respect to baseline covariates including age, sex, baseline NIHSS score, site of arterial occlusion, baseline ASPECTS score and treatment with intravenously administered alteplase. Results Permutation-based tests of group differences confirmed group balance across several baseline covariates including sex (p = 1.00), baseline NIHSS score (p = 0.95), site of arterial occlusion (p = 1.00), baseline ASPECTS score (p = 0.28), treatment with intravenously administered alteplase (p = 0.31), and age (p = 0.67). Conclusion Results from the ESCAPE trial demonstrate the feasibility and the benefit of this covariate adaptive randomization scheme in small-sample trials and for data monitoring endeavors. Trial registration ESCAPE trial – NCT01778335 – at www.clinicaltrials.gov . Registered on 29 January 2013.