Journal of Medical Statistics and Informatics

Journal of Medical Statistics and Informatics

ISSN 2053-7662
Original Research

Comparison of performance of exponential, Cox proportional hazards, weibull and frailty survival models for analysis of small sample size data

Christopher Stanley1*, Elizabeth Molyneux3 and Mavuto Mukaka2,4

*Correspondence: Christopher Stanley

1. UNC Project-Malawi, Lilongwe, Malawi.

Author Affiliations

2. The Malawi Liverpool Wellcome Trust Research Laboratories, College of Medicine, Blantyre, Malawi.

3. Department of Paediatrics and Child Health, College of Medicine, University of Malawi, Malawi.

4. Department of Public Health, College of Medicine, University of Malawi, Malawi.


Background: The Cox Proportional Hazards(PH) model is commonest survival data model used in clinical trials. However, little is known as to whether or not this approach is robust to the size of the study. We compared performance of Cox, Weibull, Exponential and Frailty models in a randomized study that had a small sample size in general.

Methods: Models were fitted to data from a three-arm randomized efficacy trial of Kaposi's sarcoma at Queen Elizabeth Central Hospital (QECH) of children aged <16 years. Patients were randomized to receive Vincristine monotherapy or Etoposide or Vincristine plus Bleomycin. The Cox, Weibull, Exponential and Frailty models were fitted to the data to obtain the adjusted effect of treatment on survival. The performance of models were compared using the Akaike's Information Criteria (AIC). Plots of log-log of survival against log of survival time, and the Schoenfeld's global tests were used to test suitability of the PH assumption.

Results: Ninety-two patients were available for analyses of which 64% were males, the mean age was 8 years (SD=2.8years) and 89% were HIV positive. Exponential model was the best fitting method with AIC=174.1. Children treated with Vincristine monotherapy survived evidently poorly compared with those on Etoposide (HR=5.8, p=0.04).

Conclusion: Exponential models can elicit more valid results than semi-parametric CoxPH model in a clinical trial with small sample size. This emphasizes the fact that when models are fitted to data, it is good practice to assess the goodness of fit and where appropriate alternative models should be fitted.

Keywords: Cox proportional hazards models, survival, parametric models, small sample size, Malawi

ISSN 2053-7662
Volume 4
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