Sample size for recurrent events data in non randomized studies with an historical control

In some exceptional circumstances, as in very rare diseases, non randomised trials with historical controls may be the only way to demonstrate efficacy and safety of a new treatment. The design of such studies needs a sound methodological approach in order to provide a good level of scientific evidence. To our knowledge, no attention has been given to the development of methods for sample size calculation for non randomized controlled trials (one treatment arm) where the end-point deals with recurrent events. In this context, guidelines for study design, including formulas for sample size, were only proposed for the typical scenario of randomized clinical trial (Bernardo and Harrington, 2001; Cook and Wei, 2003; Matsui, 2005). Here we propose an approach to power and sample size calculation for non randomised trials with historical controls that relies on simulation studies. Non parametric tests statistics will be considered, with the rate of events of the historical control as a reference. We will also develop an extension that accounts for paired comparisons in cases where information on pre-treatment event history of patients is available. Simulations will explore different models for the underlying event generation process (i.e. homogeneous, non homogeneous, mixed Poisson process) in order to evaluate the robustness of sample size calculation. The approach will be illustrated with a non randomized trial on experimental gene therapy in a very rare immunodeficiency (ADA-SCID), where a major end-point is the history of recurrent severe infections.