The main goal of this master thesis is to compute the sample size of the OPTIMAL study (OPTimizing Irradiation through Molecular Assessment of Lymph node), which is a non-inferiority clinical trial with survival data and two planned interim analyses that aims to compare two irradiation modalities in patients with breast cancer. The sample size of this study was first computed in 2014, by means of nSurvival and gsDesign functions from the R package gsDesign. However, the statistician of the study now thinks that this computation may be subotimal since nSurvival function was created to test the null hypothesis of equality of hazards. In order to be able to do this computation, a bibliographic search has been done to find sample size formulas for non-inferiority trials with survival data. In particular, two papers stand out: Jung et al (2005) and Crisp et al (2008), which have been described and compared. In addition, the method followed by nSurvival function has been explained together with nSurv, a function created in gsDesign package two years after the trial protocol had been written, which can be used directly for non-inferiority trials. However, all these methods do not consider interim analyses and thus some group sequential theory has been introduced and combined with the previous formulas to obtain methods which also take into account these analyses. In particular, the extension of the formulas for fixed sample designs to group sequential ones can be done by means of gsDesign function. Using these four procedures to compute the sample size of the OPTIMAL trial, we have obtained exactly the same results from Jung et al (2005) and Crisp et al (2008), and a similar size from nSurv (all combined with gsDesign). However, the combination of nSurvival and gsDesign functions, the method followed by the statistician of the study in 2014, underestimates the sample size by more than 200 patients as compared to the other procedures, which implied a 5% of power loss. Moreover, the sensitivity of the four methods to modifications of recurrence and dropout rates have been studied, and we have obtained similar situations as compared to the original study design.
