A progressively censored sequential likelihood ratio test for general parametric hypotheses

In life testing problems as in those arising from clinical trials, one is interested in the survival distribution function. In the case of several covariables affecting survival, one is still interested in the survival distribution as a function of the covariables, not in the parameters themselves that determine how the covariables enter into the model. Sequential procedures utilize information from the already collected observations and allow for a possible early termination of experimentation with a concurrent savings in time, cost and lives. In the present work a suitable maximum likelihood based sequential testing procedure for functions of unknown parameters is developed for time sequential observations from an underlying distribution of known form. The theoretical operating characteristic (OC) and average sample number (ASN) functions are derived for local alternatives by approximating the distribution of the test statistic with linear combinations of the standard Wiener process. Simulation studies were utilized to investigate the goodness of the asymptotic results in finite samples.