In this master thesis we investigate the properties of a chi-squared goodness-of-fit test for case-control data, of Grønnesby and Borgan (1996). This goodness-of-fit test is based on a comparison of observed and expected number of events in G groups and K disjoint time intervals. Our main focus will be estimating the level of significance and the power of the test in different situations.
Simulations shows that the distribution of the test statistic, when the true model is fitted to data, is approximately chi-squared with K(G-1) degrees of freedom. The power of the test is quite week in most of the situations we have investigated, and seems to have quite small capability of exposing that a covariate is missing or that a covariate is wrongly transformed. When a wrong model is fitted to the data, the power rises slightly, but it seems that the model fitted must be very different from the true model for the test to notice that is it wrong. However, when a model without time dependent effect of the covariates is fitted to a data-set where one of the covariates are time dependent, the power of the test rises, provided that grouping for the test is based on time.