Searching for genes contributing to longevity is a typical task in association analysis. A number of methods can be used for finding this association - from the simplest method based on the technique of contingency tables to more complex algorithms involving demographic data, which allow us to estimate the genotype-specific hazard functions. The independence of individuals is the common assumption in all these methods. At the same time, data on related individuals such as twins are often used in genetic studies. This paper proposes an extension of the relative risk model to encompass twin data. We estimate the power and also discuss what happens if we treat the twin data using the univariate model.