In this paper we propose a new method to analyze time-to-event data in longitudinal genetic studies. This method address the fundamental problem of incorporating uncertainty when analyzing survival data and imputed single-nucleotide polymorphisms (SNPs) from genome-wide association studies (GWAS). Our method incorporates uncertainty in the likelihood function, the opposite of existing methods that incorporate the uncertainty in the design matrix. Through simulation studies and real data analyses, we show that our proposed method is unbiased and provides powerful results. We also show how combining results from different GWAS (meta-analysis) may lead to wrong results when effects are not estimated using our approach. The model is implemented in an R package that is designed to analyze uncertainty not only arising from imputed SNPs, but also from copy number variants.