Click-through data has proven to be a critical resource for improving search ranking quality. Though a large amount of click data can be easily collected by search engines, various biases make it difficult to fully leverage this type of data. In the past, many click models have been proposed and successfully used to estimate the relevance for individual query-document pairs in the context of web search. These click models typically require a large quantity of clicks for each individual pair and this makes them difficult to apply in systems where click data is highly sparse due to personalized corpora and information needs, e.g., personal search. In this paper, we study the problem of how to leverage sparse click data in personal search and introduce a novel selection bias problem and address it in the learning-to-rank framework. This paper proposes a few bias estimation methods, including a novel query-dependent one that captures queries with similar results and can successfully deal with sparse data. We empirically demonstrate that learning-to-rank that accounts for query-dependent selection bias yields significant improvements in search effectiveness through online experiments with one of the world's largest personal search engines.