Statistics catch-up lecture
نویسنده
چکیده
Example 1. In a genetic study, n = 2217 patients are recruited, among which 1127 have bladder cancer. After whole genome sequencing, p = 475290 single nucleatide polymorphisms (or SNPs, a possible variation of the DNA sequence at one location) are measured on each patient. We construct a matrix X = (Xij)1≤i≤n,1≤j≤p where Xij = 1 if the ith patient has a mutation at jth location and 0 otherwise. Denote X> i for the ith row of X. Let Y = (Yi)1≤i≤n be a response vector, where Yi = 1 if the ith patient has bladder cancer and 0 otherwise. The goal is to understand how SNPs can be used to predict bladder cancer. One possible way to analyse the data is to assume a logistic model, i.e.
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