random sampling records in pooled hazards regression

[nhejazi]

paraphrasing Mark (from some years ago), our approach of estimating the conditional hazard after discretization of the support of A into ordered bins with pooled logistic (HAL) regression, with the bin number/level as a covariate itself, can be sped up by random sampling rows from the longitudinal data structure into which the data are mapped for pooled hazards regression. this is different to subsampling observations (i believe), as all observed units are represented (theoretically), though not for every bin into which they fall --- for example, one might only randomly sample those rows where the inclusion indicator is zero to avoid losing units (in this case, the minimum number of records would be 1 for those in the first bin and at least 2 for all others). this could be worth implementing to speed up the density estimation procedure.