Suggestions for Statistical Methods for Health Research

I am currently planning a research project looking at a scoring system for patients (using demographics, social circumstances) to determine whether there is a relationship between a patient's score and their length of hospital stay.

The score has 5 domains which are all equally weighted so each participant will have a score between 0 and 5. This will then be correlated with length of hospital stay, measured in days.

A small scale project of 200 patients suggested that higher scores would likely result in longer median lengths of stay, which has prompted a larger project with more robust statistics.

This time we are hoping to include up to 1250 patients, looking at the same scoring system.

I have had several suggestions for appropriate statistical methods - ANOVA, logistic regression - but as I am not overly familiar with these methods I would appreciate any thoughts that people might have.

Many thanks