# Finding significant predictors of psychiatric readmissions

The set of data I am working contains nearly 17,000 independent spells (each spell consists of a number of hospital episodes) each belonging to a unique patient ID. I have spent a very long time cleaning the data to get it into a suitable format to analyse. For example, there were several diagnosis fields containing 100s/1000s of codes.

The majority of the independent variables in the data are categorical (either nominal or binary) and there are three continuous (well discrete) IVs. The outcome variable originally was binary (True or false) depending on whether a patient readmitted within 30 days from a previous discharge. However, 97% of the spells had an outcome variable of false, leaving only 3% true. Obviously the way in which the outcome variable was coded was not suitable.

I therefore obtained data on the number of days until readmission (with a limit on the max number of days being 365 days), in order to capture more variation. Of the 16,960 spells, 12,597 (74%) had no readmission within 365 days of a previous discharge. After removing the 'no readmission' spells, I am left with a continuous outcome variable. Can you give some advice on how I should model this data in order to deduce (if any) the significant predictors of the number of days until readmission?

I have considered the following:

• Multiple regression / ANCOVA-since I have both continuous and categorical independent variables. However the data does not satisfy the necessary assumptions.
• Multinomial logistic regression-here I changed the continuous outcome variable into a categorical variable (though I understand this is not advisable due to the loss of data). There were several issues of separation which I have dealt with my either removing very small counts or collapsing categories.I am yet to deal with any correlation between the independent variables (if it exists). Am I correct in saying correspondence analysis can be used for categorical variables similarly to how PCA is used for continuous variables?

EDIT

1. 'There are usually some individuals who do not experience the event during the study, so the time to event is incomplete for these cases. The researcher knows it is greater than the length of time these individuals were studied, though not how much greater.'

2. In my data it may be the case that the patient does have a readmission but at a time point longer than a year since previous discharge but it also may be the case that the patient NEVER readmits (I do not know) So is it appropriate to make the assumption that for those who have 'no readmission within a year' that they do have a readmission at a point greater than a year?

3. Also I just wanted to check if survival analysis is still appropriate when the cases have been studied for the same time period but from different time points (each patient is studied for a year after their discharge, which varies for each patient).

• You should NOT remove the cases without readmission within 365 days, that will bias the analysis badly. What you have is censored data, and you could use survival analysis, which can handle the censoring in a proper way. Have a look at stats.stackexchange.com/questions/1053/… search this site for "survival analysis" or "censored observations". Jan 23, 2015 at 14:47
• By removing the spells with 'no readmission' I may obtain results which over estimate the statistical significance of certain predictor variables? (so increase the chance of Type I errors?) Jan 23, 2015 at 15:20
• It would bias the values of the regression coefficients, and maybe lead to wrong conclusions. Jan 23, 2015 at 15:21
• Using a multinomial logistic regression would suppress otherwise useful information inherent in a survival model of days to readmission conditioned on a censoring variable. The varying time points or origins are a type of left-censoring which is readily handled by aligning all patients to a time 0, their discharge time. If you think there may be effects due to calendrical time (e.g., day, week, month of year or even holidays like the week between Christmas and New Year), then incorporate those as separate predictors. Apr 6, 2017 at 15:24