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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

There were various additional Qs in comments, they are moved here.

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).Sorry for the questions, thank you. –

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    $\begingroup$ 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". $\endgroup$ – kjetil b halvorsen Jan 23 '15 at 14:47
  • $\begingroup$ 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?) $\endgroup$ – Rachel Jan 23 '15 at 15:20
  • $\begingroup$ It would bias the values of the regression coefficients, and maybe lead to wrong conclusions. $\endgroup$ – kjetil b halvorsen Jan 23 '15 at 15:21
  • $\begingroup$ From doing some reading about survival analysis and censored data today I have a couple of queries: $\endgroup$ – Rachel Jan 23 '15 at 18:36
  • $\begingroup$ '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. $\endgroup$ – Rachel Jan 23 '15 at 18:43
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Some thoughts. Survival analysis got its name from analysing data where we observe the time up to death, or some other non-recurring event. Your situation is similar, but different, since hospital admission and re-admission are (possibly) recurring events!

So you could have a look at the book (Springer) "The Statistical Aanalysis of Recurrent Events" by Richard Cook and Jerald Lawless.

As for the question about what to do with "no re-admission within one year"? There are of course two possibilities: they were readmitted, but later, so the observation was censored. Or, they were never readmitted. But, unless the patient is dead, we can never know if there will be some readmission later, so empirically the two possibilities cannot be distinguished, so maybe should be treated the same way.

If you are following the patients, you should now if you are still in contact with the patients, if you lost contact, the patient will be "lost to follow-up". That way you will know the total time the patient has been under observation, which will be important information for modeling.

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  • $\begingroup$ Okay thank you. I will be sure to add questions in the edit next time. Some of your answer has been cut off? $\endgroup$ – Rachel Jan 26 '15 at 13:47

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