you could look at the favourite links page of my website, there is an electronic stats book link, which I think has some useful information, I don't know the answer off the top of my head, good luck with this

http://sites.google.com/site/deborahhilton/

I agree with Mamoona that the safe bet is tijme-to-event analysis (it doesn't have to be Cox regression since there are parametric alternatives).

On the other hand, if patients are continually observed (they are, after all, a captive audience in the hospital setting), then you won't have attrition (they either die or go home). If they die, you have your 1 and if they don't you have your 0. In this case, you could perform a logistic regression.

I think the bottom line decision for you is the time-component. If you want to track patients over 40 days, some of them will leave the hospital and possibly die. The question is how you would treat those statistically, if at all? You could leave them as censored and thus the time-to-event analysis would still be the best bet.

So you suggest that timetoevent is a "stricter" analysis in terms of not overestinating survival?

Yes. It is a more appropriate analysis because it takes into account the "days alive" for those who left the hospital.

I am attaching a link to a paper I wrote a long time ago on survival analysis. You may find this helpful.

Article Evaluating Disease Management Program Effectiveness: An Intr...

Actually, the difference is the time component.  PH models are MUCH preferable, because they provide the RISK (hazards ratio, or hr) of dying over time, which a simple logistic regression would not do.  So, if you were to follow up CHF patients over time, about 50% would die over a 5 year period -- 100 percent over 10.  so a x2 or LR analysis would not be sensitive (or pretty useless) but an HR stat would give you the risk over time 

Neither chi-square nor Kaplan-Meier easily handle multiple explanatory factors and you certainly have length of stay and age and probably diagnosis category at least as explanatory variables. So, I think these two are out. If you care about estimating how mortality is functionally dependent on length of stay, then I agree with Carolyn that you should at least try a proportional hazard model and examine the non-parametric estimate of the base hazard function. Otherwise, if you view length of stay as just an adjustment, logistic regression could work for you (assuming 0-40 days is all you observe). You can still have length of stay as a factor and play with whether its effect is is linear, quadratic, or cubic but you will, I think,  end up knowing less about the function of length of stay than with a proportional hazard model.

Paris: you asked to analyze hospital mortality. The time data used is hospital stay (days), ranging from 0 to 40 days. What would be the best way to compare 2 groups (and factors/predictors)?

The time of death represents the complete observations which is a narrow representation of time to death distribution (0 day to 40 days). You should also consider the censoring distribution of those observations which represent patients alive.

If you want to deal with a simple descriptive analysis of these two distributions, the Chi-square is not appropriate, since it is not taking into account the censorings.

One approach could be the life-tables approach (by day or by 5 days interval), if you have some hundreds of deaths, But, if you have only 20-30 cases of death and 200 censorings, then you will need an analysis of the hazards functions (Nelson-Aalen is recommended) to establish the status of the survivorship functions, in terms of crossing or not. The final approach is to compare the Kaplan-Meier survivorship functions using the results from the Nelson-Aalen estimators. I published some findings about the above methodology:

Suciu, G.P., Lemeshow, S., and Moeschberger, M. (2004), Statistical Test of Equality of Survival Curves: Reconsidering the Options, Handbook of Statistics, Vol.23, Chapter 13. Eds. N.Balakrishnan and C.R.Rao, Elsevier Science B.V. p251-262, ISSN:0169-7161.

 You should be able to download from the listed publications :)

From this analysis to Cox PH regression there is one small step, but again, for ONE factor that enter the model it is suited to have about 50 observations (for the robustness of parameter estimates).  Thus, the convergence of the partial MLE is questionable otherwise (this can be seen from the size of SE, if it is too big, then there is no way to have stable parameter estimates).

And...for small sample, we can deal with comparisons of the relative risk standard deviations...which opens a Pandora's box.

In conclusion: the type and size of your data govern the next steps.

In Norway, noationwide analysis of 30-day in-and-out-of hospital 30-day mortality (logistic regression, including the hospitals as fixed effects) identified outlier hospitals. We used Kaplan-Meier curves to visualise when the profile of an outlier hospital began to deviate for other hospital. Found to be very useful for quality improvent efforts.

http://bmjopen.bmj.com/content/5/3/e006741.full?keytype=ref&ijkey=zL5imGx6Gwtbtco