If it is true, Congratulations! ... as for what to do, let's see: First, publish the data in a High Impact Magazine; secondly, to communicate it to the WHO so that the matter is evaluated by the "ad hoc" Bioethics Committees; thirdly, tell the Bioethics Committee of your Nation and your Hospital so that they decide what is best for the patient and their families and with the Head of Religious affairs, in the face of the spiritual care that WHO itself requires, if the patient or his representatives, if he is cognitively disabled, wish to receive.

In any case, I advise you to read some of my contributions here in "RG" on the topic of How to Communicate Bad News and on the Model in this regard by Buckman et al. Congratulations again and thank you !

The variable must "vary" (if it does not, it may not be a "variable") and may be a "constant" instead of a variable in the model.

One of the weaknesses of all predictive models (regardless of mathematical method used) is perfect interaction (100% explanation of variance) between two "entangled" variables. This is one of the reasons that ALL stochastic models come with a set of conditions (also known as "assumptions of the model") that must be met, in order for the results to be considered mathematically valid.

A perfect predictive model is a red-flag that warrants detailed attention to the listed assumptions of that model. After that list has been reviewed and each assumption check-listed, then the next step (in my opinion) would be to incorporate and control for additional variables that are genuine attributes of elements in the model (in this case, patients as mortality is dependent variable being modeled) that have not yet been tested as variables in the model. The sad truth is that when variables that have a non-random certainty are included in a model, the second, third, and fourth order interactions among permutations of combinations of all the variables in the model, are no longer detectable at the experiment-wise model threshold for rejection of the Null. What is the Power of the model? What is the positive predictive value, negative predictive value, sensitivity, and specificity? All 100%? Can the 100% perfect model be reproduced from a completely different data set of similar data? Third party independent replication of similar findings using similar (but totally different) data sets is the gold standard for validation. How may 100 years did it take for gravity to become validated as a 100% law of the universe (and even then it only converges to 100 % at infinity).

Perfect models are an open invitation to dig deeper, until the model can include the interactions among higher order dimensions that are to be found only by controlling for them, and eliminating them out of the variables in the model equation, until the model consists of only independently predictive variables in the model, and nothing but them in a final "trimmed" model. If one can ever arrive at that kind of perfect model, then perhaps you are no longer "squeezing the balloon" and actually have something that can serve as a true "generalizable model" that will accurately give similar results within a margin of error, as long as the data sets it is applied to are similar (same kind of patients, different hospitals, different geolocations, different seasonal time frames). Just a cautionary note, especially when dealing with human subjects (patients) is that the number one recognized external threat to experimental models is "seasonal variation". If you do not have data that spans a minimum of two years, and that can compare winter-to-winter, spring-to-spring, summer-to-summer, and fall-to-fall, then you likely do not have a "perfect" model. You need to control for the effect of month-year (with a variable that has 24 unique month-year values) that is associated with each of the case observations (of patients) in the model. That would be a good, next step if this has not been done yet. Then, the next step after that would be to perform an internal-cross validation by comparing a model of a random 20% model building selection of the data to a corresponding random 80% model validation hold-out data set. For good models with high values of area under the receiver operating characteristic (i.e. AUROC Curve) the specificity and sensitivity of two random selected models should be similar. We are all going to need to extend the time frames for inpatient mortality models due to the current impact of COVID19 on all patient populations. My suggestion is to use an additional year retrospective to 2020 and an additional year after the end of model time frame what ever that is and to try to get a symmetrical time frame with the experiment at the center of the symmetry, in order to control for the possible effect of seasonal variations upon all the variables in the model. Of course, data costs money, and time. And most of us don't have either. Always list the lack of ability to control for seasonal variation as one of the limiting factors in the model (same as for having to use a non-stratified, non-randomized, small (i.e. less than 3,500 observations) convenience sample.)

Good luck. Don't give up. List the limitations, make suggestions for better models in the future that mitigate those limitations. I sincerely hope this helps you out. There is no simple straight-forward one-size-fits-all solution to the "Perfect Model" conundrum, but there are multiple valid strategies that can be considered and a few of them have been listed above.

Predicting death? 100% accurately?

Forget academia - start a "palm reading" business.

if it is true. first publish it.

A first step to investigate this suspicious result is to check which of the independent variables help the prediction most. It may be that information about the dependent variable (whether a patient dies in ICU) is inadvertently included in the independent variables. A hypthetical example: If you include an independent variable that indicates whether a post-mortem examination was carried out, this will greatly help predicting your dependent variable. This example may sound obvious, but the same phenomenon may occur in subtler ways in real datasets.

More generally speaking, since the purpose of your model is to predict a future event (rather than classifying patient files post-hoc), your independent variables should not include any information that causally depends on the variable you are trying to predict.

If you are sure that your model is not affected by the above issue, then you should check the model accuracy on unseen data. I suppose the 100% accuracy values you mention are when predicting the same data that the model was fit on. If you have access to new data that you did not have when fitting the model, then check what the accuracy is for this new data. If not, then cross-validation is a good approach to check how well your model generalizes to unseen data ( https://en.wikipedia.org/wiki/Cross-validation_(statistics) ). If you do a k-fold cross-validation and still get 100% accuracy on each of the folds, then probably your dataset is too small.