# What kind of statistical model I should use?

Here is the project that I'm currently working on it and would be more than happy if I can get your opinion about it.

The project is about dispatching the EMS helicopters to the incident locations to transport the trauma patients to the hospital.

My goal is to develop a statistical model to decide whether an EMS helicopter or ground-based ambulance is the best option in terms of the survival odds of the patients.

Our data consists of patients transported to hospitals, the mean of transportation (HEMS or ambulance), demographics of the patient (age, gender, etc.), level of trauma, blood pressure, etc.

As such we've four categories of patients: 1. patients transported by helicopter and died, 2. transported by helicopter and survived, 3. transported by ambulance and died, and 4. transported by ambulance and survived.

My question is that what is the best statistical model for this case? Imagine that I want to decide to transport one specific patient by either HEMS or ambulance?

You're going to save lives!

Mehdi

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Imagine that I want to decide to transport one specific patient by either HEMS or ambulance?

You need a causal model.

The questions your model must be able to answer with some confidence are "Here's some patient with characteristics X at location Z. If we send an ambulance, what are the odds of surviving? If we send a helicopter, what are the odds of surviving?". That requires knowledge of the causal effect of this choice on survival:

$$\Pr( \text{Patient survives}|X=x, \ Z=z, \ \text{do}(\text{Transport=H)}) - \Pr( \text{Patient survives}|X=x, \ Z=z, \ \text{do}(\text{Transport=A)})$$

You don't want to just predict survival with whether an ambulance or a helicoptre was used. Ambulance will be positively correlated with survival odds, because they're probably more likely to send out the helicoptre in the most serious circumstances. To attempt to cleanse the correlation of transport choice and survival from such non-causal contributions, it's key that you know as much as you can how the decision to send the helicoptre was made in your data, and about the patient. Here's an in-depth discussion how to judge whether what you're estimating is a causal effect.

Here's a further idea: Under the assumption that the only thing that matters for survival is the time to hospital, you could instead model the causal effect of time to hospital on survival odds, for which there will be much more variation in your data, and then separately how ambulance and helicoptre affect time to hospital (for which you can probably use additional data).

This assumption seems reasonable to me as a non-expert, but one possible way it could be wrong would be if the crew on a helicoptre is better than the one on an ambulance or if they have better equipment, so that treatment whilst the patient is transported is better. If that's the case, this analysis would understate the benefit of helicoptre transport.

My two cents:

I would frame this as a classification problem where target label is 'died/survived'. Features are demographics, physical and transportation method.

Assuming I have enough good data, and that indeed data explains survival chances. I would go and ask the 'what if' transportation feature had this value or another. (Technically by getting fitted classifier prediction for each possible transportation feature value).

I would also prefer predict probability classification algorithm(Logistic regression for example). This will help me make better decisions on which transportation method is better(by looking at the uplift in predicted survival probability).

My first thought is to opt for a penalized logistic regression (Lasso or Ridge). By taking on some bias from the penalization, you lose some variance, which should help improve perditions. That being said, you should test against a bunch of models (including some very dumb models, like always sending out an ambulance/HERS, or a simple decision rule like if the patient is farther than 20km, send out a HERS).

I think the more salient aspect will be the model validation. Look into clinical prediction model literature for ways people are validating models which deal with life/death scenarios. Though machine learning and statistics can do a lot, you need to be damn sure of your model when it comes to someone's life.