Can predictive models make predictions for individuals or only for groups? I am an MBA Student taking courses in statistics.
In this last week, I have heard two conflicting opinions from my professors on Statistics.

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*1) Predictive Models can NOT make predictions on individuals - only on groups: My professor from my "Research Methods" class introduced us to the concept of the "Ecological Fallacy" (https://en.wikipedia.org/wiki/Ecological_fallacy). He pointed out that very often, the behavior of individuals within a group will not be similar to the average behavior of the group. He mentioned that statistical models can ONLY be used to describe variations within groups - he mentioned the importance of concepts such as "Propensity Score Matching" and correctly designing experiments while accounting for possible inconsistencies.


*He mentioned that if a pharmaceutical drug was found to be effective on a cohort of men all having similar age groups, lifestyles, backgrounds and medical histories - the best we can do is say that any man from the general public who fits this cohort profile will likely experience similar effects from this drug : we can not really make any individual prediction apart from this.


*He mentioned the field of "Survival Analysis" and told us that statistical models are routinely used to estimate the survival odds and hazard of surviving at the group level and not the individual level - he gave us an example: if you have 1 Male Asian Patient and 99 Male Non-Asian patient, you have no choice but to analyze the average survival rates of MALES ... how can you perform "Asian Specific Analysis" and make inferences about the average Asian when you only have 1 observation!?


*He closed by mentioning the new and emerging field of "Precision Medicine" in which "accurate molecular taxonomy of diseases that enhances diagnosis and treatment and tailors
disease management to the individual characteristics of each patient " (https://www.mdpi.com/2227-9717/10/6/1200/pdf) - i.e. for the first time, medical treatments are being considered for the individual patient's condition, and not for the average profile of this patient (although he mentioned that this is still in its infancy and should be used with great caution).


*With this, he largely dismissed "Data Science" as a "pseudo science" and said although many "Data Science" models have demonstrated success, the methodology is not mathematically rigorous and can only be considered as an "engineered solution" (e.g. a Random Forest predicting if an individual patient will develop a disease - he said that this should not be done for many reasons, e.g. interpretability, blackbox, lack of odd's ratio and individual prediction).


*He closed with this final example : Imagine two bridges. The first bridge can only support a load of 100 kilograms, but has been rigorously tested in theory (e.g. physics, material science) and empirically - the reputation and behavior of this bridge has been well documented and observed under various conditions. The second bridge has been demonstrated to support loads of up to 500 kilograms, but we have no idea how this bridge was built or whether it will collapse in the future when subject to even 50 kilograms. He asked us - which bridge are you more confident walking across? He said this in a rhetorical tone, and said obviously the first bridge that has demonstrated both theoretical and empirical success should be favored over the second bridge - even if the first bridge is believed to be less stronger than the second bridge. He quipped that the first bridge is Classical Statistics and the second bridge is Data Science. He told us that perhaps this example is an extreme example, but this is precisely why a drug that has initially shown strong potential for curing a disease must be rigorously studied in both theoretical and empirical settings before it can be released - and in the interim, potentially less effective but better understood drugs must be administered of which we have higher confidence in.


*2) Predictive Models CAN be used to make predictions on individuals: On the other hand, my Data Science professor thinks otherwise. I told him the views of my "Research Methods" professor and he stated that research publications would suggest otherwise. He showed me publications (e.g. https://www.sciencedirect.com/science/article/pii/S2666827021000694, https://pubs.rsna.org/doi/full/10.1148/radiol.2018180547) in which predictive models have indeed demonstrated success in making individualized predictions - for example, successfully predicting the presence of COVID-19 in individual patients. He basically said that he sees no reason as to why Predictive Models can not be used for individual prediction - and if the  opposite was true, he would have been long out of a job.
This has left me conflicted - I find myself agreeing with the opinions and views of both professors at the same time.
Can someone here provide some insights to bridge these two views together?

The problem often lies not with the models themselves, but with how they are applied and with how people make decisions.
Too often I see the same pattern in companies starting with ML/Data Science:

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*They face a hard technical problem.

*Someone high-ish up the management chain figures out it might be solvable by Data Science because everything is these days... Alternatively, they just catch on the hype and do not even have a problem formulation, just "more Data Science more better".

*They hire someone, very rarely a full team (or, if you are lucky, they actually outsource the problem).

*The new hire is able to come up with a proof-of-concept which performs better than all the old models on a small subset of test data.

*They are eager to deploy it.

They want deliverables and start using "common sense" to rationalize how the model works. The added bias tends to downplay failures and emphasize successes - even if the model itself is terrible, it may be hailed as one of the greatest achievements ever by someone on C suite just because it is "AI". And then the issue is that with many statistical models the engineer can reason about the limits of their applicability fairly well. We have a decently developed framework for examining statistical models by now, and while the similar level of rigor is achievable in theory with ML/AI, it is seldom done so in practice. Also, crucially, the cost analysis is often performed poorly or even omitted entirely. That is how you have your tale of two bridges: one could factor in the cost of it failing spectacularly and so on but take a guess what ends up being done in practice? Execs taking over the "undecisive" engineer who is "too dumb" to take advantage of their competence, and the cost-saving measure gets rolled out.
And if we are talking technical execs, many of them are engineers who will try to bridge the explanatory gap using their experience and intuition, neither of which is necessarily applicable to ML. Very basically, their reasoning would go like

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*This model is smarter than all the old and dull models we have used before.

*Old models were well-regularized and you could extrapolate their behavior well.

*Ergo, this new and smart model will not freak out when encountering something it has never seen before.

So there you have it - of course, predictive models can predict individual outcomes and even be fairly efficient at that. The problem is that the resulting models are opaque, hard to reason about, and people making decisions often will be incompetent about statistics and ML. A LOT of work data scientists/statisticians/engineers do ends up being communication and ensuring their models are applied properly - and it is just a lot easier to communicate with "classical" models. When something gets done more efficiently, it is not necessarily good, either - if this something was erroneous to begin with (remember Knight Capital?..).
