I'm uncomfortable with the term "gifted" since it implies that some people have "gifts" while others do not. Really, everyone is gifted, and it should be a project in life to help all people cultivate their gifts and be acknowledged and appreciated for them.
But admittedly, there are some students who whose talents and abilities allow them to be doing university-level academic work, or advanced work in performing arts, by mid-childhood. Leaving these children in the regular educational system could be boring or stifling for them, both intellectually and socially.
There are various sources of data about the value of various educational programs, including those catering to students with unusual talents. Testimonial accounts from the students and teachers are obviously an important source of data. There could be very glowing accounts of particular programs, or perhaps also scathing critiques, from different individuals, during or after their exposure to the programs. These are bound to influence subsequent policy. Or there could be "before" and "after" data, showing that most students in these programs do extremely well by some measure (unfortunately the measures often do not look at long-term psychological health).
But using data from testimonial accounts or "before/after" studies is fraught with problems. Students gifted in mathematics or other sciences should understand this very well -- it is a foundation of understanding treatment effects in medical statistics. If there are many students who give glowing accounts of a particular academic program, or entire cohorts who do well compared to their previous state, what does this really mean? It could mean that the program itself is excellent and should be continued. But another possibility is that gifted students are likely to thrive because of their giftedness or intelligence, and they would have thrived regardless of what type of program they were in. It is possible that the particular program was actually harmful to them compared to some conventional alternative, but they still gave a positive review because of their innate tendency to thrive adaptively. Similarly, negative reviews of a particular program could be caused by a bad program, or it could be caused by character traits in the reviewers, such as perfectionism, narcissism, or depressive symptoms.
Some positive reviews could be inaccurate judgments, skewed by other factors such as pride or narcissism. For example, graduates from an ivy league university may give inflated reviews of their educational experience because of the pride of being associated with such an elite institution. They may have had a similarly good undergraduate experience at a small local college. Of course, it is not an "either-or" issue. Ivy league education is indeed probably better in many ways, but not as much better as people believe it is.
In order to really determine the effectiveness and healthiness of a gifted program, one would have to do sufficiently powered randomized controlled studies, with both subjective and objective short and long-term assessments looking broadly at social and psychological well-being as well as academic achievement or career success. Testimonial data is useful but not sufficient. Jargon-laden theorizing by educational scholars is particularly meaningless and tiresome unless grounded by controlled data.
Aside from the need to have policy grounded in RCT data, there are a few features that need to be present to have a healthy, effective educational program for gifted children:
1) there should be specialized teaching to fully develop the students' capacities, otherwise they would be bored and understimulated. For some students, "teaching" per se is not required -- the students can teach themselves, and an external didactic teacher, especially one trained to be a high school teacher, could often just get in the way. But there should be adult mentors who are at least supporting and guiding the students' progress, and forming a warm personal connection with the students. For technical subjects, there should be access to advanced laboratory materials. And probably there should be access to experts such as university professors who can interact with and challenge the students at their level.
Some teachers who specialize in teaching gifted children may simply load the students with an enormous quantity of material. This leads to a risk of harming the children.
2) it is most likely of benefit for gifted children to be in a group of peers who have comparable abilities. This is one of the stronger arguments for a "gifted program." However, this could be achieved in other ways, such as through clubs, in a regular high school or community. For some gifted students--though not all--the regular high school social environment would be an oppressive chore to deal with
It should be noted that such peer affiliation may not always be positive. It could foster elitism in some cases, or interfere with social skills. Or ironically, for some gifted kids, a special program would take them away from peers rather than bring them closer. Peership is not necessarily about mutual expertise in mathematics or some other academic subject--it could have to do with character or shared interests. There could be a lot of variation between individuals with respect to this.
3) educators should be aware of the phenomenon of eager parents pushing their children, driven by the parents' pride or ego or perhaps well-meaning but misguided notions as to what is best or healthiest.
4) Regardless of whether children are in a gifted program or not, and regardless of these kids' talents, their academic program during childhood should allow for a balanced, healthy lifestyle. There should never be so much homework that kids would not have time for sleep. Lengthy commutes to and from some special school program, taking 1-2 hours of time daily, should be understood to have a negative impact on a teenager's mental and physical health -- these are hours that could have been spent playing or exercising or socializing or sleeping or studying.
5) Rushing children through 5 years of high school in just 2 years, even when the kids are very capable intellectually to do this, necessarily will narrow the academic breadth of learning, even for the brightest of children. Consideration should be given of broadening what is offered, over a longer period of time, rather than narrowing over a short period.
6) For particular subjects such as literature, it will not be possible to introduce as much breadth of content in a confined period, whether the students are gifted or not. Furthermore, many gifted programs are so oriented towards students who are destined to study engineering or other hard sciences, that English is glossed over. In some cases the program may be engaging in some degree of grade inflation regarding literature courses, so that the students end up spuriously receiving good enough English grades to get university admission, even though their actual performance is mediocre or poor. Mind you, this touches on the subject of university admission criteria--a genius-level student in mathematics perhaps should not be expected to have high grades in English or history in order to gain admission to an advanced university math program. Demanding high grades across the board for university entrance discriminates against those who have focal areas of excellence but also focal areas of academic weakness. However, giving high grades in English to students who lack literary skills is unfair to those who have true excellence in literature, and demeans the subject.
The converse problem is often present in university-level literature courses. There is a tradition of professors giving very low grades in university English courses, often with the highest grade being in the mid 80's, very few students earning an A, and very few students actually able to change their grade through a term by following any type of constructive feedback from the instructors. I suspect that if student essays in these courses were objectively and blindly graded by a panel of professional writers and journalists, we would not see good correlations with the professors' grading. I suspect that adherence to what Steven Pinker called "academese" is unfortunately rewarded, rather than good writing. This issue may also be amplified by insecurity within this academic community, giving a false sense of importance of the subject by giving low grades to most students.
7) For scientific subjects, cramming students through high school level courses quickly may well facilitate successful early university entrance, into engineering or physics programs etc. But often the curriculum offered is narrow. A gifted program could instead offer greater breadth rather than only greater speed of traversing curricula. For example, adjunctive courses in statistics would be tremendously useful for any science prodigy, but this material is usually neglected, in favour of advanced calculus or computer science etc. An enjoyably broad survey of scientific subjects would also be possible for gifted students, to gain a basic understanding of astronomy, geology, meteorology, climate science, ecology, botany, evolutionary biology, etc.
8) Arts subjects are often neglected in gifted programs. Breadth in arts and literature could involve studying a wider range of contemporary and historic literature, including a survey of world literature outside the usual western focus. Many gifted programs tragically do not have robust opportunities for students to participate in performing arts or fine arts activities such as dance, theatre productions, or visual arts.
9) It is absolutely unacceptable for children not to have regular physical education. This doesn't necessarily require sports teams, etc. (although this should probably be an option), but a culture of regular, daily fitness is a foundation of a mentally and physically healthy lifestyle. It is one of the things that teachers would definitely be in a leadership position to offer.
10) Subjects relating to basic well-being, self-care, etc. are often neglected. This could include courses in nutrition, food preparation, practical life skills, social and conversational skills, psychology (including an introduction to CBT), and personal finance.
11) Some gifted programs can become an insular niche. It could be valuable for new staff trainees to rotate through regularly, to prevent such programs from stagnating, and to allow constructive feedback to occur so that staff can maintain or improve skills, perhaps with constructive feedback invited from students, parents, and alumni of the program.
In assessing programs of this type, it is perilous to gather data only through something like an external review. Such reviews are often "corporate" style as though one were assessing a factory. If there were serious problems, often staff would be reticent to discuss them, since they might fear losing their jobs. The data gathered would be cross-sectional or testimonial in nature. This could highlight very serious issues with leadership, safety, incompetence etc. Once again, in order to guide sound policy on this matter, RCT data would need to be gathered systematically, such as by doing a prospective randomized study of two or three different approaches to help gifted children, compared with a control group, with a sufficient number of participants, repeated over many years of time. Such data would likely be "noisy" just as it is in psychotherapy research, because often the strengths or weaknesses of a program are strongly impacted by the particular individual teachers, rather than the style or format.
In the meantime, simple alternatives for students who are much more academically advanced than their peers could include allowing the freedom to take individual university-level courses before having graduated from high school at all. Each student could possibly have an individualized plan to help them, perhaps with exposure to advanced material in one area of their life, while having an "ordinary" childhood experience in other areas, depending on that student's wishes or needs.
Another issue with policy that is usually neglected is consideration of the well-being of the teachers and other staff. If teachers are bogged down by administrative duties such as long, pedantic meetings or obsessively detailed report cards etc., are restricted in their actions through micromanagement or rigid policy, or are simply overworked without time for their own self-care, this is harmful not only to the individual teachers but obviously to the students as well. One of the roles of a teacher, for any student, gifted or not, is as a stable, healthy, happy, mentor, who can engage in work in a sustainable, enjoyable way. A teacher who is stressed out, overworked, unhappy, trapped in an unhealthy bureaucracy, etc. is less available and effective for the students. Gifted students could be particularly harmed by this, since many of them would have a tendency to push themselves too hard, to the detriment of their mental health. They would need to have adult role models who have balanced lifestyles, and time for personal connection. A negative environment of this type cannot be hidden: children often have a really good idea about what's going on even when problems are not spoken about.
As a psychiatrist, with decades of experience working with a university student population, I have seen many gifted young people. While many young people in this population are outstandingly happy and mentally healthy, often going on to amazing achievements in their personal and professional lives, there are many mental health phenomena that are more common in this group, such as autism-spectrum symptoms, perfectionism, obsessive-compulsive phenomena (both OCD & OCPD), eating disorders, and sometimes narcissistic traits. There have been cases of major mental illnesses and suicides. In general, I have not found that people in this group have been helped dramatically by their high school gifted program, though many of them would have positive things to say about it. Usually in their accelerated program, they did not have time nor were they offered any compelling help for mental health issues or to simply have the healthy, well-balanced lifestyle that would have benefited them. Often they had inordinate pressure from parents. I can think of one very gifted scholar who didn't want to "develop" their gift at all, but felt obligated to because of the high expectations of parents, teachers, and even self. In many cases, the programs led to these students being in a university too young. In many other cases, I think these students would have thrived regardless of what type of program they were in during high school. But they probably would have had more opportunity for exploration, fun, and play had they started university at a more typical age.
This subject speaks to a broader issue of "giftedness." Everyone is gifted, in the sense that we have beautiful qualities which need to be cared for or developed. But development of gifts must occur in a way that is compatible with physical, mental, social, and community health. Gift development may require special resources, but we should resist the urge to drive this development at the fastest possible pace. Sometimes such an intensive but well-meaning drive can damage people, and damage their gifts, rather than help them.