I think that these two recent articles could be very useful to give an answer to your question.
Andreotti AM, Goiato MC, Nobrega AS, Freitas da Silva EV, Filho HG, Pellizzer EP, Micheline Dos Santos D. Relationship Between Implant Stability Measurements Obtained by Two Different Devices: A Systematic Review. J Periodontol. 2016 Oct 21:1-13.
Feng SW, Chang WJ, Lin CT, Lee SY, Teng NC, Huang HM. Modal damping factor detected with an impulse-forced vibration method provides additional information on osseointegration during dental implant healing. Int J Oral Maxillofac Implants. 2015 Nov-Dec;30(6):1333-40.
I must admit that I have not found radiographs to be a very effective way of assessing osseointegration. Radiographs may be, in some instances, an effective way of identifying clear lack of integration but when it's visible on an x-ray the implant is a almost always mobile. So the radiograph trails the mobility in most instances.
There certainly have been a number of techniques that have been used over the years. The first was simple tapping of the implant with a mirror handle to hear it either create a sharp retort, sometimes described as ringing, or to create a dull thud which is quite indicative of an implant that has not achieved integration. Tapping implants was reported early but eventually the description of reversed torque on the implant was described.
In essence if an implant could not sustain a reversal or loosening torque, a counterclockwise rotation, it was believed that such an implant would not achieve integration. There have however been a number of descriptions that look at the issue of "spinning implants". These are implants that lack rotational stability meaning that you can continue to rotate either clockwise or counterclockwise without much resistance. Balshi et al (Balshi, S. F., et al. (2007). "A retrospective analysis of 44 implants with no rotational primary stability used for fixed prosthesis anchorage." International Journal of Oral & Maxillofacial Implants 22(3): 467-471.) Provided a description of such implants and demonstrated that the cumulative survival rate of the implants that lacked primary rotational stability was no worse or better than Implants the did achieve primary stability. If an implant in such a situation were evaluated early in the healing phase it's possible that an implant could exhibit rotational movement and then if left undisturbed still achieve osseointegration. I would suggest that most clinicians who have treated a few thousand implants would probably agree that pure rotational movement at the early phases of healing let's call that less than six weeks in the absence of pain on rotation is still compatible with an implant achieving osseointegration. So the reverse torque test gradually fell out of favor. It fell out of favor because it was not an absolute. If an implant were torqued too soon and the implant unscrewed that did not mean that it would not have achieved integration had it not been allowed to remain undisturbed for perhaps another few weeks.
The periotest was used to evaluate its ability to confirm that osseointegration had occurred. Remember this was a device that was used to test tooth mobility not implant mobility. It was somewhat predictive of implants that were not reaching osseointegration milestones and probably had some value as a predictive device, Predicting failure of the implant or a negative prediction, with an implant that was not fully integrated when assessed.
The most current device, one that has been around for more than a decade, is the resonance frequency value (RFA) device from Osstell. This creates an implant stability quotient (ISQ) that can be measured at the time of implant placement in some time thereafter that would demonstrate the relative stiffness of the implant in bone. Since primary stability is a mechanical stability and since secondary stability is a Biologic stability there is a gradual decrease in mechanical stability over the early phase of healing that is counteracted by the biologic stability that occurs in later phases of healing. If you have a resonance frequency value at the time that the implant was placed and then another value sometime thereafter that demonstrates an increase in the resonance frequency value or the implant stability quotient you would consider this to be indicative of the achievement of osseointegration.
Remember, osseointegration is a biologic phenomenon. Even if an implant is loaded immediately this does not mean that it achieves immediate osseointegration. Biology takes time and we cannot anticipate that a Biologic phenomenon will ever occur immediately. This does not mean that immediate placement of implants into extraction sites or immediately loading implants that were placed in those same extraction sites is not a viable procedure. The key is to limit micro-motion to a level that allows osseointegration to still occur. Cameron et al Described the effect of micro movement on implant survival. (Cameron, H. U., et al. (1973). "The effect of movement on the bonding of porous metal to bone." Journal of Biomedical Materials Research 7(4): 301-311.) In 1973 this group started to look at motion and how it affected bone to implant contact. They described micro motion less than 29 µm as being compatible with bone healing and stated that micro motion above 150 µm would result in no osseointegration. Brunski, in an interview that was published in the newsletter, suggested that there is a critical amount of micro-motion that can be tolerated and still be compatible with Implant survival. He postulated that this was approximately 100 µm or less.
So as we look at this issue of Biologic achievement of osseointegration and try to correlate it with secondary stability the use of the resonance frequency values with an Osstell device seems pretty logical but it requires two measurements at two different time frames. Numerous articles, I think the number is over 800, have evaluated the resonance frequency values and have not established a specific value that indicates a high probability of success or a high probability of failure. It is the differential over time that gives one confidence that an increasing resonance frequency value will be associated with a high level of implant survival. I think the reason that no one specific value has been established and accepted relates to the fact that different Implant designs and different osteotomy configurations will result in different levels of insertion torque and, in all likelihood different levels of ISQ.
ultimately the goal is to have a device that you can utilize that will predict osseointegration before treatment is rendered. There have certainly been a number of reports that you can evaluate bone density and if the bone density is below a specific threshold the implant will not osseointegrate and if it's above that threshold it will. Conceptually it seemed like a good idea but then when we assess multiple splinted implants we have to realize that the splinting of Implants reduces micro motion. Further it's important to remember that the first generation of Implants in the osseointegration era were implants that were placed sub mucosal in an effort to avoid forces that could cause movement of the implant. If were evaluating bone density and using the reverse torque or the removing torque on a healing abutment in low bone density bone at an early phase of healing we will probably see a number of those implants coming out with the healing abutment. This might be a situation that could be rectified by creating a two-piece healing abutment with a center screw and a surrounding cylinder. The cylinder could be grasped with an instrument in the center screw loose and without creating torquing force on the Implant which may allow the implant in lower density bone to be impressed sooner without being disturbed at that earlier timeframe. Certainly worth consideration.