For human health we use a number of general and specific tests that help understand the condition of people. Have any such tests been done and tested for fish?
There are several metrics that determine the health of wild fish, but the metrics vary widely depending on the question at hand and the fish population. First and foremost, in my opinion and experience in working with natural production of Pacific salmon, the metrics primarily involved are: 1) growth, 2) survival, and 3) abundance. For growth, laboratory-calibrated models that can account for known effects of temperature and fish size are used to estimate ration and growth in the wild. For survival , environmental factors and spatial and temporal effects on survival are examined to identify bottle necks that may limit populations. With respect to abundance, a sufficiently long time series is used to estimate natural fish production (e.g., recruits per spawner) as function of covariates that can be used in a population viability analyses to estimate extinction potential.
Note that I use the term naturally-produced fish, there are very few true wild fish populations in the US, most are supported by hatcheries, of which a fraction reproduces in the wild to assist in the supplementation of 'wild fish'. A big challenge with salmon in the PNW is to estimate the fraction of the natural population that is supported by hatchery production, In other words, How much do our natural populations depend on the production of hatchery fish?
The judging of wild population health is largely a matter of context involving the species, their habitat, the involved stakeholders (and available funds and information), and the perceived limitations to the population that may be used to improve population status. Ultimately though, measures of growth, survival, and abundance are the primary measures of interest for management, in my opinion.
Condition factor and indices of energetics such as hepatosomatic index are good estimates of fish health in wild. But they work only if compared to a control group