Single word request: practice based on non-strict criteria

An academically suitable word may be one of the hyphenated adjectives based (amusingly, given your medical context) on ill. All are based on the idea that a solution or decision is to be based on some information but that the information is too poor to lead to a reliable result, or of such a nature that the result is very sensitive to small changes in the information.

Three candidates are ill-conditioned, ill-defined, ill-posed.

ill-defined = not clearly explained, described, or shown

Cambridge

ill-conditioned = In non-mathematical terms, an ill-conditioned problem is one where, for a small change in the inputs (the independent variables or the right-hand-side of an equation) there is a large change in the answer or dependent variable. This means that the correct solution/answer to the equation becomes hard to find

Wikipedia

ill-posed:

The mathematical term well-posed problem stems from a definition given by 20th-century French mathematician Jacques Hadamard. He believed that mathematical models of physical phenomena should have the properties that:

a solution exists; the solution is unique; the solution's behaviour changes continuously with the initial conditions.

Examples of archetypal well-posed problems include the Dirichlet problem for Laplace's equation, and the heat equation with specified initial conditions. These might be regarded as 'natural' problems in that there are physical processes modelled by these problems.

Problems that are not well-posed in the sense of Hadamard are termed ill-posed. Inverse problems are often ill-posed. For example, the inverse heat equation, deducing a previous distribution of temperature from final data, is not well-posed in that the solution is highly sensitive to changes in the final data.

Wikipedia

The academic precision of the last term may be the best fit to your specification.