If many studies ignore the same cofounder, it doesn't matter that they are consistent because they are all biased in the same way.  Consistency doesn't prove anything on its own it needs to be combined with other criteria.

Potential Flaws with Consistency Criteria

Similar results were obtained in a number of studies on different target populations. Hill stresses the importance of duplicating findings, because a single study, however statistically reliable, cannot be used to prove causation because the threat to internal validity persists.

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- Strength of the association 
- Consistency 
- Specificity of the association
- Temporal relationship 
- Coherence 
- Biological gradient
- Plausibility
- Experiment
- Analogy


Hill’s Criteria list to determine causal significance

Pearl, J., & Mackenzie, D. (2018). $\mathit{The \ Book \ of \ Why: \ The \ New \ Science \ of \ Cause \ and \ Effect.}$ Basic Books.

The Book of Why

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4589117/

Detailed introduction of Bradford Hill criteria

Criteria 1: Consistency

The greater the link between exposure and disease, the more likely it is to be cause-and-effect, including the dose-response effect.

Criteria 2: Strength of association

A particular pathogen should have a specific effect, not a cascade of effects. Associations are more likely to be causal at certain times, meaning that exposure causes only one disease.

Criteria 3: Specificity of the association

Temporal relationship may be the only criterion that epidemiologists generally agree is necessary for causal inference. The cause should be followed by the effect. “Hill explained that for an exposure-disease relationship to be causal, exposure must precede the onset of disease. Thus, epidemiologic study designs which ensure a temporal progression between the two measures are more persuasive in causal inference”. 

Criteria 4: Temporal relationship

Consistency with biological plausibility and other types of evidence. Today, coherence is another area where molecular-based research has been used to prove an understandable story about exposure to various aspects of the disease paradigm. In addition, advanced mechanistic studies can illuminate on an incoherent epidemiological literature, thereby reinforcing causal reasoning in one direction or another.

Criteria 5: Coherence

Hill wrote that “if a dose response is seen, it is more likely that the association is causal.” According to the traditional interpretation of biological gradient, a monotonic biological gradient, wherein increased exposure resulted in increased incidence of disease, provides the clearest evidence of a causal relationship. 


Criteria 6: Biological gradient

Hill’s criterion of plausibility is satisfied if the relationship is consistent with the current body of knowledge regarding the etiology and mechanism of disease; though, Hill admitted that this interpretation of biological plausibility was dependent on the current state of knowledge. 

Criteria 7: Plausibility

Hill explained that evidence drawn from experimental manipulation—particularly epidemiologic studies in disease risk declines following an intervention or cessation of exposure—may lead to the strongest support for causal inference. 


Criteria 8: Experiment

Analogy has been interpreted to mean that when one causal agent is known, the standards of evidence are lowered for a second causal agent that is similar in some way.


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