There are two ways to establish a causal link between a sedentary lifestyle and health outcomes.
The first is directly. This could be done through, for example, an experiment. You make it attractive for one group of people to sit more and for one group of people to sit less and then compare the outcomes after a number of years. This is really difficult to do. Most studies that I've heard off go for almost the next best thing. They look at the decisions themselves and try to rule out as many explanations as possible why people who decide to sit more also might have worse health outcomes (e.g. weak / sick people move less, but they also have worse health outcomes). What I have not seen yet is a study where they use some quasi-random variation such as an instrument. An instrument would be something that causes people to sit more or less but does not cause people to have worse or better health outcomes at the same time.
The second is indirectly. An indirect example would be a consistent model of health outcomes that has observable implications. If this model would also link a sedentary lifestyle to worse health outcomes, then we could be confident about this link, though not necessarily about its magnitude, because the observable implications of the model passed severe tests. This is such a model I believe.
The difference between the direct and the indirect link is this. In the case of the direct link we can run tests to rule out any alternative explanations for the effect. In the case of the indirect link we can run tests to rule out any model which has as one of its observable implications that a sedentary lifestyle leads to worse health outcomes by testing its other observable implications. In the case of the direct link we believe that there is a causal link because we have ruled out other alternative explanations that we are aware off and that we believe we have controlled for. In the case of the indirect link we believe that there is a causal link because we have ruled out any other explanations but the one that has as its implication that there is a link between a sedentary life style and worse health outcomes.
The reason that I believe that there is a link between a sedentary lifestyle and health outcomes is based on:
- The observational studies that suggest there is;
- The observational studies that suggest that the consequences of a sedentary lifestyle are bad;
- On what we know about muscle tissue and its response to exercise;
- On what we know about the brain and its response to exercise.
I don't believe in it because of any study showing a direct link, but I do believe it because of all the evidence being consistent with a models where a sedentary lifestyle is bad for health outcomes.
The reason that I act on this belief is that I notice it in myself that when I force myself to move more that I feel better and that I am more productive afterwards. I consider this a short run health outcome. Health being defined in terms of how well you are able to function.
This doesn't directly answer your question. But I hope it helps you think in broader terms than studies showing a direct link. Ask yourself what models of health you have in mind which implies such a link and what sort of evidence is consistent with this model and what evidence is not.