Does a dose-response relationship reduce sensitivity to hidden bias?

It is often said that an important consideration in judging whether an association between treatment and response is causal is the presence or absence of a dose-response relationship, that is, larger ostensible treatment effects when doses of treatment are larger. This criterion is widely discussed in textbooks and is often mentioned in empirical papers. At the same time, it is well known through both important examples and elementary theory that a treatment may cause dramatic effects with no dose-response relationship, and hidden biases may produce a dose-response relationship when the treatment is without effect. What does a dose-response relationship say about causality? It is observed here that a dose-response relationship may or may not reduce sensitivity to hidden bias, and whether it has or has not can be determined by a suitable analysis using the data at hand. Moreover, a study without a dose-response relationship may or may not be less sensitive to hidden bias than another study with such a relationship, and this, too, can be determined from the data at hand. An example concerning cytogenetic damage among professional painters is used to illustrate.