Causal null hypotheses of sustained treatment strategies: What can be tested with an instrumental variable?

Sometimes instrumental variable methods are used to test whether a causal effect is null rather than to estimate the magnitude of a causal effect. However, when instrumental variable methods are applied to time-varying exposures, as in many Mendelian randomization studies, it is unclear what causal null hypothesis is tested. Here, we consider different versions of causal null hypotheses for time-varying exposures, show that the instrumental variable conditions alone are insufficient to test some of them, and describe additional assumptions that can be made to test a wider range of causal null hypotheses, including both sharp and average causal null hypotheses. Implications for interpretation and reporting of instrumental variable results are discussed.