NINDS Office of Research Quality has presented a proposal on how to address the publication bias. It can be watched HERE (starts at ~1:17): 

We were a bit surprised that preregistration was not discussed until a Q&A session (at ~1:53:17):

On the one hand, we agree that preregistration always come with an extra effort and preregistered reports require more efforts and time that may not be there if studies need to be executed soon after the study plans have been finalized.  

On the other hand, our concern is not only that studies with negative (null) results are not published but also that we are simply not aware of such studies being conducted.  

In fact, when we talk about preregistration in clinical research, we must not forget that it started with just preregistration and, once most/all studies undergo preregistration, further measures are introduced such as mandatory uploading of study results to the clinical trial registry – and one day we will see results of most well conducted studies being published even if the results are negative/null.  

Why not following this path for preclinical research? Why can’t funders not require that all key studies / experiments are preregistered? Why can’t this be done at least for in vivo research? Why can’t animal welfare authorities mandate that?