How many hypotheses? And secondary outcomes? Just wanted your opinion on whether you think its appropriate to have a 2nd hypothesis when you have included in your study a secondary outcome? And also do you think its appropriate to have more than one secondary outcome? I believe it should be fine but wanted to double check with you guys.
 A: There are usually several secondary endpoints in clinical trials, e.g. quality of life measures, occurrances of different sorts of adverse events, overall survival (if not primary endpoint) etc. Their number is not limited.
Your study protocol should


*

*define them appropriately (Example: Overall survival is defined
as the time from study inclusion to death. Patients still alive at
study end are censored at study end.").

*mention them in the secondary study objectives (Example:
"Secondary study objectives include the assessment of safety and
quality of live...")

*broadly describe how to analyze them. Ideally, this includes the
corresponding hypotheses. (Example: "Secondary time-to-event endpoints
are compared descriptively by Kaplan-Meier plots and medians; to
exploratory compare them between treatments, the null hypothesis of
equal distribution is tested using log-rank tests at the 5% level.
Adverse events are depicted using..."


Sample size justification is usually mainly based on assumptions on the primary outcome. However, if you have key secondary endpoints, it is nice to provide additional power analyses based on the chosen sample size.
A: Yes it's acceptable to have more than one hypothesis for a study. In fact, in many cases, it's a good idea. Most grants and clinical trials will propose 3 or more hypotheses. This is good science: it is expensive and risky to conduct a trial, so maximizing the information that we glean from it is actually a point of ethics.
I think the important rules of conduct are:


*

*State the hypotheses apriori: 
You can't use data which generate a hypothesis to
test that hypothesis.

*Declare a principal hypothesis: the first or the most important hypothesis under investigation should be clear.

*State if the hypotheses are considered sequential or parallel. A sequential hypothesis might look at a cancer drug to ask 1. Is it effective? 2. Is it safe? 3. Is it well tolerated? 


In some cases, you need to perform corrections for multiple comparisons. People have widely varying opinions about the need for this. I find it can be a point of contention between researchers and their reviewers. One point I make is that, when you have different "Y"s, each hypothesis represents a different qualitative thing you want to claim about the exposure or treatment. So, with the cancer drug, you first care if its effective. Then, if its effective, you are independently interested if it's safe, and/or well-tolerated.
