# Statistical tests - help please!

#### HGHG

##### New Member
Hi all,

I am writing a project plan and I am struggling with the statistical analysis plan as I am in the early stages of learning. I was hoping someone could guide me with what stats tests I could conduct with the following primary endpoint - thank you.

Alternative hypothesis: treatment is superior to placebo in achieving a state of pain relief.
Primary endpoint: difference in time to initial meaningful pain relief comparing the treatment Vs placebo.

I am thinking of the following analysis: As time is continuous and I am are comparing between categorical data (treatment, placebo), then I need a t-test (or Mann-Whitney depending on what the distribution will look like). With a continuous outcome, I also need to look at linear regression modeling?

Thank you for your help - much appreciated.

#### GretaGarbo

##### Human
Primary endpoint: difference in time to initial meaningful pain relief
A response variable like time will often have a skewed distribution. (And there is nothing "wrong" with that. Nature is what it is.)

So I would not be surprised if you would need to transform the time variable, like taking the square root or doing the log-transformation. (Also look at Box-Cox transformation.)

Or you could use a generalized linear model with a gamma distribution. (That would be like doing a t-test but instead of a normal distribution a gamma distribution is used. And a gamma distribution is a skewed distribution. Thus I would guess that it is realistic in this case.

A warning about Mann-Whitney: That is based on assumptions too. Mann-Whitney is sensitive to "spread". I would not be surprised if the mean time variable is different for treatment and placebo, but also that the the standard deviation might be different. And then the Mann-Whitney gives an increased error rate when the "spread" is not the same.

#### HGHG

##### New Member
A response variable like time will often have a skewed distribution. (And there is nothing "wrong" with that. Nature is what it is.)

So I would not be surprised if you would need to transform the time variable, like taking the square root or doing the log-transformation. (Also look at Box-Cox transformation.)

Or you could use a generalized linear model with a gamma distribution. (That would be like doing a t-test but instead of a normal distribution a gamma distribution is used. And a gamma distribution is a skewed distribution. Thus I would guess that it is realistic in this case.

A warning about Mann-Whitney: That is based on assumptions too. Mann-Whitney is sensitive to "spread". I would not be surprised if the mean time variable is different for treatment and placebo, but also that the the standard deviation might be different. And then the Mann-Whitney gives an increased error rate when the "spread" is not the same.

Would it be best to suggest linear regression modeling and then further details/choice of tests can be made once the data is available?

Thank you very much.

#### Karabiner

##### TS Contributor
Will "initial meaningful pain relief" be achieved by each subject? No premature
termination of study participation, for example?
If not, Cox regression or even Kaplan-Meier survival analysis might be useful.

With kind regards

Karabiner

#### HGHG

##### New Member
Will "initial meaningful pain relief" be achieved by each subject? No premature
termination of study participation, for example?
If not, Cox regression or even Kaplan-Meier survival analysis might be useful.

With kind regards

Karabiner
So, the subjects may not complete the treatment/placebo intervention and so, they will be instructed to take rescue medication. In this case, I should take into account what you have suggested?

Thank you,

#### Karabiner

##### TS Contributor
Well, I do not know anything about topic, research questions, allocation to groups,
recruitment, treatment, measurements, sample size of your study. Therefore I cannot