# Finding the type of test : Continuous variable, difference between two study waves

#### Dusan11

##### New Member
Hello everyone,

I am working on a population-based study including two waves (baseline and follow-up).

My variable of interest is computed using the two waves, and is the difference in renal function between follow-up and baseline (Delta = follow-up - baseline).
Renal function normally declines over time, so values at follow-up are lower than those at baseline (hence Delta < 0, normally).
However, in the actual data, I have approximately 2/3 of values whose Delta < 0 (expected), and 1/3 of values with Delta > 0 (unexpected, but is likely due to the fact that renal function values are imprecisely measured, and the time difference between baseline and follow-up is short : 3-4 years on average).

I would like to point out the fact that I am not a statistician, but a life-scientist, working with life-scientists on this project. My other colleague (life-scientist as well) asked me whether it is possible to show that there is a difference in the "N" between those individuals whose Delta<0 (2/3 of the sample size), and those whose Delta>0 (1/3 of the sample size).
I was puzzled by this request and couldn't find a proper answer. If I take the distribution of the variable "Delta", its mean is negative, and the 95%CI doesn't include the 0, indicating that Delta is indeed negative.
However, I am wondering whether this unusual request might be realized (comparison of the 2/3 Delta <0 and 1/3 Delta > 0 in terms of "N"). Indeed, if there was NO DECLINE in renal function, Delta would be centered around zero, and approximately 1/2 would be positive and 1/2 would be negative (given the imprecision of the variable)...

Any comment/suggestion would be appreciated =)

Thanks

Dusan

#### Karabiner

##### TS Contributor
If it makes your colleague happy when you perform meaningless statistical analyses
for him, then you can do a one sample Chi² test. You would test the Null hypothesis
that the proportion of subgroup d < 0 = proportion of subgroup d > 0 = 0.5.

With kind regards

Karabiner

#### hlsmith

##### Less is more. Stay pure. Stay poor.
As @Karabiner noted - this is a worthless pursuit. In particular, you lose an insane amount of data dichotomizing it into binary groups. How do you truly define a GFR value of 95 and then two years later it is 96 - as improving clinically.

I would model the second value predicted by the first value and time between the measures. You could add any other predictors as well if your sample size allows (e.g., hypertension, smoker, etc.). The model will tell you the post value controlling for time and initial value.