Prediction of Independent Measurements

[Yughaber]

Hello! 

I have a set of data with two independent measurements, these are of two different valves (let's call them valve 1 and valve 2) placed on a patient during specific procedures that measure different pressures. I am looking for the best statistical method using SAS to analyze my data so that I can answer the following question: Will a change in the measurement/pressure of valve 1 allow me to predict a change in valve 2?

The measurements have been recorded multiple times of the same subject in different situations so that to make sure to capture the change in pressure of valve 1 and valve 2 if any at different times (thinking it would help with the statistical analysis/prediction that if something changes in valve 1 it'll allow us to predict a change coming in valve 2). The data is numeric. 

Thanks! 

[Rick_SAS]

From your description, it sounds like the first variable is "Independent," meaning that you can control its value, and the measurement at the second valve is observed, which means it is dependent on the first. 

This sounds like a classic regression problem in which you model the pressure at valve 2 as a function of the pressure at valve 1.  

Which procedure you use depends on the design of the experiment and how you want to model the relationship. 

1. Are all your measurements on the same patient, or do you have multiple patients (subjects) and measurements for each? 
2. When you graph the relationship, does it look like a straight line or does the relationship look nonlinear?
3. Is there any theory that suggests a particular parametric form for the model?

[Yughaber]

I would feel comfortable using a classic regression, however, my variables are both independent. Meaning pressure in valve 1 does not cause the pressure in valve 2 and vice versa. I have multiple subjects and multiple measurements for each subject. 

[Rick_SAS]

Regression is not about causality. You have an observational study in which you are observing two variables. You want to know whether you can predict P2 (conditionally) from the observed value of P1.  Regression can do that without requiring that P1 causes P2.

[PaigeMiller]

If you really mean you have two correlated independent variables rather than one independent and one dependent variable, the the first principal component dimension will allow this prediction. (In this case linear regression gives different answers depending on which independent variable you choose as the dependent variable.)

It sounds to me like the pressure in valve 1 does not "cause" the pressure in valve 2, and vice versa, the pressure in valve 2 does not "cause" the pressure in value 1, but they are correlated? Is this correct?

[Yughaber]

Yes! That is correct, I do have two independent variables. The pressure in valve 1 does not cause the pressure in valve 2 and vice versa but they are correlated. And so I want to know how well a change in valve 1 will allow me to predict a change in valve 2

[Yughaber]

I forgot to mention that I do have multiple measurements of those two valves (at different time frames) on the same subjects

[Rick_SAS]

Please provide some sample data so we can see its structure and the names of variables. Maybe your variables are something like
Subject   Time  Pressure1   Pressure2

[Yughaber]

Subject      valve 1 pressure standing position     valve 2 pressure standing position      valve 1 pressure sitting position     valve 2 pressure sitting position     etc. 

1                           120                                                         115                                                          90                                                 86

2                           118                                                         114                                                          89                                                 83

3                           112                                                         106                                                          80                                                 76

4                           116                                                         112                                                          87                                                 82

5                           119                                                         115                                                          85                                                 80

[PaigeMiller]

Well, other than the multiple measurements, this is a job for using the first Principal Components vector to do the predictions. Once you include the multiple measurements at different time periods, I don't know how to do this. I'll have to think about it.

[PaigeMiller]

---

@Yughaber wrote:

Subject      valve 1 pressure standing position     valve 2 pressure standing position      valve 1 pressure sitting position     valve 2 pressure sitting position     etc. 

1                           120                                                         115                                                          90                                                 86

2                           118                                                         114                                                          89                                                 83

3                           112                                                         106                                                          80                                                 76

4                           116                                                         112                                                          87                                                 82

5                           119                                                         115                                                          85                                                 80

---

Where are the different time frames that you mentioned?

By "different" do you mean that one subject/observation could be measured at times 1 3 and 5 while another subject/observation could be measured at times 1 3 8 10?

[Yughaber]

Actually, I found out that the time frames don't matter in answering the question. The change of positions have also been done to ensure that a change in pressure in valve 1 will still allow us to predict a change in valve 2. 

[Rick_SAS · Accepted solution]

If you are in a class, you should use the method that you have learned about in class. For example, you could use PROC GLM if you choose to ignore that the measurements are for different subjects. If you want a model that takes subjects into account, you could use a mixed model, like the following:

data Have;
length Position $8;
input Subject Position valve1 valve2;
datalines;
1  Standing  120 115
1  Sitting    90  86
2  Standing  118 114
2  Sitting    89  83
3  Standing  112 106
3  Sitting    80  76
4  Standing  116 112
4  Sitting    87  82
5  Standing  119 115
5  Sitting    85  80
;

proc sgplot data=Have;
   scatter x=Valve1 y=Valve2 / group=Position;
run;

proc mixed data=Have;
   class Subject Position(ref='Sitting');
   model Valve2 = Valve1 Position /  s chisq outpred=MixedOut;
   random intercept / subject=Subject;          /* each subject gets its own intercept */
run;

proc sort data=MixedOut; by Position Valve1; run;
proc sgplot data=MixedOut;
   scatter x=Valve1 y=Valve2 / group=Position;
   series x=Valve1 y=Pred / group=Position;
run;

Others might have alternative suggestions.

[Yughaber]

This looks very nice, thank you!! 

I guess my question remains with the proc mixed part of the code. Does that carry out a regression? and the (ref='Sitting') is what I am not clear on as well.

[Rick_SAS]

I have some impending deadlines,  but I suspect that others can answer your remaining questions. Good luck.