Non inferiority in observational trial

[ChristosK]

Have beeen looking at various iterations of a paired t test using the TOST option to compare non inferiority, or relative non inferiority of 4 different methods of measuring blood pressure compared to a gold standard measure.

I cant really create one variable that accounts for all the different ways of measuring BP as they are measured in the same individuals at the same time. 

Any suggestions?

[ballardw]

I would expect that you have 5 variables, one for the 'gold standard' and one for each of the other measures, all on each record.

To do pairs of gold standard with each of the others a paired statement like where the m variables below are your other measures:

paired gold*( m1 m2 m3 m4);

If your data is structured differently such as each measure on a different observation than transpose the so the data looks as I expect above.

If you are wanting to use separate TOST bounds for each comparison than run a different Proc Test for each pair.

[ChristosK]

I tried this:

proc ttest data =dataMAP TOST (55 ,97) plots;
paired BI_A_MAP *(BI_device_MAP    BI_LA_MAP     BI_UA_MAP     BI_LL_MAP);
run;

I arbitrarily chose 55, and 97 because these values are at the 95% boundaries for the gold standard (arterial line).

The BI sets of measures are the first sets of measures but these are repeated at 3 min, 15 min, 30. min, 45, and 3 min post an event towards the end of a procedure.

I would have liked to find away to combine the data from all these time points into one measure (such as an AUC), but the conditions at these subsequent times are very different, so have concerns about that.

What I am trying to figure out is whether any of these ways of measuring mean blood pressure are close enough to the gold standard so as to be clinically useful and valid.

[ballardw]

Is there any reason to believe that any of these measurements are dependent on the ones at another time? If not then each time point should just be a different observation. Unless you are trying to pair 3 min to 15 min measures??

I would expect that if the data looked something like:

Patient time BI_A_MAP BI_device_MAP    BI_LA_MAP     BI_UA_MAP     BI_LL_MAP

then the paired differences should be okay. Unless there is another question than mean difference you are trying to answer but not articulated.

[ChristosK]

Much of the information contained within a MAP blood pressure at any given time is also contained in that same measure on the same individual at a subsequent time. These times are all taken only minutes apart, although the physiological conditions will be very different.

The question seems to be whether something needs to be adjusted for given that they are not completely independent of each other.

The goal would eventually be to combine each of the serial MAP measures into one pressure representing the overall value using that measuring instrument on this sample of individuals and to compare to  the overall measure using the gold standard, and the other measuring instruments against that gold standard.

[ballardw]

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@ChristosK wrote:

Much of the information contained within a MAP blood pressure at any given time is also contained in that same measure on the same individual at a subsequent time. These times are all taken only minutes apart, although the physiological conditions will be very different.

The question seems to be whether something needs to be adjusted for given that they are not completely independent of each other.

The goal would eventually be to combine each of the serial MAP measures into one pressure representing the overall value using that measuring instrument on this sample of individuals and to compare to  the overall measure using the gold standard, and the other measuring instruments against that gold standard.

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It seems that each time you change the requirements.

The goal would eventually be to combine each of the serial MAP measures into one pressure representing the overall value 

Sounds more like a regression approach to match your multiple simultaneous (or nearly so?) readings. Do these other instruments report in similar units to your "gold standard"?

I would be very tempted to try something that looked like:

proc reg data=have;
   model goldstandard = m1 m2 m3 m4;
run;
quit;

And take a look at the r-square to see how well the model fits. You may have to consider interactions between your other measures as well. If your r-square is "good" (close to 1) Then the result would be the equation on what needs to be "adusted" if any to get close to the gold standard.

However classic warning of regressions: 1) take a good look at the data before hand and 2) don't expect truly reliable results for values from you measurement variables that were not tested with a similar gold standard value.

Note the above is a very simple linear regression. Your data may indicate that one or more of the measurements has a non-linear relationship to the standard which may need to be addressed with a transform.

If your instrument readings are not independent then I would be very distrusting of the instrument. If I read the temperature on a thermometer a 12:00 and again at 1:00 there may be some association because air temperature has it's own resistance to change. But I would not think that the behavior of the 1:00 reading is actually influenced by the device behavior at 12:00.

[ChristosK]

I have tried various approaches such as Bland Altman plots, Linn's Correlation Coefficient, paired T tests etc.

The only thing I had not yet succeeded in is getting the each measure using each device to be represented by one single value which takes into account the serial measures.

All devices are measuring the same thing : mean arterial pressure in mmHg.

The gold standard is a radial arterial catheter which directly measures the pressures at the wrist.

Blood pressure cuffs were placed on the upper arm, lower arm, and calf, but the Mean arterial pressure is oscillometric, based on the pressure at which maximum fuctuations are sensed. 

The device that the trial was on is a fingertip device that measures pulsations. An algorithm based on trials of this compared to an arterial line reads out the  pressures.

I had really great and meaningful results with the concordance coefficient, but the relationship wasn't meaningfully consistent across each sampling time, so thats why I thought I could get something more meaningful if Included data from all time points into a model.

residuals are normally distributed in all the measures.

Untimately , the goal of the project is to determine whether any of the cuff measures or device is close enough to the arterial line to be clinically valid. The reason for this is that the population under study is not a normal, healthy sample of the general population.