Testing linear trend

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Testing linear trend

Hi all.

Let's say I have 4 doses of the same medication, and record some Y response variable for a couple of patients for each dose.
If I want to test linear trend of Y for doses, I find in the SAS documentation

PROC GLM DATA=... ;
CLASS dose ;
MODEL y = dose ;
CONTRAST "linear trend" dose -3 -1 1 3 ;
RUN ; QUIT ;

and that if the contrast test ends up with a p-value small enough according to my sample size, I accept the linear trend.
If someone can explain in a mathematical (or in plain English) how come the inequality that -3 Mean(Y|dose=1) - Mean(Y|dose=2) + Mean(Y|dose=3) + 3 Mean(Y|dose=4) ^= 0 is equivalent to "Mean of Y increases linearly with dose", I'd be really delighted.
I've asked french Tech Support, but got no real explanation until now (just "that's how it works" but no further justification).

Thanks in advance.
Olivier
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