Minimum Detectable Effect Size (MDES)

[Adele3]

Hello,

I am trying to calculate the minimum detectable effect size of my main exposure variable with 80% power for my multivariable linear regression model using proc power. My model includes 6 predictor variables and a sample size of 500. When I run the below code to obtain the partialcorr (smallest detectable effect size), I am getting an error. Is someone able to provide help with my code? Thank you for your time and consideration!

proc power;
     multreg
     model = random         
     nfullpredictors = 6
     ntestpredictors = 1    
     partialcorr = . 
     ntotal = 500
     power = 0.8
     alpha = 0.05;      
run; 

[Quentin]

When your question is about an error, please post the log including the error message. 

Below is the log I get from running your code.  It looks like partialcorr=. is an invalid value.

1    proc power;
2         multreg
3         model = random
4         nfullpredictors = 6
5         ntestpredictors = 1
6         partialcorr = .
                        -
                        22
                        200
ERROR 22-322: Syntax error, expecting one of the following: a numeric constant, a datetime constant.
ERROR 200-322: The symbol is not recognized and will be ignored.
7         ntotal = 500
8         power = 0.8
9         alpha = 0.05;
10   run;

NOTE: The SAS System stopped processing this step because of errors.

Is that the error you get?

[Adele3]

Hello @Quentin, 

Yes, that is the error that I am getting. Thank you for sharing it - I will be sure to post in future. 

[FreelanceReinh]

Hello @Adele3,

In cases like this you can set NTOTAL to missing, compute the sample size for a suitable range of PARTIALCORR values (using a small step size) and then select the value which returns your planned sample size:

ods select none;
ods output output=want;
proc power;
     multreg
     model = random         
     nfullpredictors = 6
     ntestpredictors = 1    
     partialcorr = 0.1 to 0.2 by 0.0001
     ntotal = .
     power = 0.8
     alpha = 0.05;      
run; 
ods select all;

proc print data=want;
where abs(ntotal-500)<5;
var power partialcorr ntotal;
format _all_;
run;

Result:

                  Partial
Obs     Power       Corr     NTotal

252    0.80058     0.1251      504
253    0.80042     0.1252      503
254    0.80026     0.1253      502
255    0.80010     0.1254      501
256    0.80073     0.1255      501
257    0.80057     0.1256      500
258    0.80040     0.1257      499
259    0.80024     0.1258      498
260    0.80007     0.1259      497
261    0.80070     0.1260      497
262    0.80052     0.1261      496

[Adele3]

Hello @FreelanceReinh ,

This is wonderful, thank you very much for sharing your code! I greatly appreciate you taking the time to provide your help. 

In follow-up, I have run my multivariable model using PROC GLM with the EFFECTSIZE option to calculate the observed partial correlation for my exposure of interest, by taking the square root of the partial eta-squared for my exposure variable (r = √ 0.0001 = 0.01; output below). Given my observed partial correlation (r = 0.01) is smaller than the a prior partial correlation (r = 0.1256), could this suggest that:

• no meaningful effect exists between my exposure and outcome, or

• my model lacks sufficient power to detect a subtle true effect, if one exists

Thank you again for your help.

[FreelanceReinh]

You're welcome.

So, you're using PROC POWER not in the planning phase of your study, but rather for a "post-hoc calculation" ...

---

@Adele3 wrote:

Given my observed partial correlation (r = 0.01) is smaller than the a prior partial correlation (r = 0.1256), could this suggest that:

• no meaningful effect exists between my exposure and outcome, or

• my model lacks sufficient power to detect a subtle true effect, if one exists

---

Possibly, but I can't give a definitive answer off the top of my head. Therefore, I suggest that you start a new thread with this follow-up question in the Statistical Procedures forum, where it is more likely to get the attention of the linear models experts. (The "SAS Procedures" forum is rather about Base SAS procedures.) You can provide a link to the current thread to show where the "0.1256" comes from.

In parallel, I will take a look into my statistics book collection regarding your question and perhaps run a simulation.