Multiple imputed computation of F-test with 2 or more df

[data_null__]

I need help to combine (MIANALYZE) the data below.  Specifically, I need the pooled TRT*SUBGROUP interaction p-value.

                                                                                                                                              Error
Obs    _Imputation_    Source              DF              SS              MS    EMS                                         ErrorTerm           DF     FValue     ProbF
  1          1         trt                  1      414.915078      414.915078    Var(Residual) + Q(trt,trt*subgroup)         MS(Residual)       294     115.30    <.0001
  2          1         subgroup             2      418.288785      209.144393    Var(Residual) + Q(subgroup,trt*subgroup)    MS(Residual)       294      58.12    <.0001
  3          1         trt*subgroup         2       21.702703       10.851351    Var(Residual) + Q(trt*subgroup)             MS(Residual)       294       3.02    0.0505
  4          1         Residual           294     1058.009621        3.598672    Var(Residual)                               .                    .        .       .    

I have the solution and understand that for a 1 df test it would be the same as T-test.  I think MIANALYSE can pool the solution, but I don't know if I can compute the trt*subgroup test from the pooled solution. 

Obs    _Imputation_    Effect            trt      subgroup    Estimate      StdErr      DF     tValue     Probt

  1          1         Intercept                               11.0516      0.2449     294      45.13    <.0001
  2          1         trt             Active                   2.3972      0.3817     294       6.28    <.0001
  3          1         trt             Placebo                       0           .       .        .       .    
  4          1         subgroup                     High        0.9031      0.3674     294       2.46    0.0145
  5          1         subgroup                     Low        -1.3336      0.3674     294      -3.63    0.0003
  6          1         subgroup                     Mid              0           .       .        .       .    
  7          1         trt*subgroup    Active       High        0.6155      0.5372     294       1.15    0.2528
  8          1         trt*subgroup    Active       Low        -0.7093      0.5423     294      -1.31    0.1919
  9          1         trt*subgroup    Active       Mid              0           .       .        .       .    
 10          1         trt*subgroup    Placebo      High             0           .       .        .       .    
 11          1         trt*subgroup    Placebo      Low              0           .       .        .       .    
 12          1         trt*subgroup    Placebo      Mid              0           .       .        .       .    

This is my example data.  

proc format;
   value $trtfmt 'Placebo'='Placebo' 'Active'='Active';
   value $sgfmt  'Low'='Low' 'Mid'='Mid' 'High'='High';
   quit;

data ex;
  call streaminit(7);
  length trt $8 subgroup $8;
  do id=1 to 300;
    trt = ifc(rand('Bernoulli',0.5),'Active','Placebo');
    subgroup = scan('Low Mid High', rand('Table', 1/3,1/3,1/3));
    /* mean structure with true interaction: treatment benefit increases by subgroup */
    base = 10
         + (subgroup='Mid')*1
         + (subgroup='High')*2;
    tx   = (trt='Active')*( 1
         + (subgroup='Mid')*1
         + (subgroup='High')*2 );
    y = rand('Normal', base + tx, 2);
    if rand('Uniform') < 0.25 then y = .;  /* 25% missing */
    format trt $trtfmt. subgroup $sgfmt.;
    output;
  end;
run;
proc print data=ex; run;
proc mi data=ex out=ex_imp seed=31415 nimpute=3;
   class trt subgroup;
   fcs reg(y = trt subgroup trt*subgroup);
   var y trt subgroup;
   run;
ods exclude all;
ods output SolutionF=pe  CovB=covb type3=type3;
proc mixed data=ex_imp method=type3;
  by _imputation_;
  class trt subgroup;
  model y = trt subgroup trt*subgroup / covb solution ddfm=kr;
run;
ods trace off;
ods exclude none;


proc print data=pe(where=(_imputation_ eq 1)); run;
proc print data=covb(where=(_imputation_ eq 1)); run;
proc print data=type3(where=(_imputation_ eq 1)); run;
ods trace on;
proc mianalyze parms(classvar=full)=pe edf=294;* covb=covb;
   class trt subgroup;
   modeleffects Intercept trt subgroup trt*subgroup;
   ods output ParameterEstimates=int_p;
   run;
ods trace off;
proc print;       ;
   run;

[SAS_Rob · Accepted solution]

MIANALYZE can only combine individual point estimates and cannot be used to combine F-tests specifically.  The theory itself is not very well-developed for combining multiple DF tests, especially Type 3 tests from MIXED, since Rubin’s Rules apply directly to parameter estimates and their variances, not to F-statistics.  

MIANALYZE does have a TEST statement and through the MULT option you can get a joint test based on the combined parameter estimates.  It does not allow these options with a CLASS statement, but you might be able to "trick" it into computing a type 3 hypothesis by dummy coding yourself and feeding those estimates into MIANALYZE.  Whether that is statistically valid or not however is not clear however.

[Ksharp]

John.King,

If you want to pool these p-value, check " proc multtest":

https://support.sas.com/kb/30/715.html

https://communities.sas.com/t5/Statistical-Procedures/Combining-LSMEANS-Output/m-p/957451#M47946

At second post, @SAS_Rob   showed you how to use proc multtest to pool p-value.