How do I set up contrasts in npar1way?

[normanbg]

    I have a data set consisting of 4 independent samples: W_C, W_T, M_C, M_T. I wish to test the difference (W_C - W_T) - (M_C - M_T). Normally I would do a two-way ANOVA and look at the interaction term, but my samples sizes are very small.
    I thought of Kruskal-Wallis in npar1way with apriori contrasts of the form
                1        -1        -1        1
but I can't seem to find any way to set this up.
    My experience with SAS (long but limited) has taught me that it can do just about anything, and do it well, if you can figure out how.

    Can anybody help (SAS University Edition 9.4)?

[art297]

Not sure if the following exactly matches what you are trying to do, but I think it may come close: https://communities.sas.com/t5/SAS-Procedures/proc-npar1way-contrasts-statement/td-p/265531

Art, CEO, AnalystFinder.com

[normanbg]

Dear Art,

    Thank you for your quick reply.

     Actually, before posting, I did a search of the forum and came up with the exchange you refer me to. Unfortunately, the solution there is for multiple pairwise comparisons whereas I require a difference of a difference. I couldn't (and still can't) see how to get from the one to the other—can you?

[Ksharp]

Since you have a small data, why not try EXACT statement of PROC NPAR1WAY or PROC FREQ ?

[normanbg]

Dear Ksharp,

    Thank you for your quick reply.

    I do use EXACT in Npar1way but can only figure out how to test all 4 samples using Kruskal-Wallis or how to compare various pairs using a BY variable; I would be very grateful if you could be more specific on how to test the difference of a difference: (D-C) - (B-A).

[Ksharp]

Sorry. I am not expert about it. I would leave it to @SteveDenham @lvm @Rick_SAS

[normanbg]

Can I turn to them directly or do I have to wait (and hope) that one of them will chance by?

[Rick_SAS]

When someone is mentioned by name in a post, they receive a notification. It is a breach of etiquette to explicitly contact someone you don't know for help. Be patient: if someone has the knowledge and the time, they will offer a suggestion.

If you provide a reference and sample data, you are more likely to get a response

I don't know how to do what you ask. You might need to transform your data from wide to long and use two group variables to encode the data, like this

CLASS Group1 Group2;

VAR Value;

[normanbg]

Dear Rick,

     Thank you, now I know.

     It is evening here and I can answer properly only tomorrow. In the meanwhile, I have a couple of preliminary questions.

     What do you mean by 'provide a reference'?

     My data is in an Excel file (14 lines); would it be alright just to copy it (together with the sas program that reads it and the npar1way code) so the reader can get the idea, or should I convert it to an actual SAS data statement?

[Rick_SAS]

> provide a reference

A reference is a book, article, or web site where the reader can go to learn more about the question you are asking.  For example: 

"I want to run the SuperCool Test from Jones and Smith's 1999 textbook "Cool Statistical Tests"  (2nd ed, p 129)"

or

"At the web site www.SuperCoolTest.net they show how to conduct the SuperCool Test in [STATA, MATLAB, R, SPSS, PYTHON,...].

or

"The example in the SAS documentation [LINK] shows how to do the SuperCool analysis. However, my data has missing values and I get the following error: ..."

> how to supply data

Data on the forums should be supplied in the form of a SAS DATA step. Some people object to downloading Office files because of a perceived security risk. You can use PROC IMPORT to create a SAS data set, then use a macro program to generate a SAS DATA step. You can also use any of the 200 SASHELP data sets, which are distributed with SAS . For example, SASHELP.Cars, SASHELP.Class, SASHELP.Iris, SASHELP.BWeight, etc, 

[normanbg]

Oh, those kinds of references. I know all about them, I'm a scientist. I thought it was something specific to SAS.

I'll be back tomorrow, with a full (short, but functioning) sas program and a little of the science behind it.

[normanbg]

    The purpose of the experiment is to determine whether a particular drug (the treatment T) has a greater effect in genetically modified mice (Mut) than in normal mice (Wild-Type).
    Four independent groups of mice are selected: normal untreated (WT_C), normal with drug (WT_T), mutants untreated (Mut_C), and mutants with drug (Mut_T). The variable under study is a particular parameter of cardiac function we will label 'X'.
    It is well-known from the literature that T decreases X in WT mice. There is less evidence for this mutant strain, but here too T appears to decrease X. When X is (more or less) normally distributed and sample sizes are adequate, we would use a two-way ANOVA

                                                        treatment
                                                   no                yes
                        wild-type        WT_C            WT_T
         genome
                        mutant          Mut_C            Mut_T

 and test the interaction term:    genome x treatment.
    But the experiment is long and difficult and costly, and our entire sample size is only 14. So we have no choice but to use an exact nonparametric test, and I thought of npar1way with apriori contrasts of the form

                                            1    -1    -1    1

but I can find no way to set this up, basically (WT_C - WT_T) - (Mut_C - Mut_T).
    The short sas program below produces two exact Mann-Whitney tests, WT_C versus WT_T and Mut_C versus Mut_T; without the 'by' statement, one gets the exact Kruskal-Wallis test for all 4 groups. The number of cases in each group is correct (3,5,2,4) but I have not used the original X values.

ODS RTF File        ="/folders/myshortcuts/Norman/Ahmad/test-4.rtf" bodytitle;
data ahmad;
    input G$ X W;
    cards;
        WT_C 25 1
        WT_C 24 1
        WT_C 23 1
        WT_T 22 1
        WT_T 21 1
        WT_T 20 1
        WT_T 19 1
        WT_T 18 1
        Mut_C 23 2
        Mut_C 22 2
        Mut_T 15 2
        Mut_T 14 2
        Mut_T 13 2
        Mut_T 12 2
    ;
run;
proc npar1way data=ahmad plots=none wilcoxon;
    class G;
    by W;
    exact wilcoxon;
    var X;
run;
ODS RTF close;

[Rick_SAS]

I do not know how to do this analysis in NPAR1WAY; perhaps @PGStats might have an idea.

I will throw out an alternative suggestion: use QUANTREG, which has an ESTIMATE statement. The background/rationale for my suggestion is given in the article "Quantile estimates and the difference of medians in SAS." The estimate you are looking for is given below (I think, please double check my ESTIMATE statement, which is different from the one you suggested). Note that I changed the class levels to better reflect the two class variables.

data Have;
length G $3. W $1. Group $5.;
 input G X W;
 Group = cats(G, '_', put(W,1.)); /* create group variable that combines the 4 levels */
datalines;
WT  25 C
WT  24 C
WT  23 C
WT  22 T
WT  21 T
WT  20 T
WT  19 T
WT  18 T
Mut 23 C
Mut 22 C
Mut 15 T
Mut 14 T
Mut 13 T
Mut 12 T
;

proc quantreg data=Have;
 class Group;
 model X = Group / quantile=0.5;
 estimate 'Difference of Differences' Group -1 1 1 -1 / CL;
run;

:

[normanbg]

I'll look into it tomorrow. What do you think of

proc multitest data=ahmad perm;

    class G;

    contrast 'delMut - delWT' -1 1 1 -1;

    test mean (X);

run;

to follow proc npar1way (without the 'by' statement, of course), as suggested by Richter & Higgins (2006): "A SAS Companion for Nonparametric Statistics", Thomson Brooks/Cole, Belmont, CA, p.28?

[normanbg]

Dear Rick,
    Most of my (recent) SAS experience has been with version 9.1.3 and I was not familiar with QuantReg. I read the reference you gave and looked at the entry in the 9.4 manual. QuantReg would appear to be a very useful and versatile addition to my nonparametric arsenal, and I plan to devote more time to it when this project is over.
    But something is wrong with the code you suggest, and I don't (yet) know the program well enough to uncover what that is. I ran the data using QuantReg and then with npar1way followed by multtest as described in the little book by Richter & Higgins I cited above—the results were very very different: a p-value of 0.0542 from QuantReg, a p-value of 0.0075 (raw) and 0.0095 (permutation) from multtest.
    I then ran the Kruskal-Wallis routine implemented by NCSS (NCSS 10 Statistical Software (2015). NCSS, LLC. Kaysville, Utah) with custom contrasts; using 1 -1 -1 1, I got a p-value of 0.0075 here too.
    So why, you might ask, do I bother with SAS when I can get what I want with NCSS? Well, not quite. The p-value of 0.0075 provided by NCSS is the asymptotic value, and I am (was) looking for an exact value. That was why I turned to SAS>npar1way and that, I believe, is what I have now found in multtest (permutation).
    I would very much like your opinion on the npar1way>multtest combination.