Lehmann (1975) and Dmitrienko et. al. (2005) discuss and illustrate a nonparametric test proposed by van Elteren (1960) for stratified or blocked continuous response data. This test is an extension of Wilcoxon's ranksum test and is also a MantelHaenszel mean score test. As such, it can be obtained using either PROC FREQ or, beginning in SAS^{®} 9.4 TS1M3, PROC NPAR1WAY. It tests the null hypothesis of no treatment effect in the strata. Validity of the test depends only on large overall sample size and not on the strata sizes. Also, normality of the response distribution is not required, so this test can be used when a twoway analysis of variance might not be valid.
The following example from Dmitrienko et. al. (2005) tests for drug effect in a data set from a clinical trial on urinary incontinence with patients from three strata. The response is the percent change from baseline in the number of incontinence episodes per week. Because the distribution of this response is skewed and therefore not considered to be approximately normal, a nonparametric test is preferred.
These statements create the data set of patient responses.
data urininc; input Therapy $ Stratum @@; do i=1 to 10; input change @@; if (change ne .) then output; end; drop i; datalines; Placebo 1 86 38 43 100 289 0 78 38 80 25 Placebo 1 100 100 50 25 100 100 67 0 400 100 Placebo 1 63 70 83 67 33 0 13 100 0 3 Placebo 1 62 29 50 100 0 100 60 40 44 14 Placebo 2 36 77 6 85 29 17 53 18 62 93 Placebo 2 64 29 100 31 6 100 30 11 52 55 Placebo 2 100 82 85 36 75 8 75 42 122 30 Placebo 2 22 82 . . . . . . . . Placebo 3 12 68 100 95 43 17 87 66 8 64 Placebo 3 61 41 73 42 32 12 69 81 0 87 Drug 1 50 100 80 57 44 340 100 100 25 74 Drug 1 0 43 100 100 100 100 63 100 100 100 Drug 1 100 100 0 100 50 0 0 83 369 50 Drug 1 33 50 33 67 25 390 50 0 100 . Drug 2 93 55 73 25 31 8 92 91 89 67 Drug 2 25 61 47 75 94 100 69 92 100 35 Drug 2 100 82 31 29 100 14 55 31 40 100 Drug 2 82 131 60 . . . . . . . Drug 3 17 13 55 85 68 87 42 36 44 98 Drug 3 75 35 7 57 92 78 69 21 14 . ;
These statements compute the mean percent change for drug and placebo in each stratum and display them in a plot.
proc means data=urininc mean nway; class stratum therapy; var change; output out=mns mean=Mean; run; proc sgplot data=mns; series y=Mean x=Stratum / group=Therapy; xaxis type=discrete; run;
The means show a larger decrease in the number of episodes under the drug than with placebo in two of the strata.

The van Elteren test for drug effect can be performed using the STRATA statement in PROC NPAR1WAY. Both onesided and twosided pvalues are provided.
proc npar1way data=urininc; strata stratum; class therapy; var change; run;
The twosided result (p=0.0122) indicates that the percent change under the drug differs significantly from placebo. If the experimenter initially hypothesized that the drug would produce a greater decrease in episodes, this onesided test would also be significant (p=0.0061).

The test can also be done in PROC FREQ by defining a stratified, threeway table and using the CMH and SCORES=MODRIDIT options. In the TABLE statement, the variable(s) defining the strata appear first, followed by the treatment variable and finally the response variable. The NOPRINT option is used to prevent the display of each of the treatment by response tables in the various strata.
proc freq data=urininc; table stratum*therapy*change / cmh scores=modridit noprint; run;
The van Elteren test is the test comparing the rows (treatments) of the table. This is the second CMH statistic labeled "Row Mean Scores Differ." Only a twosided test is available. Note that the pvalue matches the twosided pvalue from PROC NPAR1WAY.

References
Dmitrienko, A., Molenberghs, G., ChuangStein, C., Offen, W. (2005), Analysis of Clinical Trials Using SAS^{®}: A Practical Guide, Cary, NC: SAS Institute Inc.
Lehmann, E. L. (1975). Nonparametrics: Statistical Methods Based on Ranks, San Francisco: HoldenDay, pp 132137, 145.
van Elteren, P. H. (1960). "On the combination of independent twosample tests of Wilcoxon," Bulletin of the International Statistical Institute, 37, 351361.
Product Family  Product  System  SAS Release  
Reported  Fixed*  
SAS System  SAS/STAT  All  n/a  n/a 
data a;
input blocks treatmnt consump @@;
datalines;
1 1 236 1 2 255
2 1 183 2 2 179 2 2 193
3 1 115 3 1 128 3 2 132
4 1 61 4 1 70 4 1 79 4 2 67 4 2 84 4 2 88
;
proc freq;
tables blocks * treatmnt * consump / cmh2 scores=modridit noprint;
run;
Note that Lehmann's presentation of this example shows onetailed exact and asymptotic (normal) tests. FREQ gives a twotailed, asymptotic test. Lehmann does a little rounding in his computations and gets a pvalue of 0.050. Carrying his computations out to a little more precision yields p=0.0488, and twice this (0.09765) is the twotailed pvalue which agrees with the pvalue from the second CMH statistic.
Type:  Usage Note 
Priority:  low 
Topic:  SAS Reference ==> Procedures ==> FREQ Analytics ==> Nonparametric Analysis SAS Reference ==> Procedures ==> NPAR1WAY 
Date Modified:  20180104 16:36:23 
Date Created:  20050113 15:03:54 