Example 43.3: Peto Test

The MULTTEST Procedure

Example 43.3: Peto Test

This example illustrates the use of the Peto mortality-prevalence test. In the data set, each observation represents an animal, and S1-S3 are three tumor types. A 0 in the data set indicates a nonoccurrence of the tumor, 1 indicates an incidental (nonlethal) occurrence, and 2 indicates a lethal occurrence. The time variable T indicates the time of death of the animal. A strata variable B is constructed from T, and a grouping variable Dose is drug dosage.

   data a;
      input S1-S3 T Dose;
      if T<=90 then B=1; else B=2;
      datalines;
   0  0  0  104   0
   2  0  1   80   0
   0  0  1  104   0
   0  0  0  104   0
   0  2  0  100   0
   1  0  0  104   0
   2  0  0   85   1
   2  1  0   60   1
   0  1  0   89   1
   2  0  1   96   1
   0  0  0   96   1
   2  0  1   99   1
   2  1  1   60   2
   2  0  0   50   2
   2  0  1   80   2
   0  0  2   98   2
   0  0  1   99   2
   2  1  1   50   2
   ;

   proc multtest data=a notables out=p stepsid;
      test peto(S1-S3 / permutation=20 time=T uppertailed);
      class Dose;
      strata B;
      contrast 'mort-prev' 0  1  2;
   run;

   proc print data=p;
   run;

The NOTABLES option in the PROC MULTTEST statement suppresses the display of the summary statistics for each variable. The OUT=P option requests an output SAS data set containing all p-values and intermediate statistics. The STEPSID option is used to adjust the p-values.

The TEST statement specifies an upper-tailed Peto test for S1-S3, and TIME=T indicates the variable with values that are death times. The CLASS statement contains the grouping variable Dose, and the STRATA statement contains the blocking variable B. The CONTRAST statement lists linear trend coefficients. PROC PRINT displays the requested p-value data set.

The results from this analysis are listed in Output 43.3.1.

Output 43.3.1: Peto Test

The Multtest Procedure

Model Information
Test for discrete variables:	Peto
Exact permutation distribution used:	Everywhere
Tails for discrete tests:	Upper-tailed
Strata adjustment?	Yes
P-value adjustment:	Stepdown Sidak

The preceding information corresponds to the PROC MULTTEST invocation. In this case the totals for all prevalence and fatality strata are less than 20, so exact permutation tests are used everywhere, and the STEPSID adjustments are computed from these permutation distributions.

The Multtest Procedure

Contrast Coefficients
Contrast	Dose
Contrast	0	1	2
mort-prev	0	1	2

The trend coefficients are listed in the preceding table, and they happen to be the same as the levels of the Dose variable.

The Multtest Procedure

p-Values
Variable	Contrast	Raw	Stepdown Sidak
S1	mort-prev	0.0681	0.0814
S2	mort-prev	0.5000	0.5000
S3	mort-prev	0.0363	0.0781

In the preceding "p-Values" table, the p-values for the Peto tests are listed in the Raw column, and the stepdown Sidak adjusted p-values are in the Stepdown Sidak column.

The raw Peto test is significant at the 5% level for S3, but the adjusted S3 test is no longer significant at 5%. The raw and adjusted p-values for S2 are the same because of the stepdown technique. Significant p-values support the claim that higher dosage levels promote higher mortality and prevalence.

Obs	_test_	_var_	_contrast_	_strat_	_tstrat_	_value_	_exp_	_se_	raw_p	stpsid_p
1	PETO	S1	mort-prev	1	0	0	0.00000	0.00000	.	.
2	PETO	S1	mort-prev	2	0	0	0.62500	0.85696	.	.
3	PETO	S1	mort-prev	50	1	4	2.00000	1.12022	.	.
4	PETO	S1	mort-prev	60	1	3	1.75000	1.06654	.	.
5	PETO	S1	mort-prev	80	1	2	1.57143	1.04978	.	.
6	PETO	S1	mort-prev	85	1	1	0.75000	0.72169	.	.
7	PETO	S1	mort-prev	96	1	1	0.70000	0.78102	.	.
8	PETO	S1	mort-prev	98	1	0	0.00000	0.00000	.	.
9	PETO	S1	mort-prev	99	1	1	0.42857	0.72843	.	.
10	PETO	S1	mort-prev	100	1	0	0.00000	0.00000	.	.
11	PETO	S2	mort-prev	1	0	6	5.50000	1.05221	.	.
12	PETO	S2	mort-prev	2	0	0	0.00000	0.00000	.	.
13	PETO	S2	mort-prev	50	1	0	0.00000	0.00000	.	.
14	PETO	S2	mort-prev	60	1	0	0.00000	0.00000	.	.
15	PETO	S2	mort-prev	80	1	0	0.00000	0.00000	.	.
16	PETO	S2	mort-prev	85	1	0	0.00000	0.00000	.	.
17	PETO	S2	mort-prev	96	1	0	0.00000	0.00000	.	.
18	PETO	S2	mort-prev	98	1	0	0.00000	0.00000	.	.
19	PETO	S2	mort-prev	99	1	0	0.00000	0.00000	.	.
20	PETO	S2	mort-prev	100	1	0	0.00000	0.00000	.	.
21	PETO	S3	mort-prev	1	0	6	5.50000	1.05221	.	.
22	PETO	S3	mort-prev	2	0	4	2.22222	1.08298	.	.
23	PETO	S3	mort-prev	50	1	0	0.00000	0.00000	.	.
24	PETO	S3	mort-prev	60	1	0	0.00000	0.00000	.	.
25	PETO	S3	mort-prev	80	1	0	0.00000	0.00000	.	.
26	PETO	S3	mort-prev	85	1	0	0.00000	0.00000	.	.
27	PETO	S3	mort-prev	96	1	0	0.00000	0.00000	.	.
28	PETO	S3	mort-prev	98	1	2	0.62500	0.85696	.	.
29	PETO	S3	mort-prev	99	1	0	0.00000	0.00000	.	.
30	PETO	S3	mort-prev	100	1	0	0.00000	0.00000	.	.
31	PETO	S1	mort-prev	.	.	12	7.82500	2.42699	0.06808	0.08140
32	PETO	S2	mort-prev	.	.	6	5.50000	1.05221	0.50000	0.50000
33	PETO	S3	mort-prev	.	.	12	8.34722	1.73619	0.03627	0.07811

The preceding table lists the OUT= data set. The first 30 observations correspond to intermediate statistics used to compute the Peto p-values. The _test_ variable lists the name of the test, the _var_ variable lists the name of the TEST variables, and the _contrast_ variable lists the CONTRAST label. The _strat_ variable lists the level of the STRATA variable, and the _tstrat_ variable indicates whether or not the stratum corresponds to values of the TIME= variable. The _value_ variable is the observed contrast for a stratum and the _exp_ variable is its expected value. The variable _se_ contains the square root of the variance terms summed to form the denominator of the Peto statistics.

The final three observations correspond to the three Peto tests, with their p-values listed under the raw_p variable. The stpsid_p variable contains the stepdown Sidak adjusted p-values.

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