This example illustrates the use of the Peto mortality-prevalence test. The test is a combination of analyses about the prevalence of incidental tumors in the population and mortality due to fatal tumors.

In the following data set, each observation represents an animal. The variables `S1`

–`S3`

are three tumor types, with a value of 0 indicating no tumor, 1 indicating an incidental (nonlethal) tumor, and 2 indicating
a lethal tumor. The time variable `T`

indicates the time of death of the animal, a strata variable `B`

is constructed from `T`

, and the 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=
option creates an output SAS data set `p`

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`

. The mortality strata are defined by TIME=
`T`

, the death times. The CLASS
statement contains the grouping variable `Dose`

. The prevalence strata are defined by the STRATA
statement as the blocking variable `B`

. The CONTRAST
statement lists the default linear trend coefficients. The PROC PRINT statement displays the requested p-value data set.

The results from this analysis are listed in Output 67.3.1 through Output 67.3.4.

The "Model Information" table in Output 67.3.1 displays information corresponding 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 contrast trend coefficients are listed in Output 67.3.2. They happen to be the same as the levels of the `Dose`

variable.

In the "p-Values" table in Output 67.3.3, the p-values for the Peto tests are listed in the Raw column, and the step-down Šidák adjusted p-values are in the Stepdown Šidák column.

Significant p-values in the preceding table support the claim that higher dosage levels lead to higher mortality and prevalence. 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 step-down technique.

The OUT= data set is displayed in Output 67.3.4.

Output 67.3.4: OUT= Data Set

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 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 step-down Šidák-adjusted p-values.