Analysis Variable : weeks
----------------------------------- Diet=ALHF ------------------------------------N
Mean
Median Std Dev
Minimum Maximum
Skewness
Kurtosis
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
161
97.40
97.00
25.59
60.00
145.00
0.39
-1.27
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
----------------------------------- Diet=AdLQD ------------------------------------N
Mean
Median Std Dev
Minimum Maximum
Skewness
Kurtosis
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
163
110.50
114.00
21.40
57.00
152.00
-0.41
-0.73
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
----------------------------------- Diet=EOD -------------------------------------N
Mean
Median Std Dev
Minimum Maximum
Skewness
Kurtosis
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
164
122.45
124.00
12.49
80.00
158.00
-0.72
2.44
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
proc glm data=rats;class diet;model weeks =diet;means diet /tukey;run;
Class
Diet
The GLM Procedure
Class Level Information
Levels
Values
3
ALHF AdLQD EOD
Number of Observations Used
488
Dependent Variable: weeks
Source
Model
Error
Corrected Total
R-Square
0.199700
DF
2
485
487
Coeff Var
18.63247
Sum of
Squares
51018.5889
204457.9172
255476.5061
Root MSE
20.53199
Mean Square
25509.2945
421.5627
F Value
60.51
Pr > F
<.0001
weeks Mean
110.1947
Tukey's Studentized Range (HSD) Test for weeks
NOTE: This test controls the Type I experimentwise error rate.
Alpha
0.05
Error Degrees of Freedom
485
Error Mean Square
421.5627
Critical Value of Studentized Range 3.32472
Comparisons significant at the 0.05 level are indicated by ***.
Difference
Diet
Between
Simultaneous 95%
Comparison
Means
Confidence Limits
EOD
- AdLQD
11.948
6.610
17.287 ***
EOD
- ALHF
25.054
19.698
30.409 ***
AdLQD - ALHF
13.106
7.742
18.469 ***
These Means are likely to be biased because animals in each group are still living.
If the Means are biased the ANOVA results can be misleading.
proc freq data=rats;tables dead*diet /chisq;run;
dead
Diet
Frequency‚
Percent ‚
Row Pct ‚
Col Pct ‚ALHF
‚AdLQD
‚EOD
‚ Total
ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ
0 ‚
29 ‚
37 ‚
31 ‚
97
‚
5.94 ‚
7.58 ‚
6.35 ‚ 19.88
‚ 29.90 ‚ 38.14 ‚ 31.96 ‚
‚ 18.01 ‚ 22.70 ‚ 18.90 ‚
ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ
1 ‚
132 ‚
126 ‚
133 ‚
391
‚ 27.05 ‚ 25.82 ‚ 27.25 ‚ 80.12
‚ 33.76 ‚ 32.23 ‚ 34.02 ‚
‚ 81.99 ‚ 77.30 ‚ 81.10 ‚
ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ
Total
161
163
164
488
32.99
33.40
33.61
100.00
Statistics for Table of dead by Diet
Statistic
DF
Value
Prob
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
Chi-Square
2
1.2646
0.5314
Likelihood Ratio Chi-Square
2
1.2475
0.5359
proc logistic data=rats descending;class diet;
model dead = diet / RSQ ;run;
The LOGISTIC Procedure
Model Information
Data Set
WORK.RATS
Response Variable
dead
Number of Response Levels
2
Model
binary logit
Optimization Technique
Fisher's scoring
umber of Observations Used
488
Response Profile
Ordered
Value
1
2
dead
1
0
Total
Frequency
391
97
Probability modeled is dead=1.
Class Level Information
Design
Class
Value
Variables
Diet
ALHF
1
0
AdLQD
0
1
EOD
-1
-1
Model Fit Statistics
Intercept
Only
488.725
492.915
486.725
Criterion
AIC
SC
-2 Log L
Intercept
and
Covariates
491.477
504.048
485.477
←The Difference in the
-2 Log Likelihood = 1.248 is the
Likelihood Ratio Test
This is the Cox and Snell R2
R-Square
This is the Nagelkerke R2
0.0026
Max-rescaled R-Square
0.0040
Testing Global Null Hypothesis: BETA=0
Test
Chi-Square
DF
Pr > ChiSq
Likelihood Ratio
1.2475
2
0.5359
Score
Wald
Effect
Diet
1.2646
1.2606
2
2
0.5314 Same as Pearson χ2
0.5324
Type 3 Analysis of Effects
Wald
DF
Chi-Square
Pr > ChiSq
2
1.2606
0.5324
Parameter
Intercept
Diet
ALHF
Diet
AdLQD
Analysis of Maximum Likelihood Estimates
Standard
Wald
DF
Estimate
Error
Chi-Square
1
1
1
1.3991
0.1164
-0.1737
0.1139
0.1643
0.1569
150.8286
0.5021
1.2252
Pr > ChiSq
<.0001
0.4786
0.2683
Odds Ratio Estimates
Point
95% Wald
Effect
Estimate
Confidence Limits
Diet ALHF vs EOD
1.061
0.606
1.859
Diet AdLQD vs EOD
0.794
0.464
1.356
At 130 weeks the difference in the proportions of animals still living is not significant, but
there are animals alive in each group.
Survival Analysis uses both the Status (in this case Death) and the Survival Time (Time to
Event) information.
SPSS: Analyze→Survival→Kaplan Meier
Survival Analysis for weeks
Factor Diet = ALHF
Survival Time
Mean:
99
(Limited to
145 )
Median:
97
Standard Error
2
5
95% Confidence Interval
(
94,
103 )
(
Percentiles
25.00
50.00
117.00
97.00
2.33
4.90
Value
Standard Error
87,
107 )
75.00
74.00
.33
Factor Diet = AdLQD
Survival Time
Mean:
(Limited to
Median:
Standard Error
114
152 )
114
Value
Standard Error
95% Confidence Interval
2
(
110,
118 )
2
(
111,
117 )
Percentiles
25.00
50.00
128.00
114.00
.
1.68
75.00
94.00
3.61
Factor Diet = EOD
Survival Time
Mean:
126
(Limited to
158 )
Median:
124
Value
Standard Error
Standard Error
1
1
Percentiles
25.00
50.00
129.00
124.00
.42
1.00
Survival Analysis for weeks
Total
Diet
Diet
Diet
Overall
AdLQD
ALHF
EOD
163
161
164
488
Number
Events
126
132
133
391
95% Confidence Interval
(
123,
129 )
(
122,
126 )
75.00
116.00
.99
Number
Censored
37
29
31
97
Test Statistics for Equality of Survival Distributions for Diet
Statistic
df
Significance
Log Rank
36.26
2
.0000
Percent
Censored
22.70
18.01
18.90
19.88
Survival Functions
1.0
Cum Survival
0.8
0.6
Diet
AdLQD
ALHF
EOD
AdLQDcensored
ALHFcensored
EODcensored
0.4
0.2
0.0
40
60
80
100
120
140
160
weeks
SPSS
1. 00
0. 75
0. 50
0. 25
0. 00
0
25
50
75
100
125
150
175
weeks
STRATA:
Di et =ALHF
Di et =AdLQ
D
Di et =EO
D
Censor ed Di et =ALHF
Censor ed Di et =AdLQ
D
Censor ed Di et =EO
D
SAS
proc lifetest data=rats plots=(s) outtest=Test maxtime=600;
time Weeks*dead(0); id id;
strata Diet / test=(logrank); run;
The LIFETEST Procedure
Stratum 1: Diet = ALHF
Summary Statistics for Time Variable weeks
Quartile Estimates
Point
95% Confidence Interval
Estimate
[Lower
Upper)
117.000
115.000
126.000
97.000
80.000
105.000
74.000
73.000
74.000
Percent
75
50
25
Mean
95.335
Standard Error
1.770
NOTE: The mean survival time and its standard error were underestimated
because the largest observation was censored and the estimation was
restricted to the largest event time.
Stratum 2: Diet = AdLQD
Summary Statistics for Time Variable weeks
Percent
75
50
25
Quartile Estimates
Point
95% Confidence Interval
Estimate
[Lower
Upper)
128.000
124.000
.
114.000
110.000
117.000
94.000
86.000
102.000
Mean
108.871
Standard Error
1.520
Mean
120.811
Standard Error
0.804
Stratum 3: Diet = EOD
Summary Statistics for Time Variable weeks
Percent
75
50
25
Quartile Estimates
Point
95% Confidence Interval
Estimate
[Lower
Upper)
129.000
128.000
130.000
124.000
121.000
125.000
116.500
114.000
118.000
Summary of the Number of Censored and Uncensored Values
Percent
Stratum
Diet
Total Failed
Censored
Censored
1
ALHF
161
132
29
18.01
2
AdLQD
163
126
37
22.70
3
EOD
164
133
31
18.90
--------------------------------------------------------------Total
488
391
97
19.88
Test of Equality over Strata
Test
Log-Rank
Chi-Square
36.2629
DF
2
Pr >
Chi-Square
<.0001