1 General Purpose
Trend tests are wonderful, because they
provide markedly better sensitivity for demonstrating incremental
effects from incremental treatment dosages, than traditional
statistical tests.
2 Schematic Overview of Type of Data File
The outcome variable is continuous, the
predictor variable is categorical, and can be measured either as
nominal (just like names) or as ordinal variable (a stepping
pattern not necessarily with equal intervals). In the Variable View
of SPSS “Measure” may, therefore, be changed into nominal or
ordinal, but, since we assume an incremental function the default
measure scale is OK as well.
3 Primary Scientific Question
Do incremental treatment dosages cause
incremental beneficial outcome effects.
4 Data Example
In a parallel-group study of three
incremental dosages of antihypertensive treatments.
The mean reduction of mean blood
pressure per group is tested.
|
Outcome (mean blood pressure, mm Hg)
|
Treatment group
|
|
113,00
|
1,00
|
|
131,00
|
1,00
|
|
112,00
|
1,00
|
|
132,00
|
1,00
|
|
114,00
|
1,00
|
|
130,00
|
1,00
|
|
115,00
|
1,00
|
|
129,00
|
1,00
|
|
122,00
|
1,00
|
|
118,00
|
2,00
|
5 Trend Analysis for Continuous Data
The entire data file is in
extras.springer.com, and is entitled “chapter15trendcontinuous”. We
will, first, perform a one way analysis of variance (ANOVA) (see
also Chap. 13) to see, if there are any
significant differences in the data. If not, we will perform a
trend test using simple linear regression. For analysis the
statistical model One Way ANOVA in the module Compare Means is
required.
Command:
-
Analyze....Compare Means....One-Way ANOVA....Dependent List: blood pressure Factor: treatment…click OK.
ANOVA
VAR00002
|
Sum of squares
|
df
|
Mean square
|
F
|
Sig.
|
|
|---|---|---|---|---|---|
|
Between groups
|
246,667
|
2
|
123,333
|
2,035
|
,150
|
|
Within groups
|
1636,000
|
27
|
60,593
|
||
|
Total
|
1882,667
|
29
|
The above table shows that there is no
significant difference in efficacy between the treatment dosages,
and so, sadly, this is a negative study. However, a trend test
having just 1° of freedom has more sensitivity than a usual one way
ANOVA, and it could, therefore, be statistically significant even
so. For analysis the model Linear in the module Regression is
required.
Command:
-
Analyze....Regression....Linear....Dependent: blood pressure....Independent(s): treatment....click OK.
ANOVAa
|
Model
|
Sum of squares
|
df
|
Mean square
|
F
|
Sig.
|
|
|---|---|---|---|---|---|---|
|
1
|
Regression
|
245,000
|
1
|
245,000
|
4,189
|
,050b
|
|
Residual
|
1637,667
|
28
|
58,488
|
|||
|
Total
|
1882,667
|
29
|
||||
Coefficientsa
|
Model
|
Unstandardized coefficients
|
Standardized coefficients
|
t
|
Sig.
|
||
|---|---|---|---|---|---|---|
|
B
|
Std. error
|
Beta
|
||||
|
1
|
(Constant)
|
125,333
|
3,694
|
33,927
|
,000
|
|
|
Treatment
|
−3,500
|
1,710
|
−,361
|
−2,047
|
,050
|
|
Four tables are given, we will only
use the third and fourth ones as shown above. The tables show that
treatment dosage is a significant predictor of treatment response
wit a p-value of 0,05. There is, thus, a significantly incremental
response with incremental dosages.
6 Conclusion
Trend tests are wonderful, because
they provide markedly better sensitivity for demonstrating
incremental effects from incremental treatment dosages, than
traditional statistical tests do. One way ANOVA using 2 degrees of
freedom was not significant in the example given, while linear
regression using 1 degrees of freedom was significant at
p = 0,05.
7 Note
More background, theoretical, and
mathematical information of trend testing is given in Statistics
applied to clinical studies 5th edition, Chap. 27, Springer
Heidelberg Germany, 2012, from the same authors.