Biostatistics 518
Hw 5
2/22/2015
1. Methods: We are interested in analyzing the effect of different doses of difluoro methyl
omithine (DFMO) on the synthesis of polyamines. Spermidine is an intermediate chemical in the
pathway from putrescine to spermine production, that is of clinical interest in cancer care. Most
of our analyses will focus on spermidine levels after 12 months of treatment with DFMO at
different doses, but I have included data on putrescine and spermine in my descriptive analyses
for comparison. Nineteen patients were missing measurements for their 12 month follow-up
and were excluded from all analyses. Patients who were missing data for follow-up visits other
than the 12-month point were included, and 1 person missing data on her age was included in
all but the descriptive statistics on age. This left us with 95 patients.
Inference: Results of descriptive analyses are presented in table 1 below. The number of
patients per treatment were pretty evenly spread, though there were a few more in the control
group and in the lowest dosage. As this was a randomized clinical trial, we shouldn’t have to
worry about confounding, yet there were no women in the .2g/sq m/day DFMO group. Perhaps
sex has minimal effect on this pathway, but it is concerning that the groups are that imbalanced.
Age, baseline levels of putrescine, spermidine, and spermine all appear roughly equivalent
across dosage groups. Putrescine levels had increased for all groups (including control) by the
end of the 12-month observation period, but less so for the groups on higher doses. Spermidine
levels dropped slightly for control and the .075g/sq m/day dosage group, and dropped more
dramatically at higher doses. Spermine dropped for all groups, and interestingly dropped almost
as much in the control group as for the higher dosages, and more than in the .075 dose.
Table 1: Descriptive statistics stratified by dose of DFMO.
Dosage of DFMO
0
.075
.2
.4
(g/sq m/day)
Patients (n, %)
28(29.5%)
26(27.4%)
21(22.1%)
20(21.1%)
Female (n, %)
6(21.4%)
10(40%)
0(0%)
4(20%)
Age* (years)
65.07(8.45) 45.4661.50(7.72) 47.8063.17(8.38) 45.43-77.58 64.54(7.89) 48.93-80.97
77.18
76.852
Baseline
.687(.466) .061-1.98 .70(.54) .009-2.59
.60(.42) 0-1.96
.568(.307) 0-1.31
putrescine*¹
Putrescine at 12
1.16(.835) 0-3.18
1.08(1.03) .036-4.29
.80(.79) 0-3.21
.882(1.42) 0-5.48
months*¹
Baseline
3.30(1.46) 1.40-7.05 3.33(1.46) 1.51-7.012
3.28(1.31) 1.70-6.22
3.71(1.89) .66-7.21
spermidine*¹
Spermidine at 12
3.26(1.31) 1.01-5.91 2.92(.99) 1.35-4.92
2.71(1.40) .293-6.45
1.95(.800) 0-3.42
months*¹
Baseline
8.53(5.77) 2.128.54(6.15) 4.13-37.67
9.24(7.67) 2.54-41.68
8.50(6.33) 2.28-34.04
spermine*¹
35.55
Spermine at 12
6.55(3.59) 2.327.75(3.12) 3.15-14.13
7.16(3.15) 2.96-13.83
5.93(2.58) 0-10.67
months*¹
14.55
* Descriptive statistics are mean(SD), min-max
¹units are micromole/mg protein
2
There was one missing value
2. A. Methods: We performed linear regression using mean mucosal spermidine levels after 12
months of DFMO treatment as our response and dosage group of DFMO as our predictor. We
used dummy variables in order to compare the differences between different dosages of DFMO.
We used the Huber-White sandwich estimator for standard error.
Inference: We found an overall association of DFMO treatment with lower levels of spermidine
(p<.0001), but only statistically significant lower values for the highest dosage of .4g/sq m/day
(p<.001). The mean level of spermidine after 12 months on placebo was 3.26micromole/mg
protein (95%CI: 2.76 to 3.75), compared with 2.92micromole/mg protein for the group on a
dose of .075g/sq m/day (95%CI: -.964 to .292), 2.71micromole/mg protein for the .2g/sq m/day
dosage group, and 1.95micromole/mg protein for the .4g/sq m/day group (95%CI: -1.91 to -.70).
As this was a saturated model, these values match exactly what we found in our descriptive
analyses. This would indicate that the highest dose of DFMO is necessary to lower levels of
polyamine, as the change in spermidine levels at lower doses was not statistically
distinguishable from what might be observed by chance.
b. Because this is a saturated model, we obtain the same point estimates equal to the true
sample means of spermidine at month 12 for every dose group, but now see that .075g/sq
m/day is significantly different from the .4g/sq m/day group but not from the other dosage
levels. In part a we found that the .4g/sq m/day dose group was significantly different from
treatment with placebo, but we don’t see that with this test. We can’t test for differences
between every treatment arm with this test, just against the one we choose as our reference
group.
c. Methods: We performed a linear regression using mean mucosal spermidine levels after 12
months of DFMO treatment as our response and dose as an untransformed continuous
predictor. The Huber-White sandwich estimator was used to calculate standard error.
Inference: We estimate a statistically significant 3.13 decrease in mean spermidine levels after
12 months of treatment for every 1g/sq m/day taken (p<.001). From a 95% confidence interval,
this would not be considered unusual if the true value lay between -4.50 and -1.75.
d. Methods: We ran a linear regression with mean mucosal spermidine levels after 12 months of
DFMO treatment as our response, modeling dose as a quadratic function. We used the HuberWhite sandwich estimator for standard error.
Inference: We found an overall association between DFMO treatment for 12 months and mean
mucosal spermidine levels (p<.0001) and reject the null hypothesis of no effect.
e. Methods: We performed linear regression using a binary predictor of DFMO treatment vs.
placebo to examine any change in mean mucosal spermidine levels after 12 months of
treatment. We used the Huber-White sandwich estimator for standard error.
Inference: Overall there was a statistically significant difference in mean spermidine levels after
12 months between groups on treatment and placebo (p<.01) with a tendency for groups on
treatment to have lower spermidine levels. It would not be appropriate to give an estimate for
how much lower the levels were, as there was a range of doses.
f.Methods: We performed linear regression using mean mucosal spermidine levels after 12
months of treatment as the response and including both a binary predictor for dose and dose as
a continuous variable as predictors of interest. We used the Huber-White sandwich estimator
for standard error.
Inference: We found an overall association between treatment for 12 months with DFMO and
lower mucosal spermidine levels (p<.0001). IS THAT IT?
g. Methods: We ran a linear regression with mean mucosal spermidine levels after 12 months of
DFMO treatment as our response, modeling dose as a cubic function. We used the Huber-White
sandwich estimator for standard error.
Inference: We found an overall association between DFMO treatment for 12 months and mean
mucosal spermidine levels (p<.0001) and reject the null hypothesis of no effect.
h. Table 2: Fitted values from the above models for mean spermidine levels after 12 months
(micromole/mg protein) as compared to values observed in the sample. Stratified by
dose of DFMO (g/sq m/day).
Dosage of DFMO 0
.075
.2
.4
(g/sq m/day)
ANOVA
3.26
2.92
2.71
1.95
ANOVA, .75 ref
3.26
2.92
2.71
1.95
Linear Regression 3.23
3.00
2.61
1.98
Quadratic
3.21
3.01
2.64
1.96
Binary predictor
3.26
2.56
2.56
2.56
Binary and Linear 3.26
2.98
2.60
2.00
Cubic
3.26
2.92
2.71
1.95
Sample mean
3.26
2.92
2.71
1.95
We can see that because this is a saturated model, modeling with dummy variables (ANOVA)
makes use of the exact sample means, regardless of what comparison group we use: 0 or .75, it
is merely a reparameterization. The cubic model appears to be the best representation of the
underlying relationship, as it fits the sample means much more closely than the quadratic and
linear models. Modeling dose as a binary predictor averages the dose groups together, and so
loses precision, and even including a linear trend with the binary predictor does not improve it
much. These values are plotted below, for further illustration.
2
2.5
3
3.5
Fitted values compared to Lowess curve
0
.1
.2
Dose of DFMO g/sq m/day
ANOVA
ANOVA, .75 ref
Linear regression
Quadratic
.3
.4
Binary predictor
Binary and linear
Cubic
lowess spd12 dose
3. A. Methods: We performed linear regression using mean mucosal spermidine levels after 12
months of DFMO treatment as our response and dosage group of DFMO as our predictor,
adjusting for baseline mucosal spermidine levels. We used dummy variables in order to compare
the differences between different dosages of DFMO. We used the Huber-White sandwich
estimator for standard error.
Inference: We found an overall association of DFMO treatment for 12 months with lower levels
of spermidine (p<.0002) after adjusting for baseline spermidine levels, and can reject the null
hypothesis of no association.
b. Because this is a saturated model, we obtain the same point estimates equal to the true
sample means of spermidine at month 12 for every dose group, but now see that .075g/sq
m/day is significantly different from the .4g/sq m/day group but not from the other dosage
levels. In part a we found that the .4g/sq m/day dose group was significantly different from
treatment with placebo, but we don’t see that with this test. We can’t test for differences
between every treatment arm with this test, just against the one we choose as our reference
group. The overall significant association holds.
c. Methods: We performed a linear regression using mean mucosal spermidine levels after 12
months of DFMO treatment as our response and dose as an untransformed continuous
predictor. The Huber-White sandwich estimator was used to calculate standard error, and
baseline mucosal spermidine levels were included as a covariate.
Inference: We estimate a statistically significant 3.29 decrease in mean spermidine levels after
12 months of treatment for every 1g/sq m/day taken (p<.001) after adjusting for baseline
spermidine levels. From a 95% confidence interval, this would not be considered unusual if the
true value lay between -4.72 and -1.86.
d. Methods: We ran a linear regression with mean mucosal spermidine levels after 12 months of
DFMO treatment as our response, modeling dose as a quadratic function adjusting for baseline
mucosal spermidine levels. We used the Huber-White sandwich estimator for standard error.
Inference: We found an overall association between DFMO treatment for 12 months and mean
mucosal spermidine levels after adjusting for baseline spermidine levels (p<.0001) and reject the
null hypothesis of no effect.
e. Methods: We performed linear regression using a binary predictor of DFMO treatment vs.
placebo to examine any change in mean mucosal spermidine levels after 12 months of
treatment, adjusting for baseline mucosal spermidine levels. We used the Huber-White
sandwich estimator for standard error.
Inference: Overall there was a statistically significant difference in mean spermidine levels after
12 months between groups on treatment and placebo after adjusting for baseline spermidine
levels (p<.01) with a tendency for groups on treatment to have lower spermidine levels. It would
not be appropriate to give an estimate for how much lower the levels were, as there was a
range of doses.
f.Methods: We performed linear regression using mean mucosal spermidine levels after 12
months of treatment as the response and including both a binary predictor for dose and dose as
a continuous variable as predictors of interest. We used the Huber-White sandwich estimator
for standard error and adjusted for baseline mucosal spermidine levels.
Inference: We found an overall association between treatment for 12 months with DFMO and
lower mucosal spermidine levels (p<.0001) after adjsusting for baseline spermidine levels. IS
THAT IT?
g. Methods: We ran a linear regression with mean mucosal spermidine levels after 12 months of
DFMO treatment as our response, modeling dose as a cubic function. We used the Huber-White
sandwich estimator for standard error and adjusted for baseline mucosal spermidine levels.
Inference: We found an overall association between DFMO treatment for 12 months and mean
mucosal spermidine levels (p<.0002) after adjustitng for baseline spermidine levels and reject
the null hypothesis of no effect.
4. subtract off baseline values
4g HOW DO YOU CALCULATE PROBABILITY OF DECREASED SPERMIDINE??
5. ummm either dummy variables (ANOVA) because dose is a step-wise predictor in this case, or
cubic, because it appears the underlying relationship truly was cubic. I didn’t know that until I
tested though, so I would have just gone with the ANOVA.
Q3 adjust for the thing as a coefficient, don’t just subtract out baseline!
Normally, overall test p value is just looking at overall association between predictor and response,
when you throw in covariates it could be the covariates confounding thinsg! Run testparm, tell it the
variables that are just part of your regular model (dose, your predictor), and it will test just that by itself
for the overall association.
LaNae explained that the overall p value is looking at an association overall, but if you have covariates in
there you can’t use that. That’s why you need param.