Question

In: Statistics and Probability

using this model flog(antibody ratio)jTIME, TREAT, DAYS, FEM, weight, loss, tumor} = TIME + TREAT report...

using this model

flog(antibody ratio)jTIME, TREAT, DAYS, FEM, weight, loss, tumor} = TIME + TREAT

report a confidence interval for the difference in mean log ratio between

the BD and NS treatments.

Brain

41081

Liver

1456164

Time

0.5

Treatment

BD

Day

10

Sex

Female

Weight

239

Loss

5.9

Tumor

221

44286

1602171

0.5

BD

10

Female

225

4.0

246

102926

1601936

0.5

BD

10

Female

224

-4.9

61

25927

1776411

0.5

BD

10

Female

184

9.8

168

42643

1351184

0.5

BD

10

Female

250

6.0

164

31342

1790863

0.5

NS

10

Female

196

7.7

260

22815

1633386

0.5

NS

10

Female

200

0.5

27

16629

1618757

0.5

NS

10

Female

273

4.0

308

22315

1567602

0.5

NS

10

Female

216

2.8

93

77961

1060057

3.0

BD

10

Female

267

2.6

73

73178

715581

3.0

BD

10

Female

263

1.1

25

76167

620145

3.0

BD

10

Female

228

0.0

133

123730

1068423

3.0

BD

9

Female

261

3.4

203

25569

721436

3.0

NS

9

Female

253

5.9

159

33803

1019352

3.0

NS

10

Female

234

0.1

264

24512

667785

3.0

NS

10

Female

238

0.8

34

50545

961097

3.0

NS

9

Female

230

7.0

146

50690

1220677

3.0

NS

10

Female

207

1.5

212

84616

48815

24.0

BD

10

Female

254

3.9

155

55153

16885

24.0

BD

10

Male

256

-4.7

190

48829

22395

24.0

BD

10

Male

247

-2.8

101

89454

83504

24.0

BD

11

Female

198

4.2

214

37928

20323

24.0

NS

10

Female

237

2.5

224

12816

15985

24.0

NS

10

Male

293

3.1

151

23734

25895

24.0

NS

10

Male

288

9.7

285

31097

33224

24.0

NS

11

Female

236

5.9

380

35395

4142

72.0

BD

11

Female

251

4.1

39

18270

2364

72.0

BD

10

Female

223

4.0

153

5625

1979

72.0

BD

10

Male

298

12.8

164

7497

1659

72.0

BD

10

Male

260

7.3

364

6250

928

72.0

NS

10

Male

272

11.0

484

11519

2423

72.0

NS

11

Female

226

2.2

168

Solutions

Expert Solution

> names(case1112)
[1] "Brain" "Liver" "Time" "Treatment" "Days" "Sex"
[7] "Weight" "Loss" "Tumor"
> case1102 = transform(case1102, Y = Brain/Liver)
> case1102 = transform(case1102, logliver = log(Liver))
> case1102 = transform(case1102, logbrain = log(Brain))
> case1102 = transform(case1102, SAC = as.factor(Time))
> case1102 = transform(case1102, logy = log(Brain/Liver))
> case1102 = transform(case1102, logtime = log(Time))
> case1102 = transform(case1102, Treat = relevel(Treatment, ref = "NS"))
> summary(case1112)
Brain Liver Time Treatment Days
Min. : 1334 Min. : 928 Min. : 0.5 BD:17 Min. : 9
1st Qu.: 19281 1st Qu.: 16210 1st Qu.: 1.1 NS:17 1st Qu.:10
Median : 32572 Median : 643965 Median : 3.0 Median :10
Mean : 39965 Mean : 668776 Mean :23.5 Mean :10
3rd Qu.: 50654 3rd Qu.:1318557 3rd Qu.:24.0 3rd Qu.:10
Max. :123730 Max. :1790863 Max. :72.0 Max. :11
Sex Weight Loss Tumor Y
Female:26 Min. :184 Min. :-4.90 Min. : 25 Min. :0.01
Male : 8 1st Qu.:225 1st Qu.: 1.20 1st Qu.:136 1st Qu.:0.03
Median :240 Median : 3.95 Median :166 Median :0.12
Mean :242 Mean : 3.64 Mean :183 Mean :1.50
3rd Qu.:259 3rd Qu.: 5.97 3rd Qu.:223 3rd Qu.:1.95
Max. :298 Max. :12.80 Max. :484 Max. :8.55
logliver logbrain SAC logy logtime
Min. : 6.83 Min. : 7.20 0.5:9 Min. :-4.58 Min. :-0.69
1st Qu.: 9.69 1st Qu.: 9.86 3 :9 1st Qu.:-3.39 1st Qu.:-0.25
Median :13.37 Median :10.39 24 :8 Median :-2.13 Median : 1.10
Mean :11.61 Mean :10.23 72 :8 Mean :-1.39 Mean : 1.86
3rd Qu.:14.09 3rd Qu.:10.83 3rd Qu.: 0.67 3rd Qu.: 3.18
Max. :14.40 Max. :11.73 Max. : 2.15 Max. : 4.28
Treat
NS:17
BD:17

Graphical presentation:

The following displays a scatterplot of log ratio (Y) as a function of log time, akin to Display 11.5
on page 315.
> xyplot(Y ~ Time, group = Treat, scales = list(y = list(log = TRUE), x = list(log = TRUE)),
+ auto.key = TRUE, data = case1102)

> case1102 = transform(case1102, female = ifelse(Sex == "F", 1, 0))
> xyplot(logy ~ jitter(female), xlab = "Sex", data = case1102)

> xyplot(logy ~ jitter(Days), data = case1102)

Multiple regression:

We first fit a model that reflects the initial investigation.

> lm1 = lm(logy ~ SAC + Treat + SAC * Treat + Days + Sex + Weight + Loss + Tumor,
+ data = case1102)
> summary(lm1)
Call:
lm(formula = logy ~ SAC + Treat + SAC * Treat + Days + Sex +
Weight + Loss + Tumor, data = case1102)
Residuals:
Min 1Q Median 3Q Max
-1.4056 -0.2559 0.0458 0.1957 1.1583

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.836741 3.391046 -1.13 0.271
SAC3 1.015463 0.399578 2.54 0.019
SAC24 4.337135 0.477836 9.08 1.0e-08
SAC72 5.010605 0.454953 11.01 3.5e-10
TreatBD 0.795999 0.378970 2.10 0.048
Days -0.036987 0.295645 -0.13 0.902
SexMale 0.001295 0.373368 0.00 0.997
Weight -0.000558 0.005330 -0.10 0.918
Loss -0.059544 0.030422 -1.96 0.064
Tumor 0.001551 0.001226 1.26 0.220
SAC3:TreatBD 0.179831 0.551964 0.33 0.748
SAC24:TreatBD -0.386047 0.585450 -0.66 0.517
SAC72:TreatBD 0.379104 0.569242 0.67 0.513
Residual standard error: 0.564 on 21 degrees of freedom
Multiple R-squared: 0.96,Adjusted R-squared: 0.937
F-statistic: 41.9 on 12 and 21 DF, p-value: 6.45e-12

We can then display a residual plot to assess the fit of the above model.

> plot(lm1, which = 1)

orchestra answered 1 year ago
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