The characteristics of this dataset are: 1) small number of dogs (n=4) and small number of repeated measures: (N=4-7) at different timepoints.
The main goal is to perform a mixed model analysis to test the hypothesis of interaction of time and treatment while accounting for repeated measures. for that we use a random regression model with the fixed effects of treatment, time (days of measurement, with time=0 day of infection) and their interaction. We add a random intercept for the dog and we considered adding a random slope for the dog to account for correlation and heterogeneous variances between measuring times within each dog. No dog-specific slope was significant, and we decided to include only a dog-specific intercept.
## -- Attaching packages -------------------------------------------------------- tidyverse 1.3.0 --## v ggplot2 3.3.0 v purrr 0.3.3
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## v readr 1.3.1 v forcats 0.5.0## -- Conflicts ----------------------------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack## Loading required package: emmeans## The 'lsmeans' package is now basically a front end for 'emmeans'.
## Users are encouraged to switch the rest of the way.
## See help('transition') for more information, including how to
## convert old 'lsmeans' objects and scripts to work with 'emmeans'.## Loading required package: mvtnorm## Loading required package: survival## Loading required package: TH.data## Loading required package: MASS##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
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## lmer## The following object is masked from 'package:stats':
##
## step## boundary (singular) fit: see ?isSingular## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00848096 (tol = 0.002, component 1)## boundary (singular) fit: see ?isSingular
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)## boundary (singular) fit: see ?isSingular## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## unable to evaluate scaled gradient## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge: degenerate Hessian with 1 negative eigenvalues## Warning: Model failed to converge with 1 negative eigenvalue: -4.0e-03## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)## boundary (singular) fit: see ?isSingular
## boundary (singular) fit: see ?isSingular## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)## boundary (singular) fit: see ?isSingular
## boundary (singular) fit: see ?isSingular## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)We tested for the interaction of time*treatment and we consider it significant at P < 0.15 (complete)
for (i in 1:11){
resu2<-lres[[i]]$resu
print("=======================================")
print(nms[i])
print("=======================================")
print(anova(resu2))
#compare trt (avg)
#ls<-lsmeans(resu2,~trt)
#print(pairs(ls))
#compare trt @ certain age
print(lsmeans(resu2,"trt",at=list(dpi=0))%>%pairs())
print("time 0")
print(lsmeans(resu2,"trt",at=list(dpi=120))%>%pairs())
print("time 120")
print(lsmeans(resu2,"trt",at=list(dpi=360))%>%pairs())
print("time 360")
print(lsmeans(resu2,"trt",at=list(dpi=720))%>%pairs())
print("time 720")
print(lsmeans(resu2,"trt",at=list(dpi=0)))
print("time 0")
print(lsmeans(resu2,"trt",at=list(dpi=120)))
print("time 120")
print(lsmeans(resu2,"trt",at=list(dpi=360)))
print("time 360")
print(lsmeans(resu2,"trt",at=list(dpi=720)))
print("time 720")
}## [1] "======================================="
## [1] "ONH"
## [1] "======================================="
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## trt 2260366 2260366 1 15.032 0.9685 0.3406
## dpi 90778 90778 1 15.811 0.0389 0.8462
## trt:dpi 4972643 4972643 1 15.032 2.1307 0.1650## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 1597 1623 15 0.984 0.3407
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 2127 1298 15 1.638 0.1222
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 3186 763 15 4.176 0.0008
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 4775 950 15 5.027 0.0002
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 720"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 10556 1335 15.7 7721 13391
## untreated 8959 1335 15.7 6125 11794
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 10858 1134 12.2 8392 13324
## untreated 8732 1134 12.2 6266 11198
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 11463 845 5.21 9315 13610
## untreated 8277 845 5.21 6129 10424
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 12369 954 7.53 10145 14594
## untreated 7594 954 7.53 5369 9819
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 720"
## [1] "======================================="
## [1] "Cup_Vol"
## [1] "======================================="
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## trt 2112.6 2112.6 1 15.030 0.9077 0.35580
## dpi 9392.6 9392.6 1 15.171 4.0356 0.06269 .
## trt:dpi 8241.2 8241.2 1 15.030 3.5409 0.07939 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -48.8 51.2 15 -0.953 0.3558
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -70.4 41 15 -1.717 0.1066
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -114 24.1 15 -4.711 0.0003
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -178 30 15 -5.940 <.0001
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 720"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 172 67.6 5.48 2.43 341
## untreated 220 67.6 5.48 51.25 390
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 173 63.8 4.44 2.57 343
## untreated 243 63.8 4.44 72.95 414
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 176 59.2 3.32 -2.67 354
## untreated 289 59.2 3.32 110.84 468
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 180 60.8 3.69 5.21 355
## untreated 358 60.8 3.69 183.43 533
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 720"
## [1] "======================================="
## [1] "NRR"
## [1] "======================================="
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## trt 524 524 1 15.087 0.0301 0.8646
## dpi 10712 10712 1 15.480 0.6148 0.4448
## trt:dpi 140790 140790 1 15.087 8.0799 0.0123 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 24.3 140 15 0.173 0.8646
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 113 112 15 1.011 0.3279
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 292 65.9 15 4.425 0.0005
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 559 82.1 15 6.812 <.0001
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 720"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 452 133 10.6 158 746
## untreated 428 133 10.6 134 722
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 510 118 7.59 234 785
## untreated 396 118 7.59 121 672
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 625 98.7 4 351 899
## untreated 333 98.7 4 59 607
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 797 106 5.12 527 1067
## untreated 238 106 5.12 -32 508
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 720"
## [1] "======================================="
## [1] "FaA"
## [1] "======================================="
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## trt 0.00518 0.00518 1 8.9930 0.0033 0.9551
## dpi 2.64808 2.64808 1 9.6857 1.7103 0.2211
## trt:dpi 0.24081 0.24081 1 8.9930 0.1555 0.7025## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.0828 1.43 9 -0.058 0.9551
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.227 1.11 9 -0.204 0.8431
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.515 0.652 9 -0.791 0.4494
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.948 1.1 9 -0.864 0.4099
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 720"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 3.84 1.17 11.9 1.29 6.40
## untreated 3.93 1.17 11.9 1.37 6.48
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 3.52 0.964 10.4 1.38 5.65
## untreated 3.75 0.964 10.4 1.61 5.88
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 2.87 0.696 4.92 1.07 4.67
## untreated 3.39 0.696 4.92 1.59 5.18
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 1.90 0.953 10.3 -0.213 4.02
## untreated 2.85 0.953 10.3 0.734 4.96
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 720"
## [1] "======================================="
## [1] "C_tono"
## [1] "======================================="
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## trt 0.0031103 0.0031103 1 19.919 0.2723 0.6075
## dpi 0.0000272 0.0000272 1 12.265 0.0024 0.9619
## trt:dpi 0.0105133 0.0105133 1 19.919 0.9205 0.3488## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 0.0552 0.106 19.2 0.522 0.6077
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 0.0818 0.0811 19.2 1.009 0.3255
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 0.135 0.0442 19.2 3.057 0.0064
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 0.215 0.081 19.2 2.655 0.0156
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 720"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 0.343 0.0973 14.1 0.134 0.551
## untreated 0.288 0.0973 14.1 0.079 0.496
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 0.355 0.0742 11.6 0.193 0.518
## untreated 0.273 0.0742 11.6 0.111 0.436
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 0.380 0.0425 4.54 0.267 0.493
## untreated 0.245 0.0425 4.54 0.132 0.358
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 0.417 0.0822 9.16 0.2317 0.603
## untreated 0.202 0.0822 9.16 0.0168 0.388
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 720"
## [1] "======================================="
## [1] "b_wave"
## [1] "======================================="
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## trt 0.7986 0.7986 1 27.007 0.0380 0.8468
## dpi 5.5436 5.5436 1 27.394 0.2641 0.6114
## trt:dpi 15.2310 15.2310 1 27.007 0.7256 0.4018## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.659 3.38 27 -0.195 0.8468
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 0.0553 2.66 27 0.021 0.9836
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 1.48 1.64 27 0.904 0.3742
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 3.63 2.58 27 1.408 0.1706
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 720"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 15.1 3.53 8.49 7.02 23.1
## untreated 15.7 3.53 8.49 7.68 23.8
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 15.2 3.19 5.94 7.38 23
## untreated 15.2 3.19 5.94 7.32 23
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 15.5 2.81 3.63 7.37 23.6
## untreated 14.0 2.81 3.63 5.88 22.1
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 15.9 3.15 5.64 8.06 23.7
## untreated 12.3 3.15 5.64 4.43 20.1
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 720"
## [1] "======================================="
## [1] "PhNR_wave"
## [1] "======================================="
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## trt 4.6425 4.6425 1 26.942 0.2326 0.6335
## dpi 9.2234 9.2234 1 27.886 0.4621 0.5023
## trt:dpi 0.3881 0.3881 1 26.942 0.0194 0.8901## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 1.59 3.29 27 0.482 0.6335
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 1.47 2.6 27 0.568 0.5751
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 1.25 1.6 27 0.779 0.4430
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 0.904 2.51 27 0.360 0.7216
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 720"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 17.9 2.79 17.2 12.1 23.8
## untreated 16.3 2.79 17.2 10.5 22.2
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 17.6 2.37 11.1 12.4 22.8
## untreated 16.1 2.37 11.1 10.9 21.3
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 16.9 1.84 4.67 12.1 21.7
## untreated 15.7 1.84 4.67 10.8 20.5
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 15.9 2.31 10.3 10.75 21.0
## untreated 15.0 2.31 10.3 9.85 20.1
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 720"
## [1] "======================================="
## [1] "AXL"
## [1] "======================================="
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## trt 0.83919 0.83919 1 26.960 7.569 0.0104817 *
## dpi 0.38239 0.38239 1 26.987 3.449 0.0742374 .
## trt:dpi 1.80817 1.80817 1 26.960 16.309 0.0004007 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 0.676 0.246 27 2.751 0.0105
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 0.426 0.193 27 2.206 0.0361
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.0748 0.118 27 -0.632 0.5329
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.825 0.192 27 -4.300 0.0002
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 720"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 21.5 0.345 4.95 20.6 22.4
## untreated 20.8 0.345 4.95 20.0 21.7
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 21.3 0.328 4.06 20.4 22.2
## untreated 20.9 0.328 4.06 20.0 21.8
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 21.0 0.31 3.24 20.0 21.9
## untreated 21.1 0.31 3.24 20.1 22.0
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 20.4 0.328 4.08 19.5 21.3
## untreated 21.3 0.328 4.08 20.3 22.2
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 720"
## [1] "======================================="
## [1] "ACD"
## [1] "======================================="
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## trt 0.48721 0.48721 1 30 3.8583 0.05883 .
## dpi 0.12032 0.12032 1 30 0.9528 0.33681
## trt:dpi 0.89685 0.89685 1 30 7.1022 0.01227 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 0.515 0.262 27.1 1.964 0.0598
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 0.339 0.206 27.1 1.645 0.1115
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.0137 0.126 27.1 -0.109 0.9143
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.542 0.205 27.1 -2.648 0.0133
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 720"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 4.52 0.186 29.9 4.15 4.90
## untreated 4.01 0.186 29.9 3.63 4.39
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 4.40 0.146 28 4.10 4.70
## untreated 4.06 0.146 28 3.77 4.36
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 4.16 0.091 11 3.96 4.36
## untreated 4.18 0.091 11 3.98 4.38
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 3.80 0.149 26.2 3.50 4.11
## untreated 4.34 0.149 26.2 4.04 4.65
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 720"
## [1] "======================================="
## [1] "LT"
## [1] "======================================="
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## trt 0.11483 0.11483 1 26.706 2.2428 0.1459642
## dpi 0.75252 0.75252 1 26.958 14.6975 0.0006873 ***
## trt:dpi 0.16400 0.16400 1 26.706 3.2032 0.0848425 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 0.25 0.167 27 1.498 0.1458
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 0.175 0.131 27 1.332 0.1940
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated 0.0239 0.0805 27 0.297 0.7688
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.202 0.13 27 -1.550 0.1329
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 720"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 7.58 0.133 20.4 7.30 7.85
## untreated 7.33 0.133 20.4 7.05 7.60
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 7.46 0.112 13.3 7.22 7.70
## untreated 7.28 0.112 13.3 7.04 7.52
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 7.22 0.0848 5.09 7.00 7.44
## untreated 7.19 0.0848 5.09 6.98 7.41
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 6.86 0.113 13.2 6.62 7.10
## untreated 7.06 0.113 13.2 6.82 7.31
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 720"
## [1] "======================================="
## [1] "VCD"
## [1] "======================================="
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## trt 0.01462 0.01462 1 26.891 0.1040 0.7496
## dpi 0.36587 0.36587 1 26.964 2.6028 0.1183
## trt:dpi 0.00005 0.00005 1 26.891 0.0004 0.9846## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.0892 0.277 27 -0.323 0.7496
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.0878 0.217 27 -0.404 0.6892
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.0851 0.133 27 -0.638 0.5289
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## contrast estimate SE df t.ratio p.value
## treated - untreated -0.081 0.216 27 -0.375 0.7106
##
## Degrees-of-freedom method: kenward-roger
## [1] "time 720"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 9.42 0.283 8.54 8.77 10.1
## untreated 9.51 0.283 8.54 8.86 10.2
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 0"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 9.47 0.255 5.93 8.85 10.1
## untreated 9.56 0.255 5.93 8.94 10.2
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 120"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 9.59 0.225 3.64 8.94 10.2
## untreated 9.67 0.225 3.64 9.02 10.3
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 360"## NOTE: Results may be misleading due to involvement in interactions## trt lsmean SE df lower.CL upper.CL
## treated 9.76 0.256 5.97 9.13 10.4
## untreated 9.84 0.256 5.97 9.22 10.5
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## [1] "time 720"