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4.1 Verwijderen van Linear Hypotheses: Estimate Std. Error t value Pr(>|t|) -poison: II - I == 0 0.04686 0.01744 2.688 0.07352 . +poison: II - I == 0 0.04686 0.01744 2.688 0.07355 . poison: III - I == 0 0.19964 0.01744 11.451 < 0.001 *** poison: III - II == 0 0.15278 0.01744 8.763 < 0.001 *** treat: B - A == 0 -0.16574 0.02013 -8.233 < 0.001 *** -treat: C - A == 0 -0.05721 0.02013 -2.842 0.05085 . +treat: C - A == 0 -0.05721 0.02013 -2.842 0.05088 . treat: D - A == 0 -0.13583 0.02013 -6.747 < 0.001 *** treat: C - B == 0 0.10853 0.02013 5.391 < 0.001 *** -treat: D - B == 0 0.02991 0.02013 1.485 0.61546 -treat: D - C == 0 -0.07862 0.02013 -3.905 0.00282 ** +treat: D - B == 0 0.02991 0.02013 1.485 0.61547 +treat: D - C == 0 -0.07862 0.02013 -3.905 0.00274 ** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 (Adjusted p values reported -- single-step method) @@ -721,21 +721,21 @@

4.1 Verwijderen van Fit: lm(formula = 1/time ~ poison + treat, data = rats) -Quantile = 2.8497 +Quantile = 2.8499 95% family-wise confidence level Linear Hypotheses: Estimate lwr upr -poison: II - I == 0 0.0468641 -0.0028208 0.0965491 -poison: III - I == 0 0.1996425 0.1499575 0.2493274 -poison: III - II == 0 0.1527784 0.1030934 0.2024633 -treat: B - A == 0 -0.1657402 -0.2231115 -0.1083690 -treat: C - A == 0 -0.0572135 -0.1145848 0.0001577 -treat: D - A == 0 -0.1358338 -0.1932051 -0.0784626 -treat: C - B == 0 0.1085267 0.0511554 0.1658979 -treat: D - B == 0 0.0299064 -0.0274648 0.0872777 -treat: D - C == 0 -0.0786203 -0.1359915 -0.0212490 +poison: II - I == 0 0.0468641 -0.0028243 0.0965526 +poison: III - I == 0 0.1996425 0.1499540 0.2493310 +poison: III - II == 0 0.1527784 0.1030899 0.2024668 +treat: B - A == 0 -0.1657402 -0.2231155 -0.1083649 +treat: C - A == 0 -0.0572135 -0.1145888 0.0001618 +treat: D - A == 0 -0.1358338 -0.1932091 -0.0784585 +treat: C - B == 0 0.1085267 0.0511514 0.1659020 +treat: D - B == 0 0.0299064 -0.0274689 0.0872817 +treat: D - C == 0 -0.0786203 -0.1359956 -0.0212450 
plot(comparisons,yaxt="none")
 contrastNames <- c("II-I","III-I","III-II","B-A","C-A","D-A","C-B","D-B","D-C")
 axis(2,at=c(length(contrastNames):1), labels=contrastNames,las=2)
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4.1.2 Besluitvorming

## ## Fit: lm(formula = BPSysAve ~ Age * Gender, data = bpData, weights = 1/mSd$fitted^2) ## -## Quantile = 2.3167 +## Quantile = 2.317 ## 95% family-wise confidence level ## ## ## Linear Hypotheses: ## Estimate lwr upr ## Age == 0 0.4400 0.4050 0.4750 -## Age + Age:Gendermale == 0 0.2484 0.2049 0.2919 +## Age + Age:Gendermale == 0 0.2484 0.2048 0.2919 ## Age:Gendermale == 0 -0.1916 -0.2475 -0.1357
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3 Hypotheses testen

## Estimate Std. Error t value Pr(>|t|) ## bacon == 0 -1.19081 0.13182 -9.034 <0.001 *** ## bacon + bacon:sexmale == 0 -0.87572 0.06286 -13.930 <0.001 *** -## bacon:sexmale == 0 0.31509 0.14603 2.158 0.0734 . +## bacon:sexmale == 0 0.31509 0.14603 2.158 0.0736 . ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## (Adjusted p values reported -- single-step method) @@ -754,15 +754,15 @@

3 Hypotheses testen

## ## Fit: lm(formula = permeat ~ bacon + length + sex + bacon:sex, data = pigs) ## -## Quantile = 2.3172 +## Quantile = 2.3178 ## 95% family-wise confidence level ## ## ## Linear Hypotheses: ## Estimate lwr upr -## bacon == 0 -1.19081 -1.49627 -0.88535 -## bacon + bacon:sexmale == 0 -0.87572 -1.02139 -0.73005 -## bacon:sexmale == 0 0.31509 -0.02329 0.65347 +## bacon == 0 -1.19081 -1.49634 -0.88528 +## bacon + bacon:sexmale == 0 -0.87572 -1.02142 -0.73001 +## bacon:sexmale == 0 0.31509 -0.02337 0.65355

4 Conclusie

diff --git a/Examenvoorbeeld_oefening_1.pdf b/Examenvoorbeeld_oefening_1.pdf index 96f42f6..b527843 100644 Binary files a/Examenvoorbeeld_oefening_1.pdf and b/Examenvoorbeeld_oefening_1.pdf differ diff --git a/Examenvoorbeeld_oefening_2.html b/Examenvoorbeeld_oefening_2.html index 9694934..8bddf11 100644 --- a/Examenvoorbeeld_oefening_2.html +++ b/Examenvoorbeeld_oefening_2.html @@ -692,7 +692,7 @@

3 Hypotheses testen

## Estimate Std. Error t value Pr(>|t|) ## tissueV == 0 7.9680 0.4532 17.580 <0.001 *** ## tissueV + locationR:tissueV == 0 5.5038 0.4532 12.143 <0.001 *** -## locationR:tissueV == 0 -2.4641 0.6410 -3.844 0.0193 * +## locationR:tissueV == 0 -2.4641 0.6410 -3.844 0.0195 * ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## (Adjusted p values reported -- single-step method) @@ -703,24 +703,24 @@

3 Hypotheses testen

## Fit: lm(formula = intensity %>% log2 ~ location * tissue + patient, ## data = hart) ## -## Quantile = 3.0262 +## Quantile = 3.0167 ## 95% family-wise confidence level ## ## ## Linear Hypotheses: ## Estimate lwr upr -## tissueV == 0 7.9680 6.5963 9.3396 -## tissueV + locationR:tissueV == 0 5.5038 4.1322 6.8755 -## locationR:tissueV == 0 -2.4641 -4.4039 -0.5244 +## tissueV == 0 7.9680 6.6006 9.3353 +## tissueV + locationR:tissueV == 0 5.5038 4.1365 6.8711 +## locationR:tissueV == 0 -2.4641 -4.3978 -0.5304 
2^confint(mcp)$confint
##                                Estimate         lwr         upr
-## tissueV                     250.3757829 96.85309171 647.2486482
-## tissueV + locationR:tissueV  45.3753769 17.55259829 117.3002876
-## locationR:tissueV             0.1812291  0.04730366   0.6943223
+## tissueV                     250.3757829 96.81778511 647.4846807
+## tissueV + locationR:tissueV  45.3753769 17.54619970 117.3430636
+## locationR:tissueV             0.1812291  0.04727928   0.6946804
 ## attr(,"conf.level")
 ## [1] 0.95
 ## attr(,"calpha")
-## [1] 3.023148
+## [1] 3.024308

4 Conclusie:

@@ -729,10 +729,10 @@

4 Conclusie:

0.001).

Het geometrisch gemiddelde van de expressie van Myosin3L is een factor 250 hoger in het linkerventrikel dan in het linkeratrium (p < -0.001, 95% BI [96.5, 649.4]).

+0.001, 95% BI [96.8, 647.9]).

Het geometrisch gemiddelde van de expressie van Myosin3L is een factor 45 hoger in het rechterventrikel dan in het rechteratrium (p < -0.001, 95% BI [17.6, 117.2]).

+0.001, 95% BI [17.5, 117.4]).

De opregulatie van Myosin3L in ventrikel vs het atrium is gemiddeld een factor 6 hoger in de linker- dan in de rechterzijde (p = 0.018, 95% BI [1.4, 21.1] ).

diff --git a/Examenvoorbeeld_oefening_2.pdf b/Examenvoorbeeld_oefening_2.pdf index dd160cc..c3513cf 100644 Binary files a/Examenvoorbeeld_oefening_2.pdf and b/Examenvoorbeeld_oefening_2.pdf differ diff --git a/Examenvoorbeeld_oefening_2_opgave.pdf b/Examenvoorbeeld_oefening_2_opgave.pdf index be6ad73..82b7005 100644 Binary files a/Examenvoorbeeld_oefening_2_opgave.pdf and b/Examenvoorbeeld_oefening_2_opgave.pdf differ diff --git a/Exp_design_fast_1_sol.html b/Exp_design_fast_1_sol.html index 05de769..2eaa93a 100644 --- a/Exp_design_fast_1_sol.html +++ b/Exp_design_fast_1_sol.html @@ -677,9 +677,9 @@

4.2 Simulation

alpha <- 0.05 power <- simFast(form, rodents, betas, sd, contrasts = contrast, alpha = alpha, nSim = nSim) power
-
## [1] 0.2137
+
## [1] 0.2239

We observe that the experiment is severly underpowered. We only have -a power of 21.4% to pick up the treatment effect.

+a power of 22.4% to pick up the treatment effect.

@@ -696,7 +696,7 @@

5 Power for a balanced predictorData <- data.frame(group = rep(c("ctrl","treat"),c(n1,n2)) %>% as.factor) powerBalanced <- simFast(form, predictorData, betas, sd, contrasts = contrast, alpha = alpha, nSim = nSim) powerBalanced

-
## [1] 0.2462
+
## [1] 0.2596

We observe that the power is larger for the balanced design. We could also have known this from formula of the standard error from the two-sample t-test.

diff --git a/Exp_design_fast_1_sol.pdf b/Exp_design_fast_1_sol.pdf index b7bd650..af9f814 100644 Binary files a/Exp_design_fast_1_sol.pdf and b/Exp_design_fast_1_sol.pdf differ diff --git a/Exp_design_fast_1_sol_files/figure-html/unnamed-chunk-3-1.png b/Exp_design_fast_1_sol_files/figure-html/unnamed-chunk-3-1.png index 366de59..252ca16 100644 Binary files a/Exp_design_fast_1_sol_files/figure-html/unnamed-chunk-3-1.png and b/Exp_design_fast_1_sol_files/figure-html/unnamed-chunk-3-1.png differ diff --git a/Exp_design_fast_2_sol.html b/Exp_design_fast_2_sol.html index 6872e1c..1ac51cb 100644 --- a/Exp_design_fast_2_sol.html +++ b/Exp_design_fast_2_sol.html @@ -606,10 +606,10 @@

1.3 Power for power <- simFast(form, Puromycin, betas, sd, contrasts = contrast, alpha = alpha, nSim = nSim) power -
[1] 0.4223
+
[1] 0.4285

The power to pick up a slope of \(\beta_1=10\) for this experiment is only -42.2%.

+42.9%.

2 Optimal design with 12 
powerOpt <- simFast(form, simData, betas, sd, contrasts = contrast, alpha = alpha, nSim = nSim)
 powerOpt
-
[1] 0.6081
+
[1] 0.6047

Note that the power for a design where we repeat each concentration 1 time and the minimum and maximum concentration 4 times is considerably higher than that for the designs where we repeat all data points.

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2.1 Import KPNA2 data in ## Estimate Std. Error t value Pr(>|t|) ## grade3 == 0 1.6675 0.1827 9.127 < 0.001 *** ## grade3 + grade3:node1 == 0 0.8928 0.1827 4.886 < 0.001 *** -## node1 == 0 0.6577 0.1827 3.600 0.00712 ** -## node1 + grade3:node1 == 0 -0.1170 0.1827 -0.640 0.89823 -## grade3:node1 == 0 -0.7748 0.2584 -2.998 0.02653 * +## node1 == 0 0.6577 0.1827 3.600 0.00728 ** +## node1 + grade3:node1 == 0 -0.1170 0.1827 -0.640 0.89822 +## grade3:node1 == 0 -0.7748 0.2584 -2.998 0.02662 * ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## (Adjusted p values reported -- single-step method) @@ -744,7 +744,7 @@

3.2 power of current power1 <- simFastMultipleContrasts(form, kpna2, betas, sd, contrasts, nSim = nSim) power1 
##     graden0     graden1      nodeg1      nodeg3 interaction 
-##     1.00000     0.97115     0.77105     0.02580     0.57105
+## 1.00000 0.97210 0.77340 0.02430 0.57225

We observe large powers for all contrasts, except for contrast nodeg3, which has a small effect size.

@@ -780,15 +780,15 @@

3.3 Power for increasing } powers 
##        n graden0 graden1  nodeg1  nodeg3 interaction
-##  [1,]  2 0.70525 0.21170 0.11090 0.01155     0.07710
-##  [2,]  3 0.99170 0.56765 0.29185 0.01600     0.19135
-##  [3,]  4 0.99995 0.80185 0.47860 0.01945     0.31810
-##  [4,]  5 1.00000 0.92250 0.64605 0.02170     0.45465
-##  [5,]  6 1.00000 0.96890 0.76020 0.02395     0.56840
-##  [6,]  7 1.00000 0.98930 0.85155 0.02610     0.66720
-##  [7,]  8 1.00000 0.99650 0.90705 0.03195     0.74735
-##  [8,]  9 1.00000 0.99895 0.94380 0.03340     0.81375
-##  [9,] 10 1.00000 0.99940 0.96920 0.03760     0.86985
+## [1,] 2 0.70425 0.21590 0.10945 0.01315 0.07565 +## [2,] 3 0.99330 0.56650 0.29390 0.01475 0.19335 +## [3,] 4 0.99985 0.80505 0.48135 0.01875 0.31890 +## [4,] 5 1.00000 0.91870 0.63915 0.02080 0.44875 +## [5,] 6 1.00000 0.97270 0.76385 0.02415 0.57265 +## [6,] 7 1.00000 0.98935 0.85140 0.02930 0.67180 +## [7,] 8 1.00000 0.99680 0.90725 0.03055 0.75520 +## [8,] 9 1.00000 0.99900 0.94380 0.03385 0.81975 +## [9,] 10 1.00000 0.99960 0.96910 0.03955 0.86520 
powers %>% 
   as.data.frame %>% 
   gather(contrast, power, -n) %>% 
@@ -818,7 +818,7 @@ 
3.4 Power when FC for
 power3 <- simFastMultipleContrasts(form, kpna2, betas2, sd, contrasts,nSim = nSim)
 power3
##     graden0     graden1      nodeg1      nodeg3 interaction 
-##     0.63860     0.05100     0.76620     0.02570     0.56395
+## 0.63630 0.05205 0.76120 0.02380 0.56895

It is clear that only the power of the contrasts containing \(\beta_g\) change when the effect size of \(\beta_g\) changes.

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3.4 Post-hoc analyse

## ## Linear Hypotheses: ## Estimate Std. Error t value Pr(>|t|) -## linseed - casein == 0 -104.83 23.28 -4.504 0.000201 *** -## soybean - casein == 0 -77.15 22.43 -3.440 0.004220 ** -## soybean - linseed == 0 27.68 22.43 1.234 0.441428 +## linseed - casein == 0 -104.83 23.28 -4.504 < 0.001 *** +## soybean - casein == 0 -77.15 22.43 -3.440 0.00432 ** +## soybean - linseed == 0 27.68 22.43 1.234 0.44141 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## (Adjusted p values reported -- single-step method) @@ -805,15 +805,15 @@

3.4 Post-hoc analyse

## ## Fit: lm(formula = weight ~ feed, data = chickwts) ## -## Quantile = 2.4459 +## Quantile = 2.4472 ## 95% family-wise confidence level ## ## ## Linear Hypotheses: ## Estimate lwr upr -## linseed - casein == 0 -104.8333 -161.7640 -47.9026 -## soybean - casein == 0 -77.1548 -132.0146 -22.2950 -## soybean - linseed == 0 27.6786 -27.1812 82.5384 +## linseed - casein == 0 -104.8333 -161.7946 -47.8720 +## soybean - casein == 0 -77.1548 -132.0440 -22.2655 +## soybean - linseed == 0 27.6786 -27.2107 82.5678 
plot(mcp)

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6.4 Post-hoc 
confDiet <- confint(multComp)
 confDiet$confint
##       Estimate      lwr      upr
-## 2 - 1 20.33333 12.79575 27.87091
-## 3 - 1 44.00000 36.46242 51.53758
-## 3 - 2 23.66667 16.12909 31.20425
+## 2 - 1 20.33333 12.79917 27.86750
+## 3 - 1 44.00000 36.46584 51.53416
+## 3 - 2 23.66667 16.13250 31.20083
 ## attr(,"conf.level")
 ## [1] 0.95
 ## attr(,"calpha")
-## [1] 2.793755
+## [1] 2.792487

6.5 Conclusion

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