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    • @@ -725,15 +737,15 @@

    4.1 Verwijderen van Linear Hypotheses: Estimate Std. Error t value Pr(>|t|) -poison: II - I == 0 0.04686 0.01744 2.688 0.07357 . +poison: II - I == 0 0.04686 0.01744 2.688 0.07349 . 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 0.05098 . +treat: C - A == 0 -0.05721 0.02013 -2.842 0.05093 . 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 0.00278 ** +treat: D - C == 0 -0.07862 0.02013 -3.905 0.00288 ** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 (Adjusted p values reported -- single-step method) @@ -752,15 +764,15 @@

    4.1 Verwijderen van Linear Hypotheses: Estimate lwr upr -poison: II - I == 0 0.0468641 -0.0027970 0.0965253 -poison: III - I == 0 0.1996425 0.1499814 0.2493036 -poison: III - II == 0 0.1527784 0.1031172 0.2024395 -treat: B - A == 0 -0.1657402 -0.2230840 -0.1083965 -treat: C - A == 0 -0.0572135 -0.1145573 0.0001302 -treat: D - A == 0 -0.1358338 -0.1931776 -0.0784901 -treat: C - B == 0 0.1085267 0.0511830 0.1658704 -treat: D - B == 0 0.0299064 -0.0274373 0.0872502 -treat: D - C == 0 -0.0786203 -0.1359640 -0.0212765 +poison: II - I == 0 0.0468641 -0.0027958 0.0965241 +poison: III - I == 0 0.1996425 0.1499826 0.2493024 +poison: III - II == 0 0.1527784 0.1031184 0.2024383 +treat: B - A == 0 -0.1657402 -0.2230826 -0.1083979 +treat: C - A == 0 -0.0572135 -0.1145559 0.0001288 +treat: D - A == 0 -0.1358338 -0.1931762 -0.0784915 +treat: C - B == 0 0.1085267 0.0511844 0.1658690 +treat: D - B == 0 0.0299064 -0.0274359 0.0872488 +treat: D - C == 0 -0.0786203 -0.1359626 -0.0212779 
    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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    • @@ -917,9 +929,9 @@

    4.1.2 Besluitvorming

    ## ## Linear Hypotheses: ## Estimate Std. Error t value Pr(>|t|) -## Age == 0 0.43999 0.01511 29.127 <1e-10 *** -## Age + Age:Gendermale == 0 0.24840 0.01879 13.217 <1e-10 *** -## Age:Gendermale == 0 -0.19159 0.02411 -7.946 <1e-10 *** +## Age == 0 0.43999 0.01511 29.127 < 2e-16 *** +## Age + Age:Gendermale == 0 0.24840 0.01879 13.217 < 2e-16 *** +## Age:Gendermale == 0 -0.19159 0.02411 -7.946 2.66e-15 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## (Adjusted p values reported -- single-step method) @@ -930,14 +942,14 @@

    4.1.2 Besluitvorming

    ## ## Fit: lm(formula = BPSysAve ~ Age * Gender, data = bpData, weights = 1/mSd$fitted^2) ## -## Quantile = 2.3168 +## Quantile = 2.3171 ## 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
    diff --git a/10-Recap-AlgemeenLineairModel-OverigeConcepten.pdf b/10-Recap-AlgemeenLineairModel-OverigeConcepten.pdf index 2ebdff4..aad61ad 100644 Binary files a/10-Recap-AlgemeenLineairModel-OverigeConcepten.pdf and b/10-Recap-AlgemeenLineairModel-OverigeConcepten.pdf differ diff --git a/10-Recap-AlgemeenLineairModel-OverigeConcepten_files/figure-html/unnamed-chunk-26-1.png b/10-Recap-AlgemeenLineairModel-OverigeConcepten_files/figure-html/unnamed-chunk-26-1.png index ed72855..a97ab63 100644 Binary files a/10-Recap-AlgemeenLineairModel-OverigeConcepten_files/figure-html/unnamed-chunk-26-1.png and b/10-Recap-AlgemeenLineairModel-OverigeConcepten_files/figure-html/unnamed-chunk-26-1.png differ diff --git a/10-Recap-AlgemeenLineairModel-OverigeConcepten_files/figure-html/unnamed-chunk-27-1.png b/10-Recap-AlgemeenLineairModel-OverigeConcepten_files/figure-html/unnamed-chunk-27-1.png index 213b9e8..749652d 100644 Binary files a/10-Recap-AlgemeenLineairModel-OverigeConcepten_files/figure-html/unnamed-chunk-27-1.png and b/10-Recap-AlgemeenLineairModel-OverigeConcepten_files/figure-html/unnamed-chunk-27-1.png differ diff --git a/10-Recap-AlgemeenLineairModel-OverigeConcepten_files/figure-html/unnamed-chunk-30-1.png b/10-Recap-AlgemeenLineairModel-OverigeConcepten_files/figure-html/unnamed-chunk-30-1.png index e4bc90b..3f9f0fc 100644 Binary files a/10-Recap-AlgemeenLineairModel-OverigeConcepten_files/figure-html/unnamed-chunk-30-1.png and b/10-Recap-AlgemeenLineairModel-OverigeConcepten_files/figure-html/unnamed-chunk-30-1.png differ diff --git a/Examenvoorbeeld_oefening_1.html b/Examenvoorbeeld_oefening_1.html index 60aeaa9..3821e4a 100644 --- a/Examenvoorbeeld_oefening_1.html +++ b/Examenvoorbeeld_oefening_1.html @@ -480,6 +480,18 @@
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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 0.0735 . +## bacon:sexmale == 0 0.31509 0.14603 2.158 0.0734 . ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## (Adjusted p values reported -- single-step method) @@ -779,15 +791,15 @@

    3 Hypotheses testen

    ## ## Fit: lm(formula = permeat ~ bacon + length + sex + bacon:sex, data = pigs) ## -## Quantile = 2.318 +## Quantile = 2.3202 ## 95% family-wise confidence level ## ## ## Linear Hypotheses: -## Estimate lwr upr -## bacon == 0 -1.1908 -1.4964 -0.8852 -## bacon + bacon:sexmale == 0 -0.8757 -1.0214 -0.7300 -## bacon:sexmale == 0 0.3151 -0.0234 0.6536 +## Estimate lwr upr +## bacon == 0 -1.19081 -1.49667 -0.88496 +## bacon + bacon:sexmale == 0 -0.87572 -1.02158 -0.72986 +## bacon:sexmale == 0 0.31509 -0.02373 0.65391

    4 Conclusie

    @@ -798,7 +810,7 @@

    4 Conclusie

    (p<<0.001) als mannelijke varkens (p<0.001). Voor zeugen, die een verschillende dikte van speklaag hebben, is het vleespercentage gemiddeld 1.19 %/mm lager bij zeugen met de dikste speklaag (95% BI -[0.89 %/mm, 1.5 %/mm]). Voor beren (mannelijke varkens), die een +[0.88 %/mm, 1.5 %/mm]). Voor beren (mannelijke varkens), die een verschillende dikte van speklaag hebben, is het vleespercentage gemiddeld 0.88 %/mm lager bij beren met de dikste speklaag (95% BI [0.73 %/mm, 1.02 %/mm]). Er is op het 5% significantieniveau geen significant diff --git a/Examenvoorbeeld_oefening_1.pdf b/Examenvoorbeeld_oefening_1.pdf index f84ecfd..f46f66f 100644 Binary files a/Examenvoorbeeld_oefening_1.pdf and b/Examenvoorbeeld_oefening_1.pdf differ diff --git a/Examenvoorbeeld_oefening_1_opgave.html b/Examenvoorbeeld_oefening_1_opgave.html index 1ea52c2..9073cf5 100644 --- a/Examenvoorbeeld_oefening_1_opgave.html +++ b/Examenvoorbeeld_oefening_1_opgave.html @@ -390,6 +390,18 @@
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    3 Hypotheses testen

    ## Fit: lm(formula = intensity %>% log2 ~ location * tissue + patient, ## data = hart) ## -## Quantile = 3.0268 +## Quantile = 3.0293 ## 95% family-wise confidence level ## ## ## Linear Hypotheses: ## Estimate lwr upr -## tissueV == 0 7.9680 6.5961 9.3398 -## tissueV + locationR:tissueV == 0 5.5038 4.1320 6.8757 -## locationR:tissueV == 0 -2.4641 -4.4042 -0.5240 +## tissueV == 0 7.9680 6.5950 9.3409 +## tissueV + locationR:tissueV == 0 5.5038 4.1308 6.8768 +## locationR:tissueV == 0 -2.4641 -4.4058 -0.5224 
    2^confint(mcp)$confint
    ##                                Estimate         lwr         upr
-## tissueV                     250.3757829 96.94415082 646.6406911
-## tissueV + locationR:tissueV  45.3753769 17.56910085 117.1901081
-## locationR:tissueV             0.1812291  0.04736657   0.6934001
+## tissueV                     250.3757829 96.89264124 646.9844549
+## tissueV + locationR:tissueV  45.3753769 17.55976581 117.2524081
+## locationR:tissueV             0.1812291  0.04733098   0.6939215
 ## attr(,"conf.level")
 ## [1] 0.95
 ## attr(,"calpha")
-## [1] 3.020156
    +## [1] 3.021848

    4 Conclusie:

    @@ -754,10 +766,10 @@

    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 [97.1, 645.8]).

    +0.001, 95% BI [96.8, 647.4]).

    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, 117.3]).

    +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 = 0.019, 95% BI [1.4, 21.1] ).

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    • @@ -702,9 +714,9 @@

    4.2 Simulation

    alpha <- 0.05 power <- simFast(form, rodents, betas, sd, contrasts = contrast, alpha = alpha, nSim = nSim) power
    -
    ## [1] 0.2213
    +
    ## [1] 0.2248

    We observe that the experiment is severly underpowered. We only have -a power of 22.1% to pick up the treatment effect.

    +a power of 22.5% to pick up the treatment effect.

    @@ -721,7 +733,7 @@

    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] 0.2406
    +
    ## [1] 0.2444

    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 bc32866..3db7adf 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 00a3ebc..fdb6751 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_ex.html b/Exp_design_fast_2_ex.html index fd98f65..f8044d1 100644 --- a/Exp_design_fast_2_ex.html +++ b/Exp_design_fast_2_ex.html @@ -480,6 +480,18 @@
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    • @@ -631,10 +643,10 @@

    1.3 Power for power <- simFast(form, Puromycin, betas, sd, contrasts = contrast, alpha = alpha, nSim = nSim) power -
    [1] 0.4167
    +
    [1] 0.4189

    The power to pick up a slope of \(\beta_1=10\) for this experiment is only -41.7%.

    +41.9%.

    2 Optimal design with 12 
    powerOpt <- simFast(form, simData, betas, sd, contrasts = contrast, alpha = alpha, nSim = nSim)
 powerOpt
    -
    [1] 0.6018
    +
    [1] 0.609

    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 ## ## Linear Hypotheses: ## 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 0.00704 ** -## node1 + grade3:node1 == 0 -0.1170 0.1827 -0.640 0.89814 -## grade3:node1 == 0 -0.7748 0.2584 -2.998 0.02654 * +## 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 0.0071 ** +## node1 + grade3:node1 == 0 -0.1170 0.1827 -0.640 0.8981 +## grade3:node1 == 0 -0.7748 0.2584 -2.998 0.0268 * ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## (Adjusted p values reported -- single-step method) @@ -769,7 +781,7 @@

    3.2 power of current power1 <- simFastMultipleContrasts(form, kpna2, betas, sd, contrasts, nSim = nSim) power1 
    ##     graden0     graden1      nodeg1      nodeg3 interaction 
-##     1.00000     0.96925     0.75830     0.02585     0.56685
    +## 1.00000 0.97290 0.76090 0.02525 0.57180

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

    @@ -805,15 +817,15 @@

    3.3 Power for increasing } powers 
    ##        n graden0 graden1  nodeg1  nodeg3 interaction
-##  [1,]  2 0.70550 0.22045 0.11165 0.01285     0.07505
-##  [2,]  3 0.99210 0.55885 0.29940 0.01480     0.19520
-##  [3,]  4 0.99985 0.79860 0.48735 0.01945     0.32390
-##  [4,]  5 1.00000 0.91905 0.64665 0.01990     0.44645
-##  [5,]  6 1.00000 0.97155 0.76350 0.02295     0.56855
-##  [6,]  7 1.00000 0.99030 0.84685 0.02650     0.66150
-##  [7,]  8 1.00000 0.99675 0.90680 0.03250     0.74885
-##  [8,]  9 1.00000 0.99920 0.94710 0.03445     0.82140
-##  [9,] 10 1.00000 0.99970 0.96930 0.03940     0.87100
    +## [1,] 2 0.70185 0.21485 0.11215 0.01275 0.07905 +## [2,] 3 0.99225 0.57085 0.29390 0.01785 0.19150 +## [3,] 4 0.99990 0.79840 0.48920 0.01825 0.32165 +## [4,] 5 1.00000 0.92140 0.64380 0.02170 0.44810 +## [5,] 6 1.00000 0.97050 0.76700 0.02550 0.57060 +## [6,] 7 1.00000 0.99075 0.84970 0.02690 0.67360 +## [7,] 8 1.00000 0.99610 0.91025 0.03105 0.75620 +## [8,] 9 1.00000 0.99900 0.94605 0.03335 0.81880 +## [9,] 10 1.00000 0.99955 0.96645 0.03845 0.86365 
    powers %>% 
   as.data.frame %>% 
   gather(contrast, power, -n) %>% 
@@ -843,7 +855,7 @@ 
    3.4 Power when FC for
 power3 <- simFastMultipleContrasts(form, kpna2, betas2, sd, contrasts,nSim = nSim)
 power3
    ##     graden0     graden1      nodeg1      nodeg3 interaction 
-##     0.63640     0.05235     0.76450     0.02545     0.56405
    +## 0.63785 0.05480 0.76230 0.02490 0.57180

    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 < 0.001 *** -## soybean - casein == 0 -77.15 22.43 -3.440 0.00436 ** -## soybean - linseed == 0 27.68 22.43 1.234 0.44142 +## soybean - casein == 0 -77.15 22.43 -3.440 0.00428 ** +## soybean - linseed == 0 27.68 22.43 1.234 0.44152 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## (Adjusted p values reported -- single-step method) @@ -830,15 +842,15 @@

    3.4 Post-hoc analyse

    ## ## Fit: lm(formula = weight ~ feed, data = chickwts) ## -## Quantile = 2.4475 +## Quantile = 2.4463 ## 95% family-wise confidence level ## ## ## Linear Hypotheses: ## Estimate lwr upr -## linseed - casein == 0 -104.8333 -161.8015 -47.8651 -## soybean - casein == 0 -77.1548 -132.0507 -22.2588 -## soybean - linseed == 0 27.6786 -27.2174 82.5745 +## linseed - casein == 0 -104.8333 -161.7725 -47.8941 +## soybean - casein == 0 -77.1548 -132.0228 -22.2868 +## soybean - linseed == 0 27.6786 -27.1894 82.5466 
    plot(mcp)

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    6.4 Post-hoc 
    confDiet <- confint(multComp)
 confDiet$confint
    ##       Estimate      lwr      upr
-## 2 - 1 20.33333 12.79730 27.86936
-## 3 - 1 44.00000 36.46397 51.53603
-## 3 - 2 23.66667 16.13064 31.20270
+## 2 - 1 20.33333 12.80467 27.86199
+## 3 - 1 44.00000 36.47134 51.52866
+## 3 - 2 23.66667 16.13801 31.19533
 ## attr(,"conf.level")
 ## [1] 0.95
 ## attr(,"calpha")
-## [1] 2.793181
    +## [1] 2.790448

    6.5 Conclusion

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    Werkcolleges

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