2.1.1 Introduction

There are 1000 mouse femur bones which have been measured at high resolution and a number of shape analyses run on each sample. - Phenotypical Information - Each column represents a metric which was assessed in the images - CORT_DTO__C_TH for example is the mean thickness of the cortical bone

ID	BMD	MECHANICS_STIFFNESS	CORT_DTO__C_TH	CORT_DTO__C_TH_SD
351	0.0302208	57.16318	0.186455	0.019785
356	0.0327883	54.97201	0.183007	0.015696
357	0.0360747	73.59088	0.216930	0.028019
359	0.0311451	49.85482	0.193758	0.024087

• Genetic Information (genoTable.csv)
• Each animal has been tagged at a number of different regions of the genome (called markers: D1Mit236)
• At each marker there are 3 (actually 4) possibilities
• A is homozygous (the same from both parents) from the A strain
• B is homozygous from the B strain
• H is heterozygous (one from A, one from B)

• ‘-’ is missing or erronous measurements

  ID	D1Mi	t64 D1Mi	t236 D1Mi	t7 D1Mi	t386
  101	685	A	H	H	H
  102	686	B	B	B	H
  103	687	A	A	H	H
  104	688	H	H	H	A
  105	689	H	H	-	A

2.1.2 Tasks

1. Download the two needed tables to start the analysis

• phenoTable
• genoTable

1. Using the workflow ‘ComparingSamples’ load the data and make sure you can produce the basic plots for the histogram
2. Explore the data and correlations between various metrics by using the ‘Scatter Matrix’ plotting component. Change the components to examine different variables
3. For the rest of the analysis you can connect the various components to the ‘Column Filter’ node since that is the last step in the processing
4. Use one of the T-Test nodes in the Statistics -> Hypothesis Testing section to see if there is a statistically significant difference between Gender’s when examining Cortical Bone Microstructural Thickness (Mean)

• Which value is the p-value?
• What does the p-value mean, is it significant, by what criterion?

1. Use another node from the Hypothesis Testing section to evaluate the effect on the D16Mit5 on the Lacuna Distribution Anisotropy? Is it significant?

2.1.3 Questions

1. In the ‘Independent Groups T-Test’ node we can run a t-test against all of the columns at the same time, why SHOULDN’T we do this?

• If we do, how do we need to interpret this in the results
• Is p<0.05 a sufficient signifance criteria?

2.2.1 Questions

1. We want to know if there is a statistically significant difference in

• cell volume
• cell shape
• cell density
• between the two samples given the variation in the detector
• which metric do we need here? why?

1. We see in the volume comparison a very skewed representation of the data

• why is this? (Hint check the segmented images)
• What might be done to alleviate it (hint Row Filter)

2.2.2 Hints

1. Look at the kind of noise (you can peek inside the Crappy Camera) to choose the proper filter
2. Use an automated thresholding technique for finding the bone automatic-methods
3. To do this we will need to enhance the image, segment out the bone (dense) tissue, find the mask so that we can look at the background: contouring
4. We then need to label the cells, and analyze their volume and shape: labeling
5. Use a Chunk Loop for the Segmenting Features node to prevent all of the features being dumped into the same output (they can afterwards be recombined with the original images using the Join node)
6. The final join should combine the output of the feature analysis (the end loop in this case) and the original crappy camera images. Since the Chunk Loop outputs iterations, we simply use that as the key for joining
7. Use Morphology and strongy filter parameters it might be possible to maximize the differences in the groups
8. You can make the plots in R (sometimes easier than KNIME) using the R View (Table) node and the following code (for volume)

library(ggplot2)
cur.df<-data.frame(
  sample=as.factor(knime.in$"Image Number"),
    measurement=knime.in$"Measurement_Number",
    volume=knime.in$"Num Pix"
    )
    
ggplot(cur.df,aes(x=volume))+
    geom_density(aes(color=sample,group=measurement))+
    theme_bw(25)

• Mean Volume

library(ggplot2)
library(plyr)
cur.df<-data.frame(
  sample=as.factor(knime.in$"Image Number"),
    measurement=knime.in$"Measurement_Number",
    volume=knime.in$"Num Pix"
    )
sum.df<-ddply(cur.df,.(sample,measurement),function(in.df) {
    data.frame(mean.volume=mean(in.df$volume),cell.count=nrow(in.df))
})
ggplot(sum.df,aes(x=mean.volume))+
    geom_density(aes(color=sample))+
    theme_bw(25)

• Cell Count

library(ggplot2)
library(plyr)
cur.df<-data.frame(
  sample=as.factor(knime.in$"Image Number"),
    measurement=knime.in$"Measurement_Number",
    volume=knime.in$"Num Pix"
    )
sum.df<-ddply(cur.df,.(sample,measurement),function(in.df) {
    data.frame(mean.volume=mean(in.df$volume),cell.count=nrow(in.df))
})
ggplot(sum.df,aes(x=cell.count))+
    geom_density(aes(color=sample))+
    theme_bw(25)

1. What is intraclass correlation? How can it be applied to these data?

• The following code can be used inside an R View block to calculate the ICC value (and then just click ‘Eval Script’)

library(ICC)
in.data<-data.frame(
  metric = knime.in$"Num Pix",
    group = knime.in$"Image Number"
    )
icVal<-ICCbare(metric,group,data=in.data)$ICC
icVal

• If the value for a specific metric is 0.012 how should we interpret that?

2.2.3 Big Hint (don’t read unless you’re stuck)

One possible final result looks something like this

2.3.1 Questions

1. If we change the size of the chunks to the same as the number of elements in the list do we still expect to find ‘significant’ (<0.05) values? Why or why not?
2. How does comparing against the null hypothesis being 0 relate to comparing two groups?
3. How does comparing a single column compare to looking at different metrics for the same samples?
4. What is bonferroni correction (hint: wikipedia) and how could it be applied to this simulation?

• Make the modification needed

2.4.1 Introduction

Making plots or graphics should be divided into separate independent components. - Setup is the $ggplot$ command and the data - Mapping is in the $aes$ command $$ggplot(\textrm{input data frame},aes(x=\textrm{name of x column},y=\textrm{name of y column}))+$$ - Plot is the next command (geom_point, geom_smooth, geom_density, geom_histogram, geom_contour) $$\textrm{geom_point}()+$$ - Coordinates can then be added to any type of plot (coord_equal, coord_polar, etc) - Scales can also be added (scale_x_log10, scale_y_sqrt, scale_color_gradientn) - Labels are added $$labs(x="\textrm{x label}",y="\textrm{y label}",title="\textrm{title}")$$

2.4.2 Tasks

• Start RStudio
• Load the necessary libraries

library("ggplot2","knitr")

• Load the phenoTable from the first exercise

# read the table in
phen.table<-read.csv("09-files/phenoTable.csv")
# take the first 4 rows and columns
p.sub.table<-pheno.table[c(1:4),c(35,c(1:4))]
# print it out nicely
kable(p.sub.table)

ID	BMD	MECHANICS_STIFFNESS	CORT_DTO__C_TH	CORT_DTO__C_TH_SD
351	0.0302208	57.16318	0.186455	0.019785
356	0.0327883	54.97201	0.183007	0.015696
357	0.0360747	73.59088	0.216930	0.028019
359	0.0311451	49.85482	0.193758	0.024087
- Set	up the inpu	t table as ```phen.tab	le``` and the map	ping with the x position mapped to BMD (Bone Mineral Density) and the y position as CT_TH_RAD (Cortical Bone Thickness)

ggplot(phen.table,aes(x=BMD,y=CT_TH_RAD))

• Create the first simple plot by adding a point representation to the plot

ggplot(phen.table,aes(x=BMD,y=CT_TH_RAD))+geom_point()

- Change color of the points to show if the animal is female or not (in the mapping)

ggplot(phen.table,aes(x=BMD,y=CT_TH_RAD,color=FEMALE))+geom_point()

- Show the color as a discrete (factor) value instead of a number

m.table<-mutate(phen.table,GENDER = ifelse(FEMALE==1,"F","M"))
ggplot(m.table,aes(x=BMD,y=CT_TH_RAD,color=GENDER))+geom_point()

- Make the plot in two facets (windows) instead of the same one

ggplot(m.table,aes(x=BMD,y=CT_TH_RAD,color=GENDER))+
  geom_point()+
  facet_wrap(~GENDER)

- Make the facet based on evenly (in number) dividing the points into 6 groups by the number of lacuna (LACUNA_COUNT)

m.table<-mutate(phen.table,
                GENDER = ifelse(FEMALE==1,"F","M"),
                LACUNA_NUMBER_GROUP = cut_number(LACUNA_COUNT,6)
                )
ggplot(m.table,aes(x=BMD,y=CT_TH_RAD,color=GENDER))+
  geom_point()+
  facet_wrap(~LACUNA_NUMBER_GROUP)

- Fix the labels and add a white background (theme_bw) with font-size 12

ggplot(m.table,aes(x=BMD,y=CT_TH_RAD,color=GENDER))+
  geom_point()+
  facet_wrap(~LACUNA_NUMBER_GROUP)+
  labs(x="Bone Mineral Density",y="Cortical Bone Thickness (um)",color="Gender")+
  theme_bw(12)

For more information and tutorial read about it in: http://ggplot2.org/

def countPoints(in: Array[Array[Boolean]]): Int = 
  in.flatten.map(if(_) 1 else 0).sum

2.5.1 Dynamic Languages!

It is critical to note, if you are using a statically-type language (C, C++, Fortran Java, Scala, Groovy, etc) you do not need to explicitly check type issues since that is automatically done by the compiler (you cannot give a string to a function expecting an integer, it simply will not run) If you are using a dynamically typed language (Matlab, Python, R, Mathematica, etc) you will need to make additional tests to make sure your function handles a variety of different input correctly. For example if you make the countPoints function in Matlab what happens when you give it a 3D array or a string? Either it should immediately throw an error message explaining that this input doesn’t make sense or explicitly handle this case. Otherwise you could have very unexpected behavior. The following is a perfectly reasonable function in Matlab

function [out]=isBiggerThanFive(inVar)
  if inVar>5
    disp([inVar ' is bigger than 5'])
    out=true;
  else
    disp([inVar ' is smaller than 5'])
    out=false;
  end

And if you execute isBiggerThanFive('Tom') it executes perfectly and you get Tom is bigger than 5 which is probably meaningless. It would be much better if the program throws an error saying that a string is not an appropriate type for this function.