VU Biostatistics and Experimental Design PLA.216

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1 VU Biostatistics and Experimental Design PLA.216 Julia Feichtinger Postdoctoral Researcher Institute of Computational Biotechnology Graz University of Technology

2 Outline for Today About this course Background on this week s exercise Data Types Data Visualization Outliers ROC Curve and Diagnostic Tests

3 About this course

4 Exercise Structure There are 4 exercise units and 2 hands-on session. Scheduled Dates Day Date Time Where Content FR 06/10/17 Optional FR 13/10/17 Mandatory WED 08/11/2017 Mandatory FR 01/12/2017 Mandatory FR 15/12/2017 Mandatory FR 12/01/2018 Mandatory 11:00 am 1 pm BMT01077 General Aspects, Introduction into R, Optional Hands-on Session to Learn R 10:15 12:15 am BMT01077 Hands-on Session to Learn R (with a report to finish during the session) 2 4 pm BKEG053 Data Types, Data Visualization, Outlier ROC Curve and Diagnostic Tests 11:00 am 1 pm BKEG053 Bland-Altman plot, Kappa coefficient More Introduction into R 11:00 am 1 pm BKEG053 Distributions, Data Transformations, Parametric Hypothesis Tests, Confidence Intervals, Multiple Testing 11:00 am 1 pm BKEG053 Distributions, Non-Parametric Hypothesis Tests, F-test, ANOVA

5 Exercise Structure Lecture notes, Exercises, Report Templates. are available at: Newsgroup Newsgroup server: news.tugraz.at Newsgroup: tu-graz.lv.biostatistik News client: e.g., in Thunderbird For instructions: Using a browser: webnews.tugraz.at You can ask questions anytime during the lecture or in the newsgroup. Please ask questions relating to the homework in the newsgroup only. (But don t post code in the newsgroup!) Student Assistant: Veronika Schusterbauer & Lisa Bernhard

6 Report Guidelines The use of report WORD template is absolutely mandatory. Put all results in one PDF file so convert report template to PDF when you are finished. Also submit your R code in one R file. Mandatory guidelines: Just answer the questions asked in the report template but answer them! Describe and reference all figures and tables you have generated. Table captions belong above the table, figure captions below the figure. The caption should describe the figure/table sufficiently without having to read the text. Do not forget the axis labels including units of your figure. We state if the exercise should be solved in R or on paper. If nothing is stated you decide. Document/comment on your R code. Handwritten sections have to be easily readable. Do not change the font or font size in the WORD template. State the correct number of decimal places. Do not forget to state your names. Write the report in teams of 2 students. Write the report in English. Points will be deducted after the 1 st homework if you do not follow the instructions!

7 Report Guidelines Reports are due: Report Day Date Time Report 1 FR 13/10/2017 After the session! Homework Report 2 WED 22/11/2017, 2 weeks 11:59 pm Homework Report 3 FR 15/12/2017, 2 weeks 11:59 pm Homework Report 4 FR 05/01/2018, 3 weeks Christmas 11:59 pm Homework Report 5 FR 26/01/2018, 2 weeks 11:59 pm Check the comments on report submission stated on the exercise sheet before submitting! Subject: Biostatistics Report for Exercise X where X is the exercise unit (1-5) Filename: ReportX_<LastName1>_<LastName2>.pdf where X is the exercise unit (1-5) RcodeX_<LastName1>_<LastName2>.R Send the report in PDF format and the R file to biostatistik@genome.tugraz.at

8 Background for This Week s Exercise

9 Sampling Sample vs. Population We (always) have a sample drawn from a larger population Which we use to draw inferences about the population Desirable properties of a sample are Large Random Sample vs. Population Mean Variance Standard deviation x µ s 2 σ 2 s σ (roman vs. greek symbols)

10 Data Types Variable We obtain one or more variables from each member of the sample A variable is something which measures some property of the members of the sample Two general types of variables Categorical Nominal (no ranking possible) Example: Sex {male, female} Example: Blood group {0, A, B, AB} Ordinal (can be ranked) Example: Cancer stage {I, II, III, IV} Numerical Discrete (Can take on only particular, isolated values) Typically counts Example: number of bacterial colonies on an agar plate Example: RNA-seq data Continuous (Can have any value in the range of possible values) Example: concentration of some analyte in solution Example: Microarray data

11 Data Visualization

12 Data Visualization Presentation of numerical data: Histogram hist()!! Partition comprises all values Values have to be assigned to the classes (bins) unequivocally The class width should be the same for all classes Mid-point of a class represents all values within the class The smaller the number of classes, the greater the class width and the greater the loss of information The higher the number of classes, the more of the uninteresting random effects are apparent Empirical formulas for the number of classes: k = n k = 5 log10(n) where k is the number of classes and n is the number of values Example from

13 Data Visualization Presentation of categorical data: Bar chart barplot()!! A bar chart is NOT a histogram Bar chart: each column represents a group defined by a categorical variable Histogram: plot the frequency of occurrences for data that has been divided into bins. In bar charts bars should always start from 0 Better to use bar charts than pie charts since the eye is good at judging linear measures and bad at judging relative areas

14 Central Tendency u Mean u Median u Mode Variable Nominal Ordinal Numerical (not skewed) Numerical (skewed) Central Tendency Mode Median Mean Median mean()! median()! mode()!

15 Data Visualization Presentation of numerical data: Box and Whisker Plot can be used to summarize a set of data based on the five number summary of this data. summary()!!!quantile()!! the summary statistics used to create a box and whisker plot are : the median of the data the lower and upper quartiles (25% and 75%) and the minimum and maximum values.!boxplot()!! 1st quartile = Q1 = Q25 2nd quartile = Q2 = Q50 = median 3rd quartile = Q3 = Q75 Interquartile range IQR = Q3 - Q1 = Q75-Q25! Example from

16 Data Variability Data Variability u Range u Percentiles u Quartiles u Interquartile Range u Variance u Standard Deviation u Coefficient of Variation u Standard Error of the Mean Shape u Kurtosis u Skewness quantiles()! sd()! IQR()!! Variable Ordinal Numerical (not skewed) Numerical (skewed) Variability Interquartile Range Standard Devia9on Interquartile Range

17 Outlier An outlier is an observation point that lies an abnormal distance from other values. It may be due to experimental error and then can be excluded from the data set. Outlier detection x i Q * IQR or x i Q * IQR x i Q * IQR or x i Q * IQR mild outlier extreme outlier 1st quartile = Q1 = Q25 2nd quartile = Q2 = Q50 = median 3rd quartile = Q3 = Q75 Interquartile range IQR = Q3 - Q1 = Q75-Q25 summary()!!!quantile()!!!iqr()!!!median()!!!!

18 Diagnostic Tests & ROC Curves

19 Diagnostic Tests With a diagnostic test we try to determine the presence of disease in an individual suspected of having the disease. We can get true negatives & true positives, but also false negatives and false positives. TN True negatives TP True positives FN False negatives FP False positives

20 Diagnostic Tests Formulas Specificity (SP) TN SP= =1 FPR TN FPR =1 FP FPR = = TN TN True negatives TP True positives FN False negatives FP False positives Sensitivity (SN) SN= TP TP + FN = TPR

21 Diagnostic Tests Formulas Positive and Negative Predictive Values (PPV, NPV) TN NPV= TN + FN TP PPV = TP + FP Accuracy (ACC) ACC = TP +TN n Prevalence (observed in this study) prevalence = TP + FN n

22 ROC Curve Receiver Operating Characteristic (ROC) Curve The curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) with various cutoffs. TPR is equivalent to sensitivity and FPR is equal to 1 specificity An ROC curve demonstrates the tradeoff between sensitivity and specificity the accuracy of the test, with the area under the curve as a measure of this accuracy. (0,1) point - perfect classification. line of no-discrimination - random guess Above this line better than random Below this line worse than random

23 ROC Curve Example Example chronic heart failure (CHF) The two peptides NPA and NPB are produced by the heart. Patients with CHF have higher NPA and a lower NPB concentration in the blood plasma. Use ROC curves to define if NPA and/or NPB can be used for CHF diagnosis. NPA [pmol/l] Sick Healthy [0;3) 3 34 [3;10) 6 37 [10;30) [30;100) [100;300) Total NPB [pmol/l] Sick Healthy [0;30) [30;100) [100;500) [500;1000) [1000;2000) Total

24 ROC Curve Example: NPA Cutoff = 3 >= 3 pmol/l False negatives (FN) NPA [pmol/l] Sick Healthy [0;3) 3 34 [3;10) 6 37 [10;30) [30;100) [100;300) Total True negatives (TN) Diagnosed as healthy with this cutoff Diagnosed as sick with this cutoff False positives (FP) True positives (TP) Direction!!

25 ROC Curve Example: NPA Formulas Specificity (SP) TN SP= =1 FPR TN FPR =1 FP FPR = = TN TN True negatives TP True positives FN False negatives FP False positives Sensitivity (SN) SN= TP TP + FN = TPR TP SN= TP + FN = 0.98 TN SP= = 0.27 FPR =1 SP = 0.73

26 ROC Curve Example: NPA Cutoff = 10 False negatives (FN) NPA [pmol/l] Sick Healthy [0;3) 3 34 [3;10) 6 37 [10;30) [30;100) [100;300) Total True negatives (TN) Diagnosed as healthy with this cutoff Diagnosed as sick with this cutoff False positives (FP) True positives (TP)

27 ROC Curve Example: NPA Formulas Specificity (SP) TN SP= =1 FPR TN FPR =1 FP FPR = = TN TN True negatives TP True positives FN False negatives FP False positives Sensitivity (SN) SN= TP TP + FN = TPR TP SN= TP + FN = 0.93 TN SP= = 0.56 FPR =1 SP = 0.44

28 ROC Curve Example: NPA Calculate TPR (sensitivity) and FPR (1 specificity) for a number of cutoffs Cutoff SensiMvity (TPR) Specificity FPR

29 ROC Curve Example: NPA Plot sensitivity vs. 1 specificity

30 ROC Curve Example: NPB Cutoff = 30 <= 30 pmol/l True positives (TP) NPB [pmol/l] Sick Healthy [0;30) [30;100) [100;500) [500;1000) [1000;2000) Total False positives (FP) Diagnosed as sick with this cutoff Diagnosed as healthy with this cutoff True negatives (TN) False negatives (FN) Direction!!

31 ROC Curve Example: NPB Formulas Specificity (SP) TN SP= =1 FPR TN FPR =1 FP FPR = = TN TN True negatives TP True positives FN False negatives FP False positives Sensitivity (SN) SN= TP TP + FN = TPR TP SN= TP + FN = 0.26 TN SP= = 0.79 FPR =1 SP = 0.21

32 ROC Curve Example: NPB Cutoff = 100 True posi9ves (TP) NPB [pmol/l] Sick Healthy [0;30) [30;100) [100;500) [500;1000) [1000;2000) Total False posi9ves (FP) True nega9ves (TN) False nega9ves (FN)

33 ROC Curve Example: NPB Calculate TPR (sensitivity) and FPR (1 specificity) for a number of cutoffs Cutoff TPR (SN) FPR

34 ROC Curve Example: NPB Plot sensitivity vs. 1 specificity

35 ROC Curve Example Compare the curves

36 ROC Curve Example Check the direction you have used!!!

37 VU Biostatistics and Experimental Design PLA.216 Julia Feichtinger Postdoctoral Researcher Institute of Computational Biotechnology Graz University of Technology

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