Biostatistics for biomedical profession. BIMM34 Karin Källen & Linda Hartman November-December 2015

Transcription

1 Biostatistics for biomedical profession BIMM34 Karin Källen & Linda Hartman November-December

2 Who needs a course in biostatistics? - Anyone who uses quntitative methods to interpret biological processes. But really.is it necessary with todays advanced computers and statistical packages?

3 Now more than ever! Computers (and softwares) are dumb like stones! They just do what we tell them to

4 An imaginary 2 x 2 table: Adequate methods Sub-optimal methods Correct hypothesis correct basic design Poorly specified hypothesis poor design

5 An imaginary 2 x 2 table: Adequate methods Sub-optimal methods Correct hypothesis correct basic design Porly specified hypotesis poor design The draw-back of studies with these characteristics will be detected

6 An imaginary 2 x 2 table: Adequate methods Sub-optimal methods Correct hypothesis correct basic design In a good design the use of non-optimal statistical methods could bias the results butthe effects are seldom strong. Poorly specified hypothesis poor design The draw-back of studies with these characteristics will be detected

7 An imaginary 2 x 2 table: Adequate methods Sub-optimal methods Correct hypothesis correct basic design In a good design the use of non-optimal statistical methods could bias the results butthe effects are seldom strong. Poorly specified hypothesis poor design Over-belief in sophisticated statistical methods is depressingly common. Could be difficult to detect. The draw-back of studies with these characteristics will be detected

8 The objectives of the current course in biostatistics An imaginary 2 x 2 table: Adequate methods Sub-optimal methods Correct hypothesis correct basic design Utilization of brain capacity when designing knowlege of basic statistical methods correct interpretation of the results. In a good design the use of non-optimal statistical methods could bias the results butthe effects are seldom strong. Poorly specified hypothesis poor design Over-belief in sophisticated statistical methods is depressingly common. Could be difficult to detect. The draw-back of studies with these characteristics will be detected

9 Statistics Probability Population Inferential statistics Descriptive statistics Sample

10 Statistics Descriptive statistics Methods to summarize (the variables in) a sample Summary measures Graphical methods Today: Basic numerical summaries of data graphical summaries of data Inferential statistics Methods to learn about the population that the sample is drawn from Effect measures (w confidence intervals) Tests (ttest chi2-test Mann-Whitney ) Regression modeling 10

11 Types of data Categorical Quantitative Binary/ dichotomous 2 categories >=2 categories Nominal Ordinal Discrete Continuous Order matters Only whole numbers as values Data that can take any value 11

12 Types of data - exercise Categorize the following measurements in binary/nominal/ordinal/discrete/continuous 1. Blood serum bilirubin (μg/ml) 2. Hair colour (Blonde Brunette Redhead and Grays) 3. Vital status (Dead/alive) 4. BMI (kg/m 2 ) 5. # Bacteria in a sample 6. Smoking status (Non-smoker/0-10 cigarettes per day/>10 cigarettes per day) 12

13 Types of data Categorical Quantitative Binary Nominal Ordinal Discrete Continuous Discrete variables with only a few possible values are often analysed with the same methods as for ordinal variables. Discrete variables with many possible values are often analysed with the same methods as for continuous variables. 13

14 Summary measures & Graphical presentation Chapter 2 & 3 in Norman & Streiner Chapter 3 & 4 in Kirkwood and Sterne 14

15 Graphical presentation 1: HISTOGRAM Split the data in intervals count the number (proportion) in each interval: The width of the bar tells you the interval The height of the bar tells you the number (proportion) of observations in each interval 15

16 Summary measures: Central Tendency measures Describe a center around which the measurements in the data are distributed Dispersion (or Variability) measures Describe data spread or how far away the measurements are from the center. 16

17 Central tendency measures Median The middle observation if data are sorted Mean X = X 1 + X X N N = 1 N i=1 The sum of the observations devided by the number of observations N X i Mode The most frequently occuring value 17

18 Central tendency - exercise Exercise 3.2 a-c Calculate the mean median and mode of a dataset with the following values:

19 Central tendency cont. Maternal Vitamin D: Mean = 2.3 Median= 2.2 Child Vitamin D: Mean = 1.4 Median =

20 Central tendency Mean or median The choice depends on the distribution of the data: Symmetric data Asymmetric data Ordinal data Symmetric distribution Asymmetric distribution (positive skew) 20

21 Central tendency Symmetric continuous data Maternal height: Mean=166 cm Median= cm Symmetric data: Mean = median Use the mean 21

22 Central tendency Assymetric continuous data Vitamin D in child: Mean= 1.4 Median= 1.2 Asymmetric data: Mean median Use the median 22

23 Central tendency Assymetric continuous data CD16 in % of granulocytes CD16 in % of granulocytes: Mean= 7.3 Median=

24 Central tendency Ordinal data (Hacke et al. 2008) (Kasner 2006) Use the median! Exercise: What is the median in the Alteplase group? What is the median in the Placebo group? 24

25 Central tendency Nominal data Barchart Measures of central tendency are not meaningful. Use number of observations and proportions 25

26 Central tendency measures Summary Type of data Symmetric data Asymmetric data Ordinal Nominal - Central tendency measure Mean Median Median 26

27 Measures of dispersion A measure of dispersion refers to how closely the data cluster around the measure of central tendency Symmetric distribution measure based on mean Assymetric distribution or ordinal data measure NOT based on the mean 27

28 Spread/distribution Small spread Big spread 28

29 Descibing the spread of the data If we look at the average diviation from the mean: X= 159,375 x i n x x i (x i - x) The average diviation from the mean equals x i n x

30 Describing the spread of the data If we square every term we solve the problem with 0, then divide by n to get mean deviation: x i x 2 n To get a better estimate we use n-1 in the denominator This is called the VARIANCE! x i n 1 The variance is expressed in cm which is unpractical since the mean length is expressed in cm 2 x 2 = (x- x) (x- x)

31 Descibing the spread of the data By taking the square root of the variance, you get the standard deviation (standard deviation = SD) which has the same units as what you measured s xi x n 1 2 Ex: Variance = s 2 = 60.5 cm 2 s = sqrt(60.48) = 7.8 cm 31

32 Percentile Describes how many percent of the observations that lies below ex: 10% found below 10th percentile 20% found below 20th percentilen etc Quartile Divide data into four equal groups; Lower quartile 25th percentile Median 50th percentile Upper quartile 75th percentile Q1 = (n+1)/4, Q2 = 2(n+1)/4 (Median), Q3 = 3(n+1)/4 of ordered observations Interquartile range (IQR) = The difference between the upper and the lower quartiles 32

33 Measures of dispersion Standard deviation The mean deviation from the mean value Percentiles & quartiles Range Splits the data in fixed proportions The difference between min and max 33

34 Measures of dispersion - exercise Exercise 3.2 d-e Calculate the standard deviation and range for a dataset with the following values:

35 Robustness Highly skewed data Fig 3-10 Robust to extreme observations Sensitive to extreme observations Measure WITHOUT largest observation Mean Median 4 4 Range 5 42 SD Q L; Q U 3; 5 3; 5 WITH largest observation Use Median & Quartiles for skewed data + Graphical presentation! 35

36 Summary: Summary measures Type of data Central tendency measure Dispersion measure Symmetric data Mean Standard deviation Asymmetric data Median Percentiles (e.g. Q L and Q U ) Ordinal Median Percentiles Nominal

37 Graphical presentation 2: BOX-PLOT Outlier O Observationes more than 1.5 IQR outside the box Extreme values * Observations more than 3 IQR outside the box Highest normal value (Inner fence) 1000 Upper quartile Q U Median Lower quartile Q L 0 N = Lowest normal value Låg Medium Hög Low medium high Fiskkonsumtionsgrupp Fish consumption IQR=Q U Q L = Box-length 37

38 Box-plot - exercise How can you use the boxplot to judge if a distribution is symmetric or asymmetric? Use the examples in your discussion 38

39 Box-plot: Exercise 2 Blood pressure was mesured in 39 women: BP= mmhg (Results are sorted) Create a boxplot of Blood-pressure 39

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41 Box-plot vs histogram, ex cont Blood pressure was measured in 39 women: BP= mmhg median: 149 Q1: 143 Q3: 157 min: 138 max: 170 IQR=Q3-Q1=14 Frequency bp_before

42 Box-plot cont Whats wrong with Figure 3-7? 42

43 Summary: Types of variables (binary/nominal/ordinal/discrete/continuous) - Descriptive statistics - Central tendency measures (mean median) - Dispersion measures (standard deviation percentiles) - Graphical presentation - Barplot - Histogram - Boxplot Subject Wednesday lecture: Norman & Streiner Normal distribution 4 5 Population, samples generalisability Reference interval, Confidence interval 6 7 Kirkwood and Sterne 6 4.5, 6, 7 43