Complete Blood Count (CBC) and components

Clinical Laboratory - Complete Blood Count (CBC)

Hemoglobin (Hb)

• Hemoglobin is an iron-containing oxygen-transport metalloprotein in red blood cells.
• Normal Hb values:
  • Male: 13.5-17.5 g/dL
  • Female: 11.5-15.5 g/dL
• Clinical significance:
  • Increased Hb may indicate dehydration, polycythemia vera, or severe burns.
  • Decreased Hb may indicate anemia, hemorrhage, hemolysis, or kidney disease.

Hematocrit (Hct)

• Hematocrit is the percentage of red blood cells in the blood.
• Normal Hct values:
  • Male: 41.0-53.0%
  • Female: 36.0-46.0%
• Clinical significance:
  • Increased Hct may indicate dehydration, polycythemia vera, or severe burns.
  • Decreased Hct may indicate anemia, hemorrhage, hemolysis, or kidney disease.

Red Blood Cell (RBC)

• Red blood cells carry oxygen from the lungs to the body tissues and carbon dioxide from tissues back to the lungs.
• Normal RBC values:
  • Male: 4.5-5.5 x $10^6/µL$
  • Female: 4.0-5.0 x $10^6/µL$
• Clinical significance:
  • Increased RBC count may indicate dehydration, polycythemia vera, or severe burns.
  • Decreased RBC count may indicate anemia, hemorrhage, hemolysis, or kidney disease.

White Blood Cell (WBC)

• White blood cells protect the body against infection.
• Normal WBC value: 4.0-10.0 x $10^3/µL$
• Clinical significance:
  • Increased WBC count may indicate infection, inflammation, or leukemia.
  • Decreased WBC count may indicate drug toxicity or bone marrow failure.

Platelet (PLT)

• Platelets are cell fragments in the blood that help stop bleeding.
• Normal PLT value: 150-400 x $10^3/µL$
• Clinical significance:
  • Increased platelet count may indicate thrombocytosis or some types of anemia.
  • Decreased platelet count may indicate thrombocytopenia or some types of anemia.

Chapter 14: Graphics

Introduction

• The basics of producing graphics using Python are introduced.
• How to work with the graphics.py package is explained.
• How to create simple drawings using the package is shown.
• Instructions on writing programs that respond to mouse clicks and keyboard entry are given.

Overview

• Computer graphics involve the generation and display of pictures using a computer.
• graphics.py package by John Zelle is used in the book for creating graphics in Python.

The graphics.py Package

• Download the non-standard package graphics.py and save it where Python can find it. Place it in the same folder or a site-packages directory.
• Import the package for use in a program with the command from graphics import *.

Simple Example

• Opens a graphics window and draws a circle.
• from graphics import * imports all the names from the graphics module.
• win = GraphWin("My Circle", 100, 100) creates a 100x100 pixel window titled "My Circle."
• Circle c is constructed with its center at (50, 50) and a radius of 10 pixels.
• c.draw(win) draws the circle in the window.
• The code waits for a mouse click and then closes the window.

Coordinate System

• A GraphWin has a default coordinate system with (0, 0) in the upper left corner and (200, 200) in the lower right. $x$ and $y$ Coordinates increase to the right and downward.
• The default coordinates can be changed; for example, win.setCoords(0.0, 0.0, 10.0, 10.0) places (0.0, 0.0) in the lower left and (10.0, 10.0) in the upper right.

Pixel Addresses

• The resolution of a display is the number of pixels that make up the display.
• Each pixel on the screen has a unique address to determine its position.

Creating Graphics Objects

The Point Class

• Point is the basic building block for all figures, specified by $x$ and $y$ coordinates.
• Example to create a point, also gets values:

  p = Point(50, 60)
  p.getX()
  p.getY()
  

The Circle Class

• To draw a circle, specify the coordinates of the center point and the radius.

  center = Point(100, 100)
  circ = Circle(center, 30)
  circ.draw(win)
  

The Rectangle Class

• To draw a rectangle, specify the coordinates of two opposite corners.

  p1 = Point(30, 40)
  p2 = Point(120, 150)
  rect = Rectangle(p1, p2)
  rect.draw(win)
  

The Line Class

• To draw a line, specify the two endpoints.

  line = Line(Point(30, 40), Point(120, 150))
  line.draw(win)
  

The Oval Class

• An oval is specified by two corner points of the bounding box.

  oval = Oval(Point(20, 30), Point(180, 90))
  oval.draw(win)
  

The Polygon Class

• A polygon is a closed shape with an arbitrary number of sides, specified by listing its vertices in order.

  p1 = Point(30, 50)
  p2 = Point(60, 30)
  p3 = Point(150, 70)
  poly = Polygon(p1, p2, p3)
  poly.draw(win)
  

The Text Class

• A Text object displays a string of characters on the screen centered at a specified point.

  message = Text(Point(100, 70), "Hello World!")
  message.draw(win)
  

The Entry Class

• An Entry object is a box for entering text, centered at a specified point with a set number of characters displayed.

  inputBox = Entry(Point(100, 70), 10)
  inputBox.draw(win)
  

Drawing Multiple Objects

• Multiple objects can be drawn in the same window in code.

  from graphics import *
  
  def main():
      win = GraphWin("Shapes", 400, 400)
      win.setBackground("white")
  
      circ = Circle(Point(100, 100), 30)
      circ.setFill("blue")
      circ.draw(win)
  
      rect = Rectangle(Point(30, 40), Point(120, 150))
      rect.setOutline("red")
      rect.draw(win)
  
      line = Line(Point(30, 40), Point(120, 150))
      line.draw(win)
  
      oval = Oval(Point(20, 30), Point(180, 90))
      oval.setFill("yellow")
      oval.draw(win)
  
      poly = Polygon(Point(30, 50), Point(60, 30), Point(150, 70))
      poly.setFill("green")
      poly.draw(win)
  
      message = Text(Point(100, 70), "Hello World!")
      message.draw(win)
  
      inputBox = Entry(Point(100, 70), 10)
      inputBox.draw(win)
  
      win.getMouse()
      win.close()
  
  main()
  

Object Methods

• All graphics objects support a move(dx, dy) function that moves the object dx units in the $x$ direction and dy units in the $y$ direction. An example is circle.move(10, 20).
• The fill color on filled graphics objects (Circle, Rectangle, Oval, Polygon) can be set using setFill(color).

setOutline(color)

• All graphics objects support a setOutline method that sets the outline color of the object.

  circle.setOutline("red")
  rectangle.setOutline("blue")
  line.setOutline("yellow")
  oval.setOutline("green")
  polygon.setOutline("black")
  

setWidth(pixels)

• All graphics objects support a setWidth method that sets the width of the outline of the object.

  circle.setWidth(5)
  rectangle.setWidth(5)
  line.setWidth(5)
  oval.setWidth(5)
  polygon.setWidth(5)
  

setText(string)

• The Text object supports a setText method that changes the text that is displayed.

  message.setText("Goodbye!")
  

setTextColor(color)

• The Text object supports a setTextColor method that changes the color of the text.

  message.setTextColor("red")
  

setSize(point)

• The Text object supports a setSize method that changes the size of the text.

  message.setSize(14)
  

setFace(family)

• The Text object supports a setFace method that changes the font of the text.

  message.setFace("courier")
  

setStyle(style)

• The Text object supports a setStyle method that changes the style of the text.

  message.setStyle("italic")
  

getMouse()

• The getMouse method waits for the user to click the mouse inside the window and returns the Point where the mouse was clicked.

Simple Animation

• Code to animate a circle across the screen.

  from graphics import *
  import time
  
  def main():
      win = GraphWin("Circle", 400, 400)
      win.setBackground("white")
      circ = Circle(Point(100, 100), 30)
      circ.setFill("blue")
      circ.draw(win)
  
      for i in range(100):
          circ.move(2, 0)
          time.sleep(0.05)
  
      win.getMouse()
      win.close()
  
  main()
  

• Code to animate a bouncing ball across the screen.

  from graphics import *
  import time
  
  def main():
      win = GraphWin("Bouncing Ball", 400, 400)
      win.setBackground("white")
      circ = Circle(Point(50, 50), 10)
      circ.setFill("blue")
      circ.draw(win)
  
      dx = 5
      dy = 3
  
      while True:
          circ.move(dx, dy)
          center = circ.getCenter()
          if center.getX() < 10 or center.getX() > 390:
              dx = -dx
          if center.getY() < 10 or center.getY() > 390:
              dy = -dy
          time.sleep(0.02)
  
      win.close()
  
  main()
  

Mouse Clicks and Input

• getMouse returns the clicked Point in the window.

  from graphics import *
  
  def main():
      win = GraphWin("Click Me!", 400, 400)
      win.setBackground("white")
  
      for i in range(10):
          p = win.getMouse()
          circ = Circle(p, 10)
          circ.setFill("blue")
          circ.draw(win)
  
      win.close()
  
  main()
  

• The Entry object can be used to get text input from the user. The getText method returns the string that the user typed into the entry box.

  from graphics import *
  
  def main():
      win = GraphWin("Name", 400, 400)
      win.setBackground("white")
  
      nameBox = Entry(Point(200, 200), 20)
      nameBox.draw(win)
  
      win.getMouse()
      name = nameBox.getText()
  
      message = Text(Point(200, 100), "Hello " + name + "!")
      message.draw(win)
  
      win.getMouse()
      win.close()
  
  main()
  

Case Study: Simple Dice Game

Problem Description

• Simulate rolling two dice with rectangles and dots.
• Allow to roll again by clicking the mouse, until the user quits.

Initial Plan

• main() controls the program.
• rollDice() returns a random integer between 1 and 6.
• drawDice(win, x, y, value) draws a die with the given value at the location (x, y).

Developing the Algorithm

• Create a graphics window.
• Draw the first pair of dice.
• While the user doesn't click the quit button:
  • Wait for a mouse click.
  • Roll the dice.
  • Update the display to show the new dice values.
• Close the window.

Python Implementation

from graphics import *
from random import randrange

def rollDice():
    return randrange(1, 7)

def drawDice(win, x, y, value):
    # Draw the die as a rectangle
    rect = Rectangle(Point(x - 30, y - 30), Point(x + 30, y + 30))
    rect.setFill("white")
    rect.draw(win)

    # Draw the dots
    if value == 1:
        drawDot(win, x, y)
    elif value == 2:
        drawDot(win, x - 20, y - 20)
        drawDot(win, x + 20, y + 20)
    elif value == 3:
        drawDot(win, x, y)
        drawDot(win, x - 20, y - 20)
        drawDot(win, x + 20, y + 20)
    elif value == 4:
        drawDot(win, x - 20, y - 20)
        drawDot(win, x + 20, y + 20)
        drawDot(win, x - 20, y + 20)
        drawDot(win, x + 20, y - 20)
    elif value == 5:
        drawDot(win, x, y)
        drawDot(win, x - 20, y - 20)
        drawDot(win, x + 20, y + 20)
        drawDot(win, x - 20, y + 20)
        drawDot(win, x + 20, y - 20)
    elif value == 6:
        drawDot(win, x - 20, y - 20)
        drawDot(win, x + 20, y + 20)
        drawDot(win, x - 20, y + 20)
        drawDot(win, x + 20, y - 20)
        drawDot(win, x - 20, y)
        drawDot(win, x + 20, y)

def drawDot(win, x, y):
    dot = Circle(Point(x, y), 5)
    dot.setFill("black")
    dot.draw(win)

def main():
    win = GraphWin("Dice", 400, 200)
    win.setBackground("green")

    # Initial dice values
    dice1 = rollDice()
    dice2 = rollDice()

    # Draw the initial dice
    drawDice(win, 100, 100, dice1)
    drawDice(win, 300, 100, dice2)

    # Display the total
    total = dice1 + dice2
    totalText = Text(Point(200, 30), "Total: " + str(total))
    totalText.draw(win)

    # Roll the dice until the user clicks the mouse
    while True:
        click = win.getMouse()

        # Roll the dice
        dice1 = rollDice()
        dice2 = rollDice()

        # Clear the dice
        for item in win.items[:]:
            item.undraw()

        # Draw the new dice
        drawDice(win, 100, 100, dice1)
        drawDice(win, 300, 100, dice2)

        # Update the total
        total = dice1 + dice2
        totalText = Text(Point(200, 30), "Total: " + str(total))
        totalText.draw(win)

    win.close()

main()

Chapter Summary

• Introduced the basics of computer graphics using the graphics.py package.
• graphics.py is not standard, so it must be downloaded and saved where Python can access it.
• GraphWin creates the graphics window.
• Default coordinate 0, 0 is in the upper left corner and 200, 200 in bottom right
• Point establishes the basic building blocks for figures
• Classes for creating graphic objects are Circle, Rectangle, Line, Oval, Polygon, Text and Entry.
• move moves the object
• setFill sets the interior color, supported by filled graphics objects only.
• setOutline sets the outline colour.
• setWidth` sets the lines' width, by pixel size.
• setText changes the text that is displayed (for Text object).
• 'setTextColor' changes the text colour (for Text object).
• 'setSize' changes the text size (for Text object).
• setFace changes the font (for Text object).
• setStyle changes the style (italic, bold, etc).
• getMouse waits for the user to click the mouse.
• 'Entry' is the object to achieve text input from user.

Lecture 18: Hypothesis Testing

Statistical Hypothesis

• A statistical hypothesis is an assumption about a population parameter that may or may not be true.

Steps for Hypothesis Testing

• State the null hypothesis ($H_0$).
• State the alternative hypothesis ($H_1$).
• Set α, the acceptable probability of wrongly rejecting $H_0$.
• Compute the test statistic.
• Determine the $p$-value.
• Reject $H_0$ if $p \le \alpha$.

Null Hypothesis $H_0$

• A statement of "no effect," "no difference," or "equality."
• $H_0$ is assumed to be true unless there is enough evidence to reject it.
• Examples: $\mu = 100$, $\mu_1 = \mu_2$, $p = 0.5$

Alternative Hypothesis $H_1$

• A statement contradicting the null hypothesis.
• Provides Evidence to support $H_1$.
• Examples: $\mu \ne 100$ (two-tailed), $\mu > 100$ (right-tailed), $\mu < 100$ (left-tailed)

Type I and Type II Errors

• Type I Error: Rejecting $H_0$ when it is true. P(Type I Error) = α
• Type II Error: Failing to reject $H_0$ when it is false. P(Type II Error) = β

Test Statistic

• A value calculated from the sample data to determine whether to reject the null hypothesis.
• Examples: $z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$ (z-test), $t = \frac{\bar{x} - \mu}{s / \sqrt{n}}$ (t-test)

P-value

• Probability of observing a test statistic as extreme as, or more extreme than, the one computed, assuming $H_0$ is true.
• A small $p$-value suggests that the observed data is inconsistent with $H_0$.
• Reject $H_0$ if the $p$-value is less than or equal to $\alpha$.

Diagram

• Is $p \le \alpha$?
  • Yes: Reject $H_0$
  • No: Fail to Reject $H_0$

The P-value Flow Chart

• Start
• Assume $H_0$ is true.
• Is $p \le \alpha$?
  • Yes: Reject $H_0$
  • No: Fail to Reject $H_0$
• Conclusion

Lecture 10: Hypothesis Testing

Concepts

• Introduces hypothesis testing.
• Discusses terminology, including types of hypotheses, test statistic, and P-value.
• Explains calculating a P-value for a basic text.

Motivating Example: Extrasensory Perception (ESP)

Terminology

• Subject: The person being tested.
• Trial: A single test of the subject.
• Run: A collection of trials.

Setup

• The experimenter has a deck of 10 cards, 5 red and 5 blue.
• In each trial, the experimenter shuffles the deck, draws a card, looks at it, and asks the subject to guess the color of the card.
• This is repeated for 100 trials (i.e. one run).
• The experimenter records the number of correct guesses.

Question

• If someone does not have ESP, how many correct guesses would we expect?
• Would we ever expect someone to get all 100 correct?

Model

• Let $X$ be the number of correct guesses.

• If the subject is guessing randomly, then we can model $X$ as:

  $$ X \sim Bin(n = 100, p = 0.5) $$

Terminology

• Null Hypothesis ($H_0$): The assumption that the subject does not have ESP, and is just guessing.
• Alternative Hypothesis ($H_A$): The assumption that the subject has ESP, and is doing better than guessing.

Example

• The subject guesses correctly 63 times out of 100.
• Is this provide strong indication refuting $H_0$?
• How "weird" is this result if the null hypothesis is true?

p-value

• The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the value actually observed, assuming that the null hypothesis is true.
• "Extreme" is defined with respect to the alternative hypothesis.
• The test statistic is the number of correct guesses.
• The p-value is the probability of observing 63 or more correct guesses, if the subject is just guessing. $$ P(X \geq 63) = \sum_{i = 63}^{100} {100 \choose i} (0.5)^i (0.5)^{100 - i} \approx 0.0017 $$

Interpreting the p-value

• The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the value actually observed, assuming that the null hypothesis is true.
• In the example, the p-value calculates to being 0.0017.
• It means that if the subject is just guessing, the probability of observing 63 or more correct guesses is 0.0017.
• The small probability gives strength to rejecting the null hypothesis.

Hypothesis Testing

• Can only be done after a procedure for using sample data to evaluate the credibility.
• 1. State the null and alternative hypotheses.
• 2. Choose a significance level ($\alpha$).
• 3. Calculate the test statistic.
• 4. Calculate the p-value.
• 5. Make a decision
  • Reject the null hypothesis if the p-value is lower than alpha value.
  • Otherwise fail to reject the null hypothesis.
• The significance level ($\alpha$) is the probability of rejecting the null hypothesis when it is true and is also known as a Type 1 error.
• 0.05 and 0.01 are common values for α.

Example: Increased Germination

Scenario

• A farmer buys a fertilizer advertised that it increases the seeds germination rate.
• The farmer plants 100 seeds with the new fertilizer and 87 of them germinate.
• Historically, the germination rate for these seeds is 75%.
• Is there evidence that the new fertilizer increases the germination rate

Model

• Let X be the number of seeds that germinate.
• germination can be modeled as: $$ X \sim Bin(n = 100, p = 0.75) $$

Hypothesis Testing

1. State the null and alternative hypotheses:

• $H_0$: The fertilizer has no effect on the germination rate (i.e., $p = 0.75$).
• $H_A$: The fertilizer increases the germination rate (i.e., $p > 0.75$).

2. Choose a significance level:

• Let's choose $\alpha = 0.05$.

3. Calculate the test statistic:

• The test statistic is the number of seeds that germinate, which is 87.

4. Calculate the p-value:

• The p-value is the probability of observing 87 or more seeds germinate, if the fertilizer has no effect. $$ P(X \geq 87) = \sum_{i = 87}^{100} {100 \choose i} (0.75)^i (0.25)^{100 - i} \approx 0.0027 $$

5. Make a decision:

• The p-value (0.0027) is less than $\alpha$ (0.05), so we reject the null hypothesis.
• We conclude that the fertilizer increases the germination rate.

One-sided vs. Two-sided Tests

• Use a one-sided test
• Because we were only interested in whether the fertilizer increased the germination rate.
• If we were interested in whether the fertilizer had any effect on the germination rate (i.e., either increased or decreased it), we would use a two-sided test.
• We get a p-value of test to see the probability of finding a result at equal limits in either side.

Example: Two-Sided Test

• Check whether a find if a coin is fair.
• Tossed coin to 100 times showing 40 heads
• Showing evidence the coin is biased?

Hypothesis Testing

1. State the null and alternative hypotheses:

• $H_0$: The coin is fair (i.e., $p = 0.5$).
• $H_A$: The coin is biased (i.e., $p \neq 0.5$).

2. Choose a significance level:

• Let's choose $\alpha = 0.05$.

3. Calculate the test statistic:

• The test statistic is the number of heads, which is 40.

4. Calculate the p-value:

   $$ P(X \leq 40 \text{ or } X \geq 60) = \sum_{i = 0}^{40} {100 \choose i} (0.5)^i (0.5)^{100 - i} + \sum_{i = 60}^{100} {100 \choose i} (0.5)^i (0.5)^{100 - i} \approx 0.0568 $$

5. Make a decision:

• The p-value (0.0568) is greater than $\alpha$ (0.05), so we fail to reject the null hypothesis.
• We conclude that there is no evidence that the coin is biased.

Summary

• A procedure for using data to evaluate the strength of a hypothesis of a population.
• Hypothesis testing is a formal approach by:
  • Define the null and alternative hypotheses.
  • Set a significance level (α).
  • Determine and calculate test statistic.
  • Obtain the P-value.
• Decide the validity by:
  • Reject the null hypothesis.
  • Otherwise fail to reject the null hypothesis.
• Use a test when only interested in when the test statistic is extreme on one limit.
• A 2 sided test is performed when the statistic is either extreme or has equal probability.