MATH600 - BIOSTATISTICS Reviewer.docx

8/13/2019 MATH600 - BIOSTATISTICS Reviewer.docx

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BIOSTAT

INTRODUCTION

STATISTICSA science whereby inferences aremade about specific random phenomena on the

basis of relatively limited sample material. Mathematical Statisticsconcerns the

development of new methods of statistical inference

and requires detailed knowledge of abstract

mathematics for its implementation.

Applied Statisticsinvolves application ofmathematical statistical methods to specific subject

areas such as economics, psychology, and public

health.

BIOSTATICSTICSA branch of applied statistics thatapplies statistical methods to medical and biological

problems.

Standard statistical methods may not necessarily beapplicable for all studies.

New Bio statistical methods are developed byBiostaticians.

ROLE OF BIOSTATISTICS IN MEDICAL RESEARCH

Observation:

Blood pressure readings of patient X obtained using,

Automatic measuring device = 115 mmHg;Highest reading = 130 mmHg

Standard blood pressure cuff = 90 mmHgWhy is there a difference in blood pressure readings

between an automatic machine vs. a human

observer?Are the two methods of determining blood pressure

comparable?

Study Questions:

Are the methods of automatic vs. manual

determination of blood pressure comparable?

To address this question, we designed and carried

out the following small-scale study of blood pressure

monitoring machines.

Q & A:

1. No. of machines to be tested.- 4; since machines may or may not be

comparable in quality.

2. No. of participants for each machine to betested.

- 100 people at each test location basedon sample size determination method.

3. Order of taking measurements:

ManualAutomated or vice versa (For our

study, simultaneous readings were

logistically feasible)

- To rule out any effects that themeasurement menthod may have, the

order of measurement was randomized

(flipping coin, using a table of randomnumbers, etc.)

4. Critical data to be captured viaquestionnaire to aid in comparison between

the methods.

*Age

*Sex

*Previous Hypertension History

*Body Size (since this variable was seento

influence accurate reading)

5. Format of recording data to ease futuredata entry into computers

*Each person assigned a unique

identification number (ID)

*Using a coding form that was keyed in and

verified

*Same coding form entered twice to ensure

accuracy of records

6. Checking accuracy of computerized data.*Using editing programs to check that all

values of variables fell within specific range

*Outliers or aberrant values were manually

checked

NEXT STEPS:

Data

Collection

DataEntry

Data

Editing

Data

Analysis


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DATA ANALYSISData obtained from the study can

be summarized using descriptive statistics

*Descriptive material can be Numeric or Graphic

> If Numeric, data can be tabulated or presented as

frequency distribution

> If Graphic, data can be summarized pictorially

Choice of numeric or graphic descriptive statistics isdependent on type of distribution of data.

1. Continuous Data: Where there are infinite numbers possible

values (e.g. blood pressure measurements)

Means and standard deviations may beused

2. Discrete Data: Where there are onlu a few possible values

(e.g. sex)

Percentages of people for each value maybe considered

INFERENTIAL STATISTICSdetermining whether the

difference in blood pressure readings is real or by

chance

Sample size = 98 people from the general population

Estimated mean difference = 14 mmHg

Error in estimated mean difference = ?

True mean difference = d = ?

Inferring the characteristics of a population from a

sample is the central concern of statistical inference.

To accomplish this aim, we need to develop a

probability model, which would tell us how likely it

is to obtain a 14-mmHg difference between the two

methods in a sample of 98 people if there were no

real difference between the two methods over theentire population of users of the machine.

A small enough probability would indicate that the

difference between the two methods is real.

For our study, we used a probability model based on

t-distribution.

The probability was found to be


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NEGATIVELY SKEWED DISTRIBUTIONS -arithmetic mean tends to be smaller than

the median.

MODE

- The most frequently occurring valueamong all the observations in a sample.

Data distributions may have one or moremodes.

UNIMODALOne Mode BIMODALTwo Modes TRIMODAL and so onThree or More

Modes

GEOMETRIC MEAN

Many types of laboratory data can be expressed as

multiples of 2 or a constant multipled by a power of

2, that is,

SOME PROPERTIES OF ARITHMETIC MEAN

Original sample:

Translated sample: X1 + Cz , Xn + C (Where c is some

constant)

Let Yi = Xi + C I = 1, , n then y = x + c

MEASURES OF SPEED

The mean obtained by the two methods is the same.

However, the variability or spread of the

Autoanalyzer method appers to be greater.

RANGE OR VARIABILITY RANGEis the difference between the

largest and smallest observations in a

sample

Once the sample is ordered, it is very easyto compute the range.

Range is very sensitive to extremeobservations or outliers.

Larger sample size (n), the largest range andthe more difficult the comparison between

the ranges from data sets of varying sizes.

*A better approach to quantifying the spread in data

sets is percentiles or quantiles.

*Percentiles are less sensitive to outliers and are not

greatly affected by the sample size.

The pth percentile is the value Vp such that p percent

of the sample points are less than or equal to VpThe pth percentile is defined by

The (k+1)th largest sample point if np/100 isnot an integer (where k is the largest

integer less than np/100)

The average of the (np/100)th and(np/100+1)th largest observations if np/100

is an integer

Frequently used percentiles are

Quartiles (25th, 50th, and 75thpercentiles) Quintiles (20th, 40th, 60th, and 80th

percentiles) Deciles (10th, 20th, , 90thpercentiles)

To compute percentiles, the sample points must be

ordered.

If n is large, a stem-and-leaf plot or a computer

program may be used.

VARIANCE AND STANDARD DEVIATION

If the center of the sample is defined as the

arithmetic mean, then the measure that can

summarize the difference (or deviations) between

the individual sample points and the arithmetic

mean can be expressed as

That is,

The sum of the deviations of the individual

observations of a sample about the sample mean is

always zero.

Standard deviation d is a reasonable measure of

spread if the distribution is bell-shaped.

MEAN DEVIATION

The difference d does not help distinguish the

difference in spreads between two methods.

Mean Deviation, expressed as may

be used.

Alternatively, sample variances or variance, which is

the average of the squares of the deviations from

the sample mean may be used

Another commonly used measure of spread is the

sample standard deviation

COEFFICIENT OF VARIATION (CV)

Defined as 100% x (s/X)

Remains the same regardless of units used

Useful in comparing variability of different samples

with different arithmetic means

Useful for comparing the reproducibility of different

variables.

GRAPHIC METHODS


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Graphic methods of displaying data give a quick

overall impression of data. The following are some

graphic methods:

*BAR GRAPHS:

> Used to display grouped data;

> Difficult to contrast;> Identity of the sample points within the respective

group is lost

*STEM-AND-LEAF PLOTS:

> Easy to compute the median and other quantiles

> Each data point is converted into stem and leaf,

e.g. 438 (stem: 43; leaf:8)

*BOX PLOTS:

> Uses the relationships among the median, upper

quantile, and lower quantile to describe the

skeweness or symmetry of a distribution

An outlying calue is a value x such that either:

x>upper quartile +1.5 x (upper quartilelower

quartile)

x< lower quartile1.5 x (upper quartilelower

quartile)

An extreme outlying value is a value x such that

either:

X > upper quartile + 3.0 x (upper quartilelower

quartile)

X < lower quartile3.0 x (upper quartilelower

quartile)

A vertical bar connects the upper quartile tothe largest nonoutlying value in the sample

A vertical bar connects the lower quartile tothe smallest nonoutlying value in the

sample

OBTAINING DESCRIPTIVE STATISTICES USING A

COMPUTER

Numerous statistical packages may be used Excel may be used to compute average (for

the arithmetic mean), median (for the

median), StDev (for the standard deviation),

Var (for the Variance), GeoMean (for the

Geometric Mean), and Percentile (for

obtaining arbitrary percentiles from a

sample).

SUMMARY:

Numeric or graphic methods for displaying data help

in:

Quickly summarizing a data set And/or presenting results to others

A data set can be described numerically in terms of

measure of location and a measure of spread:

Measure of Location

Arithmetic Mean

Median

Mode

Geometric Mean

Measure of Spread

Standard Deviation

Quantiles

Range

Graphic methods include: Bar Graphs and more

exploratory methods such as Stem-and-Leaf Plots

and Box Plots.

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MATH600 - BIOSTATISTICS Reviewer.docx