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Chapter1:introduction to medical statistics
 

Chapter1:introduction to medical statistics

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    Chapter1:introduction to medical statistics Chapter1:introduction to medical statistics Presentation Transcript

      • Introduction to Medical Statistics
      • Chapter-1
    •  
    •  
      • Statistics :
      • The discipline concerned with the treatment of numerical data derived from groups of individuals (P. Armitage).
      •  
      • The science and art of dealing with variation in data through collection, classification and analysis in such a way as to obtain reliable results ( JM Last).
      • Medical Statistics:
      • Application of mathematical statistics in
      • the field of medicine
      •  
      • Why we need to study statistics?
      • Three reasons:
      • (1)Basic requirement of medical research.
      • (2)Update your medical knowledge.
      • (3)Data management and treatment.
    • Basic concepts
      • Homogeneity: All individuals have similar characteristics and belong to same category.
      • Variation: the differences in height, weight…
      1. Homogeneity and Variation
      • Population : The whole collection of
      • individuals that one intends to study
      • ---- Homogeneity but with Variation
      • Sample : A representative part of the population.
      • Randomization : An important way to make the sample representative.
      2. Population and sample
    • Random
      • By chance!
      • Random event : the event may occur or may not occur in one experiment.
      • Before one experiment, nobody is sure whether the event occurs or not.
      • However, there must be some regulation in a large number of experiments.
    • 3. Probability
      • Measure the possibility of occurrence of a
      • random event.
      • A : random event
      • P(A) : Probability of the random event A
      • P(A)=1 , if an event always occurs.
      • P(A)=0, if an event never occurs.
    • Estimation of Probability----Frequency
      • n : number of observations (large enough)
      • m : number of occurrences of random event A
      • m / n : relative frequency or frequency of random
      • event A
      • P(A)  frequency
    • 4. Parameter and statistic
      • Parameter : A measure of certain property of the
      • Population. It is usually presented by Greek letters, such as μ , π ---- usually unknown
      • Statistic : A measure of certain property of a sample.
      • It is usually presented by Latin letters, such as s , p
    • The Basic Steps of Statistical Work
      • 1. Design of study
      • 2. Collection of data
      • 3. Data Sorting
      • 4. Data Analysis
    • About This course -- Teaching and Learning
      • Aim :
      • Training statistical thinking
      • Learning some skill for dealing with medical
      • data
      • Focus :
      • Essential concepts and statistical thinking
      • ---- lectures and practice session
      • Skill on computer and statistical software
      • ---- practice session
      • Practice session
      • ---- experiments and discussion
      • Text book
      • Fang Ji-Qian. Medical Statistics and Computer
      • Experiments. Singapore: World Scientific 2005
      • Reference book
      • 1. 方积乾 . 医学统计学与电脑实验 ( 第三版 ). 上海科学技术出版社 2006
      • 2. 方积乾 . 生物医学研究的统计方法 . 北京 : 高等教育出版社 2007
      • SPSS 软件下载地址:
      • ftp://202.116.102.7/pub/ 统计工具 /spss11
      • 课件下载地址:
      • ftp://202.116.102.6/ 统计 /2005 全英班
      • 电脑开机密码为学号后四位
    • Chapter   1 Descriptive Statistics
    •  
    •  
    •  
    • Chapter   1 Descriptive Statistics
      • Statistics: Statistical description
      • Statistical inference
      • Statistical description:
      • Describes the feature of the sample.
      • Main forms: tables, plots and numerical indexes
    • 1.1 Variables and Data
      • 1.1.1 Structure and feature of data
      • (1) Basic observed unit
      • A patient is defined as an observed unit.
      • (2) Recording item
      • Group : treatment
      • Response variables ( 反应变量 ) :
      • systolic pressure, diastolic, pressure, ECG and
      • effectiveness
      • Covariates ( 伴随变量 ) : age and gender
      • Variables: describe the properties of individuals.
      • Different types of variables  statistical methods
    • 1.1.2 Types of variables
      • 1. Quantitative Variable ( 定量变量 )
      • Continuous variable ( 连续变量 )
      • Values obtained through measurement : height,
      • weight, blood pressure, pulse and …
      • Taking values in a continuous interval.
      • Discrete variable ( 离散变量 )
      • Taking values in a set of integers.
      • Example 1.1 The variable for gender can be
      • defined with a binary variable X .
      • Binary variable is a simplest special case of it.
      • 2. Qualitative Variable ( 定性变量 )
      • Categorical variable ( 分类变量 ) :
      • Taking “values” within several possible categories, such as Gender (male, female), Occupation.
      • Ordinal variable ( 有序变量 ) :
      • There exists order among all possible categories, such as education (primary school, high school, university, postgraduate)
    • 1.2 Frequency Table and Histogram
      • Useful for description of sample data
      • Intuitive basement of probability distribution.
      • 1.2.1 Frequency table
      • 1. Discrete-type frequency table
    • Table 1.3 The frequency table for occupation of 108 patients
    • Table 1.4 The frequency table for the results of certain semi-quantitative test among 150 patients
    • 2. Continuous type frequency table
      • Example 1.3 120 normal male adults were randomly selected from
      • the residents of a county. Their red cell counts (1012 /L) were
      • observed and listed as the follows:
      • 5.12 5.13 4.58 4.31 4.09 4.41 4.33 4.58 4.24 5.45 4.32 4.84
      • 4.91 5.14 5.25 4.89 4.79 4.90 5.09 4.04 5.14 5.46 4.66 4.20
      • 4.21 3.73 5.17 5.79 5.46 4.49 4.85 5.28 4.78 4.32 4.94 5.21
      • 4.68 5.09 4.68 4.91 5.13 5.26 3.84 4.17 4.56 3.52 6.00 4.05
      • 4.92 4.87 4.28 4.46 5.03 5.69 5.25 4.56 5.53 4.58 4.86 4.97
      • 4.70 4.28 4.37 5.33 4.78 4.75 5.39 5.27 4.89 6.18 4.13 5.22
      • 4.44 4.13 4.43 4.02 5.86 5.12 5.36 3.86 4.68 5.48 5.31 4.53
      • 4.83 4.11 3.29 4.18 4.13 4.06 3.42 4.68 4.52 5.19 3.70 5.51
      • 4.64 4.92 4.93 4.90 3.92 5.04 4.70 4.54 3.95 4.40 4.31 3.77
      • 4.16 4.58 5.35 3.71 5.27 4.52 5.21 4.37 4.80 4.75 3.86 5.69
      • Please try to establish a frequency table for this set of data.
      • (1) Range R
      • maximum= 6.18,
      • minimum=3.29,
      • range R =6.18 - 3.29=2.89.
      • (2) Length of sub-intervals i
      • Divide the whole range into 8-15 sub-intervals.
      • R /10=2.89/10= 0.289≈ 0.30
      • then let i =0.30.
      • 1.2.2 Frequency plot and histogram
      • 1. Frequency plot for discrete variable
      • – bar chart
    • 2. Frequency plot for continuous variable – histogram
    • 1.3 Measurement for average level
      • Numerical characteristics ( 数字特征 ): Average level ( 平均水平 ) Variation ( 变异 )
      • 1.3.1 Arithmetic mean ( 算术均数 )
      • Useful when the histogram looks symmetric.
      • Denote the observed values of the individuals with
      • , the arithmetic mean
      • (1.1)
      • 1.3.2 Geometric mean ( 几何均数 )
      • It is useful when the histogram of the logarithms
      • is close to symmetric.
      • Example The concentrations of certain antibody are measured for a set of sample and the
      • corresponding titers are 4, 8, 16, 16, 64, 128.
      • Arithmetic mean = 39.3
      • Geometric mean = 20.16
      • 1.3.3 Median ( 中位数 )
      • When the histogram shows skew, the median can
      • be applied to measure the average level.
      • Median = the value in the middle
      • Example1 Data set {1,1,2,2, 3 ,4,6,9,10}
      • Median = 3
      • Example2 Data set {1,1,2,2, 3,4 ,6,9,10,13}
      • Median = ( 3 + 4 )/2=3.5
      • When n is odd,
      • Median = the observed value with rank ( n +1)/2
      • When n is even,
      • Median =  values with rank n /2+ values with rank ( n +1)/2  2
    • Think about
      • How to calculate P percentile ( 百分位数 )?
      • P 25 ?
      • P 75 ?
    • 1.4 Measurement for Variation
      • 1.4.1 Range ( 极差 )
      • R = maximal value - minimal value
      • R is worse in robustness.
      • Disadvantage : Based on only two observations, it
      • ignores the observations within the two extremes.
      • The more the observations, the greater the
      • range is.
      • 1.4.2 Inter- quartile range ( 四分位数差距 )
      • Lower Quartile ( 下四分位数 ):
      • 25 percentile, P 25 or
      • Upper Quartile ( 上四分位数 ):
      • 75 percentile, P 75 or
      • Difference between two Quartiles
      • = P 75 - P 25 = -
      • = 13.120 – 8.083 = 5.037
    • 1.4.3 Variance and standard deviation
      • Deviation ( 偏差 ) from the mean:
      • Squared deviation:
      • Population variance ( 总体方差 ):
      • average squared deviation throughout the population,
      • Population standard deviation ( 总体标准差 ):
      • When the population mean ( 总体均数 )
      • is unknown, it is replaced by
      • Squared deviation:
      • Sample variance ( 样本方差 ) :
      • average squared deviation throughout the sample
      • Sample standard deviation ( 样本标准差 ) :
      • Degrees of freedom ( 自由度 ) : ( n -1)
      • Example The weight of male infant
      • 2.85,2.90, 2.96, 3.00, 3.05, 3.18
      Conventionally, mean and standard deviation are often expressed together as For instance, for height, mean and standard deviation are 170  6 (cm)
    • 1.4.4 Coefficient of variation Example 9-10 For normal young males, comparing their height and weight, which one has more variation? Coefficient of variation ( 变异系数 ) is defined as
    • 1.5 Relative Measures and Standardization Approaches
      • 1.5.1 Ratio, frequency and intensity
      • Relative measures are widely used in vital
      • Statistics( 生命统计 ) and epidemiology( 流行病学 ).
      • Caution : There are three types of relative
      • measures although they are often named with “…
      • rate”.
      • Ratio ( 比 ):
      • It is simply a ratio of any quantity to another
      • For example, mass index ( 身体指数 )
      • 2. Relative frequency ( 频率 )
      • A special type of ratio:
      • Both of the numerator( 分子 ) and denominator( 分母 ) are counted numbers;
      • The numerator is a part of the denominator;
      • Within the interval of [0,1]
      • For example,
      • 3. Intensity ( 强度 )
      • Another special type of ratio:
      • The denominator: total observed person-years
      • ( 人 - 年 ) during certain period;
      • The numerator: number of certain event happening during the period.
      • Not necessary within the interval of [0,1]
      • For example,
      • Unit: “person/person-year”
      • The mortality rate can be regarded as adjusted
      • relative frequency per year.
      • In general, intensity could be understood as
      • “ relative frequency per unit of time”, reflecting
      • the chance of certain event happening in a unit of
      • time.
    • 1.5.2 Crude death rate and standardization Table 1.9 Age specific mortality rates ( 年龄别死亡率 ) for two cities
      • Which city has a higher mortality?
    • 1. Direct standardization ( 直接标准化 )
      • Select a “standard population”( 标准人口 )
      • Taking the sum of populations of the two cities as a “standard population”
      • If the mortality rate were applied to the “standard population” correspondingly, Expected numbers of death =?
    • 2. Indirect standardization ( 间接标准化 )
      • Standard mortality ratio (SMR) ( 标准化死亡比 )
      • City A: SMR = 63/58.12 = 1.084
      • Indirect standardized mortality rate = 17.2×1.084 = 18.64 (‰)
      • City B: SMR = 131/142.30 = 0.920
      • Indirect standardized mortality rate = 17.2×0.920 = 15.83 (‰)
    • Summary
      • 1. Statistics: Sample  Population
      • 2. Frequency table and histogram
      • 3. Average level
      • Arithmetic mean, median, geometric mean
      • 4. Variation
      • Range, inter-quatile, standard deviation
      • Coefficient of variation
      • 5. Relative measures
      • Ratio, frequency and intensity
      • 6. Crude death rates are not compariable
      • Two approaches for standardization
    •