1、Medical Statistics (full English class)Ji-Qian FangSchool of Public Health Sun Yat-Sen UniversityIntroduction to Medical StatisticsMedical Statistics: Application of mathematical statistics inthe field of medicineWhy we need to study statistics? Three reasons:(1)Basic requirement of medical research

2、.(2)Update your medical knowledge.(3) Management and treatment for your own data.Basic conceptsHomogeneity: All individuals have similar characteristics and belong to same category. Variation: the differences in some features such as height, weight1. Homogeneity and VariationRandom By chance!Random

3、event: the event may occur or may not occur in one experiment. Before an experiment, nobody is sure whether the event occurs or not. However, there must be some regulation in a large number of experiments.3. ProbabilityMeasure the possibility of occurrence of a random event. A : random event P(A) :

4、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 : relative frequency or frequency of event A P(A) frequency The Basic Steps

5、 of Statistical Work1. Design of study2. Collection of data3. Data Sorting4. Data Analysis5. Interpret the resultsAbout This course- Teaching and LearningAim: Training essential concepts and statisticalthinking Learning some skills in design and analysisLectures - Concepts and thinkingPractice sessi

6、on - experiments and discussion Chapter1 Descriptive StatisticsChapter1 Descriptive Statistics Statistics: Statistical description Statistical inference Statistical description: Describes the feature of the sample. Main forms: tables, plots and numerical indexes1.1 Variables and Data1.1.1 Structure

7、and feature of data 1.1.2 Types of variables1. Quantitative Variable (定量變量)Continuous variable (連續變量) Values obtained through measurement : height, weight, blood pressure, pulse and Taking values in a continuous interval.Discrete variable (離散變量) Taking values in a set of integers. 2. Qualitative Var

8、iable (定性變量)Categorical variable (分類變量) : Taking “values” within several possiblecategories, such as Gender (male, female),occupation. Binary variable is a simplest special case of it. Example 1.1 The variable for gender can be defined with a binary variable X.Ordinal variable (有序變量) : There exists

9、order among all possiblecategories, such as education (primary school,high school, university, postgraduate)Table 1.3 The frequency table for occupation of 108 patientsTable 1.4 The frequency table for the results of certain semi-quantitative test among 150 patients2. Continuous type frequency table

10、 Example 1.3 120 normal male adults were randomlyselected 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 4.844.91 5.14 5.25 4.89 4.79 4.90 5.09 4.04 5.14 5.46 4.66 4.204.21 3.73 5.17 5.79

11、5.46 4.49 4.85 5.28 4.78 4.32 4.94 5.214.68 5.09 4.68 4.91 5.13 5.26 3.84 4.17 4.56 3.52 6.00 4.054.92 4.87 4.28 4.46 5.03 5.69 5.25 4.56 5.53 4.58 4.86 4.974.70 4.28 4.37 5.33 4.78 4.75 5.39 5.27 4.89 6.18 4.13 5.224.44 4.13 4.43 4.02 5.86 5.12 5.36 3.86 4.68 5.48 5.31 4.534.83 4.11 3.29 4.18 4.13

12、4.06 3.42 4.68 4.52 5.19 3.70 5.514.64 4.92 4.93 4.90 3.92 5.04 4.70 4.54 3.95 4.40 4.31 3.774.16 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 R=6.183.29=2.89(2) Length of sub-intervals i

13、 Divide the whole range into 8-15 sub-intervals R/10=2.89/10= 0.289 0.30 then let i =0.301.2.2 Frequency plot and histogram 1. Frequency plot for discrete variable bar chart2. Frequency plot for continuous variable histogram 1.3 Measurement for average level Numerical characteristics (數字特征): Average

14、 level (平均水平) Variation (變異)1.3.1 Arithmetic mean (算術均數) Useful when the histogram looks symmetric. Denote the observed values of the individuals with , the arithmetic mean (1.1)1.3.2 Geometric mean (幾何均數) It is useful when the histogram of the logarithms is close to symmetric.Example The concentrat

15、ions 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 (中位數) When the histogram shows skew, the median can be applied to measure the average level. Median = the value in the middleEx

16、ample 1 Data set 1,1,2,2,3,4,6,9,10 n = 9 Median = 3Example 2 Data set 1,1,2,2,3,4,6,9,10,13 n = 10 Median = (3+4)/2=3.5When 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/2 + 12 Think about Px = x-percentile = x% of the values

17、 less than it and (1- x%) of the values greater than it Median = the value in the middle = 50% of the values less than it and 50% of the values greater than it = 50 percentile = P50 How to calculate x-percentile (百分位數)? P25 ? P75 ? 1.4 Measurement for Variation1.4.1 Range (極差) R = maximal value - mi

18、nimal valueR is worse in robustness. Disadvantage: Based on only two observations, itignores the observations within the two extremes. The more the observations, the greater therange is.1.4.2 Inter- quartile range (四分位數差距) Lower Quartile (下四分位數): 25 percentile, P25 or Upper Quartile (上四分位數): 75 perc

19、entile, P75 or Difference between two Quartiles = P75 - P25 = - = 13.120 8.083 = 5.0371.4.3 Variance and standard deviationDeviation (偏差) from the mean: Squared deviation: Population variance (總體方差): average squared deviation throughout the population, Population standard deviation (總體標準差): When the

20、 population mean (總體均數) is unknown, it is replaced by Squared deviation: Sample variance (樣本方差) : average squared deviation throughout the sample Sample standard deviation (樣本標準差) : Degrees of freedom (自由度) : (n-1) Example The weight of male infant 2.85,2.90, 2.96, 3.00, 3.05, 3.18Conventionally, me

21、an and standard deviation are often expressed together asFor instance, for height, mean and standard deviation are 1706 (cm)1.4.4 Coefficient of variationExample 9-10 For normal young males, comparing their height and weight, which one has more variation?Coefficient of variation (變異系數) is defined as

22、1.5 Relative Measures and Standardization Approaches1.5.1 Ratio, frequency and intensity Relative measures are widely used in vital Statistics(生命統計) and epidemiology(流行病學). Caution: There are three types of relative measures although they are often named with “ rate”. Ratio (比): It is simply a ratio

23、 of any quantity to anotherFor example, mass index (身體指數)2. Relative frequency (頻率) 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 0,1For example,3. Intensity (強度) Another special type of ra

24、tio: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 0,1For 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 standardizationTable 1.9 Age specific mortality rates (年齡別死亡率) for two cities Which city has a high