Medical Statistics (full English class) Ji-Qian Fang School of Public Health Sun Yat-Sen University

Chapter 8 Introduction to Medical Statistics

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.

8.1 Basic concepts Homogeneity: All individuals have similar values or belong to same category. Example: all individuals are Chinese, women, middle age (30~40 years old), work in a textile mill ---- homogeneity in nationality, gender, age and occupation. Variation: the differences in height, weight… 1. Homogeneity and Variation

Toss a coin: The mark face may be up or down ---- variation! Treat the patients suffering from pneumonia with same antibiotics: A part of them recovered and others didn’t ---- variation! If there is no variation, there is no need for statistics. Can you give an example of variation in medical field?

Population: The whole collection of individuals that one intends to study. Sample: A representative part of the population. Randomization: An important way to make the sample representative. 2. Population and sample

Questions: Which one is “population”? All the cases with hepatitis B collected in a hospital in Guangzhou. All the deaths found from the permanent residents in a city. All the rats for testing the toxicity of a medicine.

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. Question: Please give some examples of random event. 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.

Number of observations: n (large enough) Number of occurrences of random event A: m P(A)  m/n (Frequency or Relative frequency) Question: Please give some examples for probability of a random event, and frequency of that random event Estimation of Probability----Frequency

4. Parameter and statistic Parameter : A measure of population or A measure of the distribution of population. Parameter is usually presented by Greek letter such as μ,π. -- Parameters are unknown usually

To know the parameter of a population, we need a sample Statistic: A measure of sample or A measure of the distribution of sample. Statistic is usually presented by Latin letter such as s and p. Questions: Please give an example for parameter and statistics. Does a parameter vary? Does a statistic vary?

5. Sampling Error The difference between observed value and true value. Three kinds of error: (1) Systematic error (fixed) (2) Measurement error (random) (3) Sampling error (random)

Sampling error The statistics of different samples from same population: different each other! The statistics: different from the parameter! The sampling error exists in any sampling research. It can not be avoided but may be estimated.

8.2 Types of data 1. Numerical Variable and Measurement Data The variable describe the characteristic of individuals quantitatively -- Numerical Variable The data of numerical variable -- Measurement Data

2. Categorical Variable and Enumeration Data The variable describe the category of individuals according to a characteristic of individuals -- Categorical Variable The number of individuals in each category -- Enumeration Data

Special case of categorical variable : Ordinal variable and rank data There exists order among all possible categories -- Ordinal variable The data of ordinal variable, which represent the order of individuals only -- Rank data

Examples Which type of variables they belong to? RBC ( /l) Diastolic/systolic blood pressure (8/12 kappa) Percentage of individuals with blood type A (20%) Protein in urine (++) Transition rate of cell ( 90%)

8.3 The Basic Steps of Statistical Work 1. Design of study Professional design: Research aim Subjects, Measures, etc.

Statistical design: Sampling or allocation method, Sample size, Randomization, Data processing, etc.

2. Collection of data Source of data Government report system Registration system Routine records Ad hoc survey

Data collection – Accuracy, complete, in time Protocol: Place, subjects, timing; training; pilot; questionnaire; instruments; sampling method and sample size; budget Procedure: observation, interview filling form, letter telephone, web

3. Data Sorting 3. Data Sorting Checking Hand, computer software Amend Missing data? Grouping According to categorical variables (sex, occupation, disease…) According to numerical variables (age, income, blood pressure …)

4. Data Analysis Descriptive statistics (show the sample) mean, incidence rate … -- Table and plot Inferential statistics (towards the population) -- Estimation Hypothesis test (comparison)

About Teaching and Learning Aim: Training statistical thinking Skill of dealing with medical data. Emphasize: Essential concepts and statistical thinking -- lectures and practice session Skill of computer and statistical software -- practice session Practice session --Experiments and Discussion