Medical Statistics Medical Statistics Tao Yuchun Tao Yuchun 1

Preface Preface Introduction to Medical Statistics

Statistics The science of collecting, analyzing, presenting, and interpreting data. —(Encyclopaedia Britannica 2009) Branch of mathematics that deals with the collection, organization, and analysis of numerical data and with such problems as experiment design and decision making. —(Microsoft Encarta Premium 2009)

A science dealing with the collection, analysis, interpretation, and presentation of masses of numerical data. —( Webster's International Dictionary ) The science and art of dealing with variation in data through collection, classification, and analysis in such a way as to obtain reliable results. —( John M. Last, A Dictionary of Epidemiology )

The science of the collection, organization, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments. —( From Wikipedia, the free encyclopedia )

Medical Statistics deals with applications of statistics to medicine and the health sciences, including epidemiology, public health, forensic medicine, and clinical research. Medical Statistics has been a recognized branch of statistics in the UK for more than 40 years but the term does not appear to have come into general use in North America, where the wider term ' biostatistics ' is more commonly used.

Why we need to study Medical Statistics? Three reasons: (1) Basic requirement of medical research. (2) Update your medical knowledge. (3) Data management and treatment.

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

Throw 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. Many examples of variation in medical field: height, weight, pulse, blood pressure, … …

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

limited population and limitless population All the cases with hepatitis B collected in a hospital in Changchun. (limited) All the deaths found from the permanent residents in a city. (limited) All the rats for testing the toxicity of a medicine. (limitless) All the patients for testing the effect of a medicine. (limitless) hypertensive, diabetic, …

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. Example Example: weather, traffic accident, … There must be some regulation in a large number of experiments.

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 f(A)  m/n (Frequency or Relative frequency) Example Example: Throw a coin event: n=100, m ( Times of the mark face occurred )=46 m/n=46%, this is the frequency; P(A)=1/2=50%, this is the Probability. Estimation of Probability----Frequency

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,σ. -- 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, p, t.

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

II. Types of data 1. Numerical Data ( Quantitative Data ) The variable describe the characteristic of individuals quantitatively -- Numerical Data The data of numerical variable -- Quantitative Data

Categorical Data ( Enumeration Data ) The variable describe the category of individuals according to a characteristic of individuals -- Categorical Data The number of individuals in each category -- Enumeration Data

Special case of categorical data : Ordinal Data ( rank data ) There exists order among all possible categories. ( level of measurement) -- Ordinal Data The data of ordinal variable, which represent the order of individuals only -- Rank data

Examples Which type of data they belong to? RBC ( /mcL) Diastolic/systolic blood pressure (8/12 kPa) or ( 80/100 mmHg) Percentage of individuals with blood type A (20%) (A, B, AB, O) Protein in urine (++) ( －, ±, +, ++, +++) Incidence rate of breast cancer ( 35/100,000)

III. 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.

Collection of data Source of data Government report system such as: cholera, plague (black death) … Registration system such as: birth/death certificate … Routine records such as: patient case report … Ad hoc survey such as: influenza A (H1N1) …

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.

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 …)

Data Analysis Descriptive statistics (show the sample) mean, incidence rate … -- Table and plot Inferential statistics (towards the population) -- Estimation -- Hypothesis testing (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 ( Excel and SPSS )

C Practice session --Experiments and Discussion ( in classroom or in Computer-room ) (