Types of Errors Type I error is the error committed when a true null hypothesis is rejected. When performing hypothesis testing, if we set the critical values or limits at 1.96 the standard error of the difference, and regard a mean outside this range as coming from another population, we shall on average be wrong about one time in 20 (5 %) if the null hypothesis is in fact true.

Types of Errors If we do obtain a mean difference bigger than 1.96 standard errors we are faced with two choices: either An unusual event has happened, or The null hypothesis is incorrect. Imagine tossing a coin four times and getting the same face each time !!!!. This has nearly the same probability (6.3%) as obtaining a mean difference bigger than two standard errors when the null hypothesis is true. Do we regard it as a lucky event or suspect a biased coin? If we are unwilling to believe in unlucky events, we reject the null hypothesis, in this case that the coin is a fair one.

Types of Errors To reject the null hypothesis when it is true is to make what is known as a type I error. The level at which a result is declared significant is known as the type I error rate, denoted by .

Types of Errors If we do not reject the null hypothesis when in fact there is a difference between the groups we make what is known as a type II error. The type II error rate is often denoted as .

Types of Errors The power of a study is defined as (1 -) and is the probability of not rejecting the null hypothesis when it is false. The most common reason for type II errors is that the study is too small.

Choosing samples Factors to be considered when devising a sampling scheme The nature of the population The cost of sampling (time & money) Convenience Desired precision Probability sampling: Subjects have known probability of being included in the sample and are chosen by a random mechanism. Non-probability sampling: Samples are selected according to convenience (easy and simple)

Choosing samples Simple Random Sample (SRS): Here a random sample is one in which each individual (object) in the population to be sampled has equal chance to be selected. Units can be numbered and numbers are selected randomly (see the figure).

Choosing samples Systematic sampling It is a process by which every nth object is selected. Consider a mailing list for a survey. The list is too large for us to mail to everyone in this population. Therefore, we select every 6th or 10th name from the list to reduce the size of the mailing while still sampling across the entire list (A-Z). In the pharmaceutical industry this might be done during a production run of a certain tablet where at selected time periods (every 30 or 60 minutes) tablets are randomly selected as they come off the tablet press and weighed to ensure the process is within control specifications. In this production example, the time selected during the hour can be randomly chosen in an attempt to detect any periodicity (regular pattern) in the production run.

Choosing samples Stratified sampling the population is divided into groups (strata) with similar characteristics and then individuals or objects can be randomly selected from each group.

Choosing samples For example, in a study we may wish to ensure a certain percentage of smokers (25%) are represented in both the control and experimental groups in a clinical trial (n=100 per group). First the volunteers are stratified into smokers and non-smokers. Then, 25 smokers are randomly selected for the experimental group and an additional 25 smokers are randomly selected as controls. Similarly two groups of 75 non-smoking volunteers are randomly selected to complete the study design. Stratified sampling is recommended when the strata are very different from each other and all of the objects or individuals within each stratum are similar.

Choosing samples Cluster sampling "multistage" sampling Is employed when there are many individual "primary" units that are clustered together in "secondary", larger units that can be subsampled. For example, individual tablets (primary) are contained in bottles (secondary) sampled at the end of a production run. For example, assume that 150 containers of a bulk powder chemical arrive at a pharmaceutical manufacturer and the quality control laboratory needs to sample these for the accuracy of the chemical or lack of contaminants. Rather than sampling each container we randomly select ten containers. Then within each container of the ten containers we further extract random samples (from the top, middle bottom) to be assayed.

What is Epidemiology? The study of the distribution and determinants of disease in populations. Three key aspects: groups of people measurement comparison

What Can Epidemiology Do? Determine the impact of disease in groups of people. Detect changes in disease occurrence in groups of people. Measure relationships between exposure and disease. Evaluate the efficacy of health interventions and treatments.

What Can’t Epidemiology Do? Can not tell an individual the cause of his or her disease. One study cannot prove a particular exposure caused an illness. Should not be conducted without good measurement of exposure and disease.

Common Steps in Establishing a Relationship Between Exposure and Disease Physician reports series of cases Descriptive analyses describe what is the problem, who is affected and where disease is occurring Analytic studies test the exposure-disease hypothesis in a study group Disease experimentally reproduced by exposure in animal studies Observation that removing exposure lowers disease

Measures of Disease Frequency The most basic measure of disease frequency is a simple count of affected individuals. However, counting is not enough! Why is a simple count not enough? 3 cases of cancer per year from a city of 1,000 people is very different than 3 cases per year from a city of 100,000 people

Measures of Disease Frequency So, in epidemiology we must know: the size of the population from which the affected individuals come, and the time period the information was collected.

Basic Measure of Disease Frequency Rate basic measure in epidemiology the frequency with which an event occurs in a group of people used to compare the occurrence of disease in different groups the measure of time is a critical part of a rate! Such as, the number of newly diagnosed cases of breast cancer per 100,000 women during 1999.

Basic Measure of Disease Frequency Rate Common Rates: mortality (death) rate is the number of deaths in a defined group of people during a specified time period. birth rate is the number of live births in a defined group of people over a specified time period.

Basic Measure of Disease Frequency Incidence a type of rate the number of new cases that develop in a group of individuals during a specific time period If there were 150,00 new cases of lung cancer in the United States during 1997, the incidence rate would be:(150,000/260,000,000) = 0.000058 0.000058 x 100,000 people = 58 cases per 100,000 people, per year

Measures of Association How much greater the frequency of disease is in one group compared with another. Often presented in the form of a two-by-two table.

Measures of Association Disease Yes No Total a+b c+d a b c d Yes Exposure No Total a+c b+d a+b+c+d

Measures of Association Lung cancer Yes No Total 370 715 70 300 15 700 Yes Smoking No Total 85 1,000

Measures of Association Relative Risk (RR): Measures how likely the exposed group will develop a disease compared to the unexposed group.

Measures of Association Lung cancer Yes No Total 70 300 370 Smoking 15 700 715 85 1,000 1,085

Measures of Association Relative Risk = 70/(70+300) = 9.0 15/(15+700) Which means… participants who smoked were 9 times more likely to develop lung cancer than those who did not smoke.

Measures of Association RR of 1.0 indicates that the occurrence of disease in the exposed an unexposed groups are identical: No association observed between exposed and unexposed groups RR greater than 1.0 indicates a positive association, or an increased risk among the exposed. RR less than 1.0 means that there is a decreased risk among the exposed group.

Standardized Mortality Ratios (SMRs) the ratio of the observed number of deaths to the expected number of deaths A standard group of people is used to determine the expected number of deaths. the standard is often the US population, a state, or a county. serves as the comparison group

Standardized Mortality Ratios (SMRs) Our hypothetical study found 58 lung cancer deaths between 1948 and 1963: based on US population rates, we know that 42.9 cancer deaths were expected in a similar population. SMR = (58/42.9) =1.35 Our study group had a risk of cancer mortality approximately 35% greater than those in the general population.