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### Chapter 7

Obtaining Subjects

Learning Objectives

- Determine the valid connection between the study sample, study population, and theoretical population
- Identify and assemble appropriate sampling frames
- Select samples using appropriate sampling methods
- Recruit and retain study participants
- Maximize internal and external validity
- Calculate the required sample sizes

Sampling

- It is extremely rare that a study can include every last individual in a population of interest
- Costly and time consuming
- No fool-proof method for identifying everyone in the population

- For this reason, most studies select a sample of individuals from the population of interest
- Ideally, the sample will be a good “representation” of the population

Sampling Concepts

- Target or theoretical population – entire group to which the study results pertain
- Study population – members of the target population that are accessible by the researcher
- Sampling frame – concrete list of members of the study population
- Sample – Subgroup of individuals selected from the sampling frame

Connection between Components

- Representative – degree to which the sample includes individuals with similar or identical characteristics to those of the target population
- Generalizable - generalizability is the degree to which study results are valid for members of the study population not included in the sample
- The degree of both of these depends on the accuracy and rigor in which the sample was selected

Sampling Methods

- Probability-based methods – ability to assign a numeric value to the probability of any one person being chosen for the study
- Ideally use a random method in which all individuals have an equal probability of being selected
- Simple random
- Systematic random
- Stratified random

Simple Random Sample

- Ideal but rarely achievable
- Every individual in the sampling frame has the same probability of being selected for the sample
- If we have a population size of N and want a sample size of n, then each individual should have a (n/N) probability of being selected
- Say N=1000 and we want n=100
- p = 100/1000 = 0.10 or 10% chance of being selected

- If each person has the same chance of being selected, there should be no systematic difference between those selected and those not selected – the sample would NOT be biased

Simple Random Selection

- Assign everyone in the sampling frame a number from 1 to N
- Generate numbers randomly
- Random numbers tables (found in old stats. books)
- Computerized number generators
- Mechanical method like lottery ball selector

- Select the individual with the corresponding number generated

Systematic Random Sample

- Appropriate when it is not possible or practical to assign numbers to each individual in the frame
- Appropriate when random numbers cannot be generated
- Choose every kth individual where
k = N/n

- If N=1000 and n=100 then k = 1000/100

Systematic Random Selection

- Organize individuals on a list or physically, such as boxes of biological specimens
- Calculate k
- Randomly select a number between 1 and k
- Start with the unit with the randomly selected number on the list, then keep counting down the list and choose every kthindividual or specimen

Stratified Random Sample

- Appropriate strategy to ensure that individuals with specific characteristics will be selected
- Sampling frame units are first stratified or grouped according to the characteristic(s) of interest for inclusion (e.g., racial/ethnic groups), then individuals are selected randomly from each group or strata
- Proportionate – individuals are selected to be the same proportion of the strata relative to the whole study population
- Disproportionate – individuals are oversampled (at a greater proportion) or undersampled (at a lesser proportion) relative to the study population depending on the needs of the study

Stratified Random Selection

- Make separate lists of individuals from the sampling frame for each strata of interest
- For example, a list of females and a separate list for males

- Assign numbers to each individual or record their original numbers separately for each strata
- Generate random numbers and select that assigned number from each strata

Nonprobability Samples

- Samples for which individuals have an unknown probability for being selected
- Appropriate when no sampling frame is available, for example:
- Homeless individuals who don’t visit shelters
- Victims of domestic violence who don’t contact the police or seek medical care

- Not possible to determine the representativeness of the sample, but this type of selection is the only one available for some types of target populations

Convenience Sampling

- Include anyone who is eligible, no method of selection is used
- Individuals who respond to advertisements or contact letters
- Students in school class
- Attendees at an event such as a health fair

Purposive Sampling

- Sampling with a “purpose” – to include only individuals with relevant characteristics (e.g., injection drug users not in treatment)
- Still, no sampling frame is available
- Variations

Variations of Purposive Samples

- Expert sample – include only individuals with expertise relevant to the study topic
- Modal instance sample – include individuals who possess the “average” characteristics of the target population
- Heterogeneity sample – include those who represent the broad array of characteristics of the target population
- Quota sample – recruit a prescribed number of individuals with predetermined characteristics, then stop recruiting people with those characteristics when the desired number is achieved
- Snowball sample – locate the first few individuals with the desired characteristics, ask them to give contact information of others like them, contact and recruit their recommendations

Note about Nonprobability Samples

- Conclusions cannot be drawn about the generalizability of sample results to the target population because the sample representativeness cannot be evaluated
- Such conclusions would be biased, by definition

Sample Recruitment and Selection

- Process similar to “marketing”
- Study must be promoted to the potential participants
- “…the communication link between sellers and buyers for the purpose of influencing, informing, or persuading a potential buyer's purchasing decision” (Boone and Kurtz, 2011).

Method of Initial Contact

- Ideally use the same method of communication that will be used for the data collection
- in-person
- traditional mail
- telephone
- internet

- Initial contact can also be made through referrals by professionals (e.g., physicians, pharmacists, therapists)

Method of Initial Contact (cont.)

- Introductory letter, script for a phone call or in-person contact, and brochures
- Should be appropriate reading level and language for the target population
- Must be reviewed and approved by the IRB

Informing the Potential Participant(for the purpose of persuasion)

- Task necessary even before the informed consent process
- Who is conducting the study (e.g., funding agency, investigator’s institution, name and contact information)
- What is the purpose of the study and plan for disseminating results
- What, generally, will be asked of the subject
- When will the data collection take place
- Where will the data collection take place

Elements of the Persuasion

- Significance
- Improving health for subject and/or society
- Potential subject will contribute to the improvement

- Legitimacy
- Funding agency
- Credentials of the investigator(s)

- Protection
- Confidentiality
- Monitoring by the IRB

Incentives to Participate

- Cash/material incentives are not considered benefits in the IRB review
- BUT, they are very powerful persuaders for study participation
- Proper value of incentive
- Enough to be attractive
- Not so much to be coercive

Screening

- Often subject eligibility must be determined
- Evaluate the presence of inclusionary criteria and absence of exclusionary criteria
- Proper time to screen is after potential subjects have expressed willingness to participate
- Details of the screening depend on the research question

Thinking Ahead to Retention

- Value of cohort and experimental studies rely on retention of subjects from baseline to follow-up(s)
- Incentive structure to maximize retention
- Perhaps increasing value with each subsequent follow-up

- Screening process can also include the collection of, sometimes extensive, contact information
- Contact information should be verified and possibly updated through the course of the study

Validity of the Sample

- Internal validity – extent to which the sample is a good representation of the study population
- External validity – extent to which the sample is a good representation of the target or theoretical population
- Without internal validity it is impossible to have external validity

Internal and External Validity

Theoretical Population

External Validity

Study Population

Internal Validity

Sample

Threats to Validity

- External threats
- Improperly defined target population
- Incomplete, inaccurate, or inappropriate sampling frame

- Internal threats
- Sampling errors
- High non-response
- High study attrition

Types of Threats

- Selection bias - systematic error committed when sampling from the sampling frame; if a random procedure is planned and claimed but is not conducted properly, then selection bias may be the result
- Non-response bias - selected subjects who consent to participate in the study are systematically different in a way that may affect results from selected persons who do not participate
- Attrition bias - a systematic relevant difference between those retained and those lost to follow-up in cohort and experimental studies

Sample Size

- How many subjects are needed for the study?
- Statistical power – sample size is large enough to be able to detect hypothesized results that are statistically significant
- Too small – limited statistical power
- Too large – even weak and clinically insignificant results are found to be statistically significant
- Related to Type I and Type II errors

Type I Error

- Type I error - the error we make when we REJECT a TRUE null hypothesis (incorrectly concluding we HAVE support for our alternative hypothesis when we actually should NOT reject the null hypothesis)
- Can be seen as a false positive result
- Assign a maximum probability for making this error, called α, as usually 0.05 or no greater than a 5 percent chance of making this mistake
- Alternatively, we are 95 percent confident that our result is not due to chance and may be a real result

Type II Error

- Type II error - error we make when we do NOT reject a null hypothesis when the null hypothesis is really FALSE (incorrectly concluding we do NOT have support for our alternative hypothesis when we actually SHOULD reject the null hypothesis)
- Can be seen as a false negative
- Assign a maximum probability for making this error as usually 20 percent
- Probability is represented by β, and (1-β) is referred to the statistical power or a study.
- Want to have at least an 80 percent chance of rejecting a false null hypothesis
- Want to have 80 percent power to detect real results in our study

Sample Size and Statistical Power

- Statistical power is largely dependent on sample size
- Example of role of n in a confidence interval formula
- The confidence interval around the mean estimate includes the standard value of Z (representing the alpha of 0.05) and sample size (n) in the denominator
- The larger the n, the smaller the interval will be. The smaller the interval, the more precise is the estimate
- Knowing or assuming the sample mean and standard deviation (σ) and using the Z value with 95 percent confidence, we can solve for n using the above formula
- Solving for n is a power analysis.

Power Analysis

- Precise analysis depends on the study design and appropriate assumptions
- Examples follow
- Assumptions are educated guesses about values needed to solve for n
- Confidence level is typically 95%
- Desired power is usually 80%

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