Shooting right Sampling methods FETP India

Competency to be gained from this lecture Select a sample from a population to generate precise and valid estimates

Key issues Sampling Sampling error Validity and precision Sample size calculation

Definition of sampling Procedure by which some members of the population are selected as representatives of the entire population Sampling

Sample Population

Study population The study population is the population to which the results of the study will be inferred Sampling

The study population depends upon the research question How many injections do people receive each year in India?  Study population: Population of India How many needle-sticks to health care workers experience each year in India?  Study population: Health care workers of India How many hospitals have a needle-stick prevention policy in India?  Study population: Hospitals of India Sampling

The sample needs to be representative of the population in terms of time Seasonality Day of the week Time of the day Sampling

The sample needs to be representative of the population in terms of place Urban Rural Sampling

The sample needs to be representative of the population in terms of persons Age Sex Other demographic characteristics Sampling

Definition of sampling terms Sampling unit (Basic sampling unit, BSU)  Elementary unit that will be sampled People Health care workers Hospitals Sampling frame  List of all sampling units in the population Sampling scheme  Method used to select sampling units from the sampling frame Sampling

Why do we sample populations? Obtain information from large populations Ensure the efficiency of a study Obtain more accurate information Sampling

Population Sample Infinite/finite size Characterized by unknown parameters Finite size Characterized by measurable parameters (e.g., mean, standard dev.) A sample is a part of the population, selected by the investigator to gather information (measures) on certain characteristics of the original population Sampling

Practical example The Ministry of Health of a country X wants to estimate the proportion of children in elementary schools who have been immunized against childhood infectious diseases The task must be completed in one month The objective is to estimate the proportion of immunized children Sampling

Planning and implementing a sample survey Sampling plan  Methodology used for selecting the sample from the population Estimation procedures  Algorithms or formulas used for obtaining estimates of population values from the sample data and for estimating the reliability of these population estimates Sampling

The various steps of a survey (1/2) 1.Describe the objective of the survey 2.Define the target population 3.Prepare a “sampling frame” 4.Analysis plan: Develop “table shells” for the results 5.Choose the sampling method 6.Calculate the sample size (s) Sampling

The various steps of a survey (2/2) 7.Develop, field test and revise data collection instrument(s) 8.Train the data collectors 9.Conduct the survey 10.Monitor the field work 11.Tabulate, analyze and interpret the results 12.Use the results Sampling

Collaborative sample design for steps 5 and 6 The statistician, the epidemiologist, and those who will use the data from the survey work together to choose the right sample design Sampling

Taking several samples If you take repeated samples out of a population, each result will be a little different Their distribution is called a sampling distribution Sampling error

Population mean A sampling distribution A sample mean 1 Standard Error Sampling error

MeanSD 95%99% The standard normal curve What is the value of mean and standard deviation?

Properties of the standard normal curve If every member of the population has an equal chance to be in the sample  We can plot our results on the normal curve by calculating a z score This tells us how likely the results are due to chance Example:  95% of the sample means will be within two standard deviations of the population mean Sampling error

Chance How likely is the result due to chance? Measured by the confidence level, example 95% or 0.95 We are 95% confident the population mean is within the confidence interval around our sample mean Sampling error

The validity and reliability of these extrapolations depend on:  How well the sample was chosen  How well the measurements were made Although hypothesis can be tested based on data collected on sample surveys, the primary objective is always estimation Sampling error

Quality of the measures: The precision If the results are precise, they do not vary if the measures are repeated Precision is expressed by the confidence we have in the results Precision is estimated by the confidence interval around the measure We can estimate the variability by computing the confidence interval True value Precision, validity

The sample size increases precision and reduces the confidence interval Lower limit Upper limit x Precision, validity

Estimating precision If every member of the target population had an equal chance of being in the sample Confidence interval provides an estimate of how closely the sample population proportion estimates the target population  Example: ± 10%. Precision, validity

Quality of the measures: The validity Absence of systematic error A valid measure reflects the true value in the population In contrast, a biased measure gives an unreliable “point of view” TrueObserved Precision, validity

Appropriate study design and sampling frame lead to valid results True Observed Precision, validity

Assuring validity Good design Interviewer training Quality assurance Precision, validity

10%5% A valid and precise measure Precision, validity

10%5% A precise measure that is not valid Precision, validity

10%5% A valid measure that is not precise Precision, validity

10%5% A measure that is not valid nor precise Precision, validity

Truth is everything It is easier to control bias and errors in a small sample than in a big one Better have:  A small sample that gives a true estimate Than:  A large sample that gives a false estimate Precision, validity

Type of samples Non-probability samples  Probability of being selected is unknown  Convenience samples Biased Best or worst scenario  Subjective samples Based on knowledge Time/resource constraints Probability samples Sampling techniques

Type of samples Non-probability samples Probability samples  Every unit in the population has a known probability of being selected  Only sampling method that allows to draw valid conclusions about population Sampling techniques

Random sampling in probability samples Removes the possibility of bias in selection of subjects Ensures that each subject has a known probability of being chosen Allows application of statistical theory Sampling techniques

Sampling error No sample is a perfect mirror image of the population Magnitude of error can be measured in probability samples Expressed by standard error of mean, proportion, differences… Function of:  Sample size  Variability in measurement Sampling techniques

Methods used in probability samples 1.Simple, random sampling 2.Systematic sampling 3.Stratified sampling 4.Cluster sampling 5.Multistage sampling Sampling techniques

1. Simple, random sampling Principle  Equal chance for each statistical unit Procedure  Number all units  Randomly draw units Advantages  Simple  Sampling error easily measured Disadvantages  Need complete list of units  Does not always achieve best representativity Sampling techniques

Example of simple, random sampling Numbers are selected at random

2. Systematic sampling Principle  A unit drawn every k units  Equal chance of being drawn for each unit Procedure  Calculate sampling interval (k = N/n)  Draw a random number (  k) for starting  Draw every k units from first unit Advantages  Ensures representativity across list  Easy to implement Disadvantage  Dangerous if list has cycles Sampling techniques

Example of systematic sampling Every eighth house is selected

3. Stratified sampling Principle  Classify population into homogeneous subgroups (strata)  Draw sample in each strata  Combine results of all strata Advantage  More precise if variable associated with strata  All subgroups represented, allowing separate conclusions about each of them Disadvantages  Sampling error difficult to measure  Loss of precision if small numbers sampled in individual strata Sampling techniques

Example of stratified sampling Estimate vaccination coverage in a country One sample drawn from each region Estimates calculated for each stratum Each strata weighted to obtain estimate for country Sampling techniques

4. Cluster sampling Principle  Random sample of groups (“clusters”) of units  All or proportion of units included in selected clusters Advantages  Simple: No list of units required  Less travel/resources required Disadvantages  Imprecise if clusters homogeneous (Large design effect)  Sampling error difficult to measure Sampling techniques

Cluster sampling The sampling unit is not a subject, but a group (cluster) of subjects. It is assumed that:  The variability among clusters is minimal  The variability within each cluster is what is observed in the general population Sampling techniques

The two stages of a cluster sample 1.First stage: Probability proportional to size Select the number of clusters to be included Compute a cumulative list of the populations in each unit with a grand total Divide the grand total by the number of clusters and obtain the sampling interval Choose a random number and identify the first cluster Add the sampling interval and identify the second cluster By repeating the same procedure, identify all the clusters 2.Second stage In each cluster select a random sample using a sampling frame of subjects (e.g. residents) or households Sampling techniques

Self-weighting in cluster samples Stage one: The larger units are more likely to be selected in the first round  Unit B twice as large as unit A will have twice the chance of being selected Stage two: Individuals in larger unit selected are less likely to be selected in the second round  Individual in unit B will have half the chance of being selected within the unit The two effects cancel each other and each person in the population has the same probability of being sampled

30 x 7 cluster sampling in the expanded programme of immunization Procedure:list of all villages (areas) with total population VillageInhabitantsCumulative ,715 Divide the cumulative total by 30 clusters we wish to select 4,715 : 30= Sampling techniques

30 x 7 cluster sampling in the expanded programme of immunization Find a random number with three digits (= Sampling interval) e.g. 123 Choose from the cumulative distribution the clusters by adding 157 (sampling interval) *1st cluster **2nd =280 In each village (area) choose 7 children Total sample 30 X 7= 210 Sampling techniques

Design effect (Use Epitable software) Global variance p(1-p) Var srs = n Cluster variance p= global proportion pi= proportion in each stratum n= number of subjects k= number of strata Σ (pi-p)² Var clus = k(k-1) Design effect = Var srs Var clust Sampling techniques

Example of cluster sampling Section 4 Section 5 Section 3 Section 2Section 1 Sampling techniques

5. Multistage sampling Principle  Several chained samples  Several statistical units Advantages  No complete listing of population required  Most feasible approach for large populations Disadvantages  Several sampling lists  Sampling error difficult to measure Sampling techniques

Steps in estimating sample size Identify major study variable Determine type of estimate (%, mean, ratio,...) Indicate expected frequency of factor of interest Decide on desired precision of the estimate Decide on acceptable risk that estimate will fall outside its real population value Adjust for estimated design effect Adjust for expected response rate (Adjust for population size) Sampling techniques

Sample size formula in descriptive survey (Use Epitable) z: alpha risk expressed in z-score p: expected prevalence q: 1 - p d: absolute precision g: design effect z² * p * q 1.96²*0.15*0.85 n = = 544 d²0.03² Cluster sampling z² * p * q 2*1.96²*0.15*0.85 n = g* = 1088 d² 0.03² Simple random / systematic sampling Sampling techniques

Remember Probability samples are the best Beware of …  Refusals  Absentees  “Do not know” Sampling techniques

Summary of methods used in probability samples 1.Simple, random sampling Draw subjects from list with random number 2.Systematic sampling Draw every xth subject 3.Stratified sampling Take one sample for each strata 4.Cluster sampling Select clusters and then select individuals 5.Multistage sampling Sample stage by stage Sampling techniques

Key issues We cannot study the whole population so we sample it Taking a sample leads to sampling error, which is measurable Good design and quality assurance ensure validity and while appropriate sample size will ensure precision Probability samples are the only ones that allow use of statistics as we know them