Outcomes & Impact Better data. Better decisions
Wei Zhang Ph.D.
Research Statistician
Texas Children's Hospital Outcomes & Impact
Service (TCHOIS)
Assistant Professor
Congenital Heart Surgery, Baylor College of
Medicine
Introduction to Sampling Methods
Overview
• Purpose of Sampling
• Some Definitions
• Sample Designing Process
• Importance of Probability Sampling
• Four Commonly Used Probability Sampling Techniques
• Sample Size Determination
Purpose of Sampling
• Who = Target Population
• Bronchiolitis or Sepsis
• What = Parameter
• Characteristics of population
• Problem: Cannot study whole
• Solution: Sample
• Subset of “who”
• Calculate a statistics for “what”
http://korbedpsych.com/R06Sample.html
Some Definitions
• Observation Unit
• Target Population
• Study Population or Sampling Population
• Sampling Frame
• Sample
• Sampling Unit
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Advantages of Sampling
• Less Resource
• More Accuracy
• Reduced Inspection Fatigue
Disadvantages of Sampling
• May not be representative
• Chance of over or under estimation
• Associated with both sampling and non-sampling errors
Causes of Sample Failed to be Representative
Sampling Population not
Reflecting Target Population
Not Enough Sample
http://www.slideshare.net/krishna1988/sa
mpling-techniques-market-research
Medical expertise
Medical
expertise and IT
Medical expertise
and statistical
consultation
Medical expertise
Sampling Techniques
Non-probability Sampling – unequal chance of being selected
• Convenience sampling
• Judgement sampling
• Snowball sampling
• Quota sampling
Probability Sampling – equal chance of being selected
• Simple random sampling
• Systematic sampling
• Stratified sampling
• Clustered sampling
Sampling Techniques
Non-probability sampling – unequal chance of being selected
• Convenience sampling
• Judgement sampling
• Snowball sampling
• Quota sampling
Probability Sampling – equal chance of being selected
• Simple random sampling
• Systematic sampling
• Stratified sampling
• Clustered sampling
Why Probability Sampling?
• Avoid selection bias
• Be able to assess representativity based on sample size
Simple Random Sampling (SRS)
• Similar to draw numbered balls from
a bag.
• Each unit in the target population is
equally likely to be selected.
Simple Random Sampling – How to Do it
• List all units in the sampling population
• Generate a random number per unit
• Use Excel: E.g. “=randbetween(1,100)” if
100 patients in the target population
• If sample 10, then take patients with the
10 smallest numbers.
Simple Random Sampling - Example
Retrospective Chart Review on 30 Day Readmission Rate
• Sampling Population: A disease group defined by certain
ICD codes
• Sampling Frame: A list of MRNs pulled by these ICD
codes from the EMR system
• N patients were selected randomly
• m out N were readmitted within 30 days
• Rate = m/N*100%
Simple Random Sampling - Pros and Cons
Pros:
• Very simple technique
• Based on probability law
• No personal bias
Cons:
• Does not work well when population is heterogeneous
• Less efficient
• Need to get the whole list before sampling
Systematic Random Sampling
• Used when no list or the list is in roughly random order
• Results comparable to simple random sampling
http://www.mathcaptain.com/statistics/systematic-sampling.html
Systematic Random Sampling - How to Do it
Given that patients arrive at no specific order,
• Include first “n” patients everyday
• Sample every “k”th patients
Systematic Sampling - Example
NSQIP Sampling Algorithm
• 8-day cycle to assure cases having equal chance of being
selected
• Operative log provides a list of surgical cases in a cycle
• Apply inclusion and exclusion rules to the log
• Select first 35 cases in consecutive order
• Consecutive order: date of operation, in room time, OR room
number
Systematic Sampling – Pros and Cons
Pros:
• Easy to implement
• Can be used without the whole list of units
Cons:
• Not in general a simple random sample
• May yield bias if there are periodic features
Stratified Random Sampling (STRS)
• Heterogeneous Sampling Population (SP)
• Divide SP into “K” number of homogeneous subgroups called
strata
• Sample n1,n2,……nk units from 1st ,2nd,…..kth strata by simple
random sampling
https://www.pinterest.com/pin/410179478533148229/
Stratified Random Sampling – Allocation of Sample Size
• Proportional allocation
• Optimum allocation
Stratified Random Sampling - Example
Appendectomy LOS Study Stratified by Simple and Complex
• To study post-op length of stay of 1000 appy patients
• 60% are simple
• LOS of complex cases had much larger variation
• Stratify 100 samples into 30 simple and 70 complex
• The total average LOS is the weighted average of simple and
complex
𝐴𝑣𝑔𝐿𝑂𝑆 𝑡𝑜𝑡𝑎𝑙
= 0.6 𝐴𝑣𝑔𝐿𝑂𝑆𝑆𝑖𝑚𝑝𝑙𝑒 + 0.4 𝐴𝑣𝑔𝐿𝑂𝑆𝑐𝑜𝑚𝑝𝑙𝑒𝑥
Stratified Random Sampling – Pros and Cons
Pros:
• More representative
• Higher precision than simple random sampling
• Administratively easier
• Each stratum can be analyzed separately
Cons:
• Stratification needs to be done properly
• Division into homogeneous strata with multiple characteristics may
be difficult
Cluster Sampling
• Divide a sample population into “K” number of subgroups
called clusters
• Take an simple random sampling of clusters
• Observe all elements within the clusters in the sample
Stratified vs. Cluster
http://keydifferences.com/difference-between-stratified-and-cluster-sampling.html
Cluster Sampling - Example
• Patients grouped by zip codes
• Simple random sample from a list of zip codes
• Collect information of all patients within the selected zip codes
Cluster Sampling – Pros and Cons
Pros
• Reduces cost
• No sampling frame necessary
Cons
• Decrease precision
Sample Size and Sampling Error
Standard deviation (std)
• describe on average how each unit differs from sample mean
95% confidence interval
• a range of values that you can be 95% certain contains the true
mean of the population
Margin of error
• Half the width of confidence interval
Determine Sample Size
• Nature of population: size, heterogeneous/homogenous
• Goal of study
• Sampling technique
• Desired precision and reliability
• Financial and resource constraints
One Sample Proportion
• Rate or rapid transferring to a higher level of care
• Rate of interventions
• False positive rate of sepsis diagnosis
• Percentage of bronchiolitis patients who went to ICU
Online Tool:
https://select-statistics.co.uk/calculators/sample-size-calculator-
population-proportion/
One Sample Mean
• Average of LOS of sepsis population or bronchiolitis
population
Online Tool:
https://select-statistics.co.uk/calculators/sample-size-calculator-
population-mean/
Two Sample Proportion Comparison
• Any reduction on readmission rate after intervention?
• Does the education decrease the rate of chest x-rays in the
acute asthma population?
• Compare proportion of patients that received 1st fluid bolus
within 20 minutes in 2017 and 2018.
Online Tool:
https://select-statistics.co.uk/calculators/sample-size-calculator-two-
proportions/
Two Sample Mean Comparison
• Any decrease on LOS after intervention?
Online Tool:
https://select-statistics.co.uk/calculators/sample-size-calculator-two-
means/
Summary
Thoroughly think through sampling design process
• Well defined target population
• Sampling population and sampling frame to reflect target population
• Sampling algorithm to adapt questions and population
• Sample size to balance estimation errors and practical constraints
Outcomes & Impact Better data. Better decisions
