YY Teo Associate Professor Saw Swee Hock School of Public Health, NUS Department of Statistics

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ST1232 Statistics in the Life Sciences

• YY TeoAssociate ProfessorSaw Swee Hock School
  of Public Health, NUSDepartment of Statistics
  Applied Probability, NUSLife Sciences Institute,
  NUSGenome Institute of Singapore, ASTAR

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Lesson Structure

• 13 weeks of 2 lectures (of 2 hours) per week
• Practically, 17-18 lectures planned, newspaper
  statistics, conferences, etc.
• Tutorials in computer labs from week 3 onwards
  (11 weeks of tutorials)
• Consultation (Fridays 2pm 3.30pm)
• 3 assessments
• tutorial participation (10)
• mid-term quiz (30)
• end-of-term exam (60)

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Resources

• Lectures, slides, tutorials
• Fred Ramsey and Dan Schafer (2001) The
  Statistical Sleuth. 2nd edition, Duxbury Press
• Julie Pallant. SPSS Survival Manual A
  Step-by-Step Guide to Data Analysis Using SPSS
  for Windows. 3rd edition, Open University Press
• http//www.statistics.nus.edu.sg/statyy/ST1232

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Tutorials

• Note the available time slots and sign up at the
  CORS system http//www.nus.edu.sg/cors/. The
  tutorial will be at S16-05-102 (Com lab 2)
• T1 Mondays (8am 9am)
• T2 Mondays (9am 10am)
• T3 Tuesdays (8am 9am)
• T4 Tuesdays (9am 10am)
• T5 Wednesdays (9am 10am)
• T6 Wednesdays (10am 11am)
• T7 Wednesdays (11am 12pm)
• T8 Thursdays (9am 10am)
• T9 Thursdays (10am 11am)
• T10 Thursdays (11am 12pm)
• T11 Fridays (8am 9am)
• T12 Fridays (9am 10am)
• T13 Fridays (10am 11am)

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Medical Statistics

• Quantitative basis to human diseases and traits
• Progression from observational science!
• Statistics and mathematics required for this
  advancement, from observational to quantitative

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Statistics in medical research
Medical statistics
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Pregnancy Test Kit
A woman buys a pregnancy test kit, and is
interested to find out whether she is pregnant.
One hypothesis in this case (status quo), is
that she is not pregnant. The other hypothesis
(hypothesis of interest), is that she is
pregnant. Test kit may show ve indicating
there is evidence to suggest pregnancy ve
indicating lack of evidence to suggest pregnancy
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Pregnancy Test Kit
The test kit may either be accurate, or
inaccurate.
Actually pregnant
Actually not pregnant
Correct ve diagnosis(Sensitivity, or Power)
Incorrect ve diagnosis
Test kit shows ve
Incorrect ve diagnosis
Correct ve diagnosis(Specificity)
Test kit shows ve
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Sensitivity or Specificity?

• Objective of the experiment

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Sensitivity or Specificity?

• Objective of the experiment
• HIV diagnostic kit, 99.9 sensitive and 99.5
  specific

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Sensitivity or Specificity?

• Objective of the experiment
• HIV diagnostic kit, 99.9 sensitive and 99.5
  specific

Correct identification of HIV ves
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Sensitivity or Specificity?

• Objective of the experiment
• HIV diagnostic kit, 99.9 sensitive and 99.5
  specific

Correct identification of HIV ves
Correct identification of HIV -ves
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Sensitivity or Specificity?

• Objective of the experiment
• HIV diagnostic kit, 99.9 sensitive and 99.5
  specific
• Tests on immigrants, assume 1,001,000
  applications each month, of which 1000 are truly
  HIV-positive

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Sensitivity or Specificity?

• Objective of the experiment
• HIV diagnostic kit, 99.9 sensitive and 99.5
  specific
• Tests on immigrants, assume 1,001,000
  applications each month, of which 1000 are truly
  HIV-positive HIV ve x 1000 HIV ve x
  1,000,000

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Sensitivity or Specificity?

• Objective of the experiment
• HIV diagnostic kit, 99.9 sensitive and 99.5
  specific
• Tests on immigrants, assume 1,001,000
  applications each month, of which 1000 are truly
  HIV-positive HIV ve x 1000 HIV ve x
  1,000,000

On average, 999 correctly identified, 1
incorrectly diagnosed as HIV -ve
On average, 995,000 correctly identified as HIV
-ve, 5000 incorrectly diagnosed as HIV ve
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Sensitivity or Specificity?
On average, 999 correctly identified, 1
incorrectly diagnosed as HIV -ve
On average, 995,000 correctly identified as HIV
-ve, 5000 incorrectly diagnosed as HIV ve
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Height and Weight
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Height and Weight
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Height and Weight
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Height and Weight
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Scientific Process
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Research hypothesis - What is your scientific
question? - What are you trying to achieve?
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Scientific Process
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Human Diversity
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Human Diversity

• Even within human race, variation exists between
  people of different ethnicities, cultures and
  populations
• Genetic basis to a substantial fraction of such
  variation

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Human Diversity

• Even within human race, variation exists between
  people of different ethnicities, cultures and
  populations
• Genetic basis to a substantial fraction of such
  variation
• Observable differences physical appearances,
  build, weight

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Human Diversity

• Even within human race, variation exists between
  people of different ethnicities, cultures and
  populations
• Genetic basis to a substantial fraction of such
  variation
• Observable differences physical appearances,
  build, weight
• Variation in susceptibility to diseases
• Influenced by evolutionary processes, over many
  generations
• Cross-sectional observation of adaptation and
  natural selection

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Target population

• Depends entirely on your research hypothesis!

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Target population - Everyone in Singapore? -
Every female individuals in Singapore? - Every
female individuals of a certain age in
Singapore? - Every femal individuals of a certain
age in Singapore, and who could be pregnant?
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Target population - Everyone in Singapore? -
Everyone of a certain age in Singapore? -
Everyone of a certain age in NUS? - Everyone of
a certain age from a specific population group in
Singapore
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Target populations

• Depends entirely on your research hypothesis!
• Example Interest to investigate the genetic
  factors that increase the risk to type 2 diabetes
  in Chinese adults in Singapore.
• Target population(s)
• Every Chinese adult in Singapore that is affected
  by type 2 diabetes
• Normal Chinese adults (unaffected by type 2
  diabetes) of the same age band
• Classic case-control design in medical
  epidemiology.

But, is this sufficient???
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Samples versus Population

• Obviously not possible to perform an experiment
  on every diabetic Chinese adult in Singapore
• Select a representative set of individuals from
  the appropriate population to perform the
  experiment on
• This set of individuals is known as your samples.

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Scientific Process
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What is your intuition?

• A pharmaceutical firm is developing a medical
  drug, that purportedly treats severe headache.
• During the clinical trials (testing the efficacy
  and safety of the drug), it was tested on 10
  people, of which 7 reported that it worked to
  reduce headaches, while 3 claimed it had no
  effect.
• Another pharma also developed a competing
  treatment, but tested on 1000 people, of which
  704 reported it helped to reduce headaches, while
  294 claimed it had no effect, and 2 people
  claimed their headaches worsen.

Which setting do you think gives you more
information about the developed drug? And why?
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Sample Size Determination

• Types of effects that can be detected depends
  entirely on sample sizes.

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Pregnancy Test Kit
The test kit may either be accurate, or
inaccurate.
Actually pregnant
Actually not pregnant
Correct ve diagnosis(Sensitivity, or Power)
Incorrect ve diagnosis
Test kit shows ve
Incorrect ve diagnosis
Correct ve diagnosis(Specificity)
Test kit shows ve
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Sample Size Determination

• An issue commonly discussed in medical research!
• Power calculations, sample size, effect sizes,
  statistical significance?

Power calculations
Sample size
Effect sizes
Statistical Significance
Require ? evidence, means Power ?
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Scientific Process
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Sample Selection

• Simple Random Sample
• Every sample in the population has an equal
  chance of being selected (e.g. phonebook
  sampling)
• Stratified Sample
• Every sample in the population belongs uniquely
  to a specific category (e.g. gender)
• Cluster Sampling
• Each cluster has the characteristics of the
  population, and sampling is performed within the
  cluster rather than in the population (e.g.
  diabetic patients in one hospital in Singapore,
  compared to all diabetic patients in Singapore)
• Multistage Sampling
• A combination of different sampling schemes

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Scientific Process
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Data exploration and Statistical analysis

1. Exploratory data analysis
2. Probability and Bayes Theorem
3. Theoretical distributions (Uniform, Bernoulli,
   Binomial, Poisson, Normal)
4. Confidence Interval
5. Hypothesis testing (t-test, ANOVA, test of
   proportions, Chi-square tests)
6. Non-parametric tests
7. Linear regression and correlation
8. Logistic regression

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Data exploration and Statistical analysis

1. Data checking, identifying problems and
   characteristics
2. Understanding chance and uncertainty
3. How will the data for one attribute behave, in a
   theoretical framework?
4. Theoretical framework assumes complete
   information, need to address uncertainties in
   real data
5. Testing your beliefs, do the data support what
   you think is true?
6. What happens when the assumptions of the
   theoretical framework are not valid
7. Modeling relationships between multiple outcomes
   and a numerical response
8. Ditto, but with a two-state outcome.

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Data
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Scientific Process
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Statistics Truths or Lies

• 21st century age of information
• Responsible for driving scientific progress in
  multiple disciplines
• Core skills for data analysis
• Ability and knowledge to ingest and digest
  information is at a premium

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Statistics Truths or Lies
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Computers and Statistics
Computers and Statistics

• Excel, SPSS, Minitab, Stata, Mathlab, R, etc
• RExcel for this course
• http//www.stat.nus.edu.sg/statyy/ST1232/bin/RExc
  el_installation.docx
• Advantages
• Speed, accuracy, ease of data manipulation
• Easy to produce plots, cross-tabulation tables,
  summary statistics
• Disadvantages
• Inappropriate analysis / use of wrong tests
• Data dredging

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Brief introduction to RExcel and SPSS
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Features

• RExcel and SPSS extremely similar in terms of
  data entry and usage
• Spreadsheet-based data entry system

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Link data in Excel to R
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Features

• RExcel and SPSS extremely similar in terms of
  data entry and usage
• Spreadsheet-based data entry system
• Remember a unique individual/entry per row!
• Drop-down menu option for data analysis

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Features

• RExcel and SPSS extremely similar in terms of
  data entry and usage
• Spreadsheet-based data entry system
• Remember a unique individual/entry per row!
• Drop-down menu option for data analysis
• While both are extremely intuitive, SPSS is
  slightly more user-friendly, in terms of defining
  variables and format of output

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In RExcel
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Output is in the R Commander tab
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Features

• RExcel and SPSS extremely similar in terms of
  data entry and usage
• Spreadsheet-based data entry system
• Remember a unique individual/entry per row!
• Drop-down menu option for data analysis
• While both are extremely intuitive, SPSS is
  slightly more user-friendly, in terms of defining
  variables and format of output
• Details will be given in the subsequent lectures
• Important to know the usage and interpretation
  of both SPSS and RExcel well, examinable and
  practically important!

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Reminders

• Book your tutorial slots!
• Work on your tutorials before going to the
  classes!