Applied biostatistics

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Applied biostatistics

• Francisco Javier Barón López
• Dpto. Medicina Preventiva
• Universidad de Málaga España
• baron_at_uma.es

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Classical hypothesis tests

• Comparing two groups
• A group receive a treatment.
• Other group receives placebo treatment.
• The outcomes are similar?
• How is the outcome measured?
• Numerically
• t-test (students t)
• Binary outcome Yes/No, Healthy/Sick,
• chi-squared

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Numerical outcome

• Problem
• The numerical differences obtained when comparing
  two treatments are big enough to attribute it to
  random sampling?
• Classiffication
• Independent samples
• Paired samples

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Paired samples

• How
• We have two measurements of the same individual
• We have couples of similar individuals (matched
  study)

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Paired samples

• Null hypothesis
• Mean difference among paired observations is 0
• We reject it when p is small (plt0.05)
• Two approaches
• Parametric (t-test)
• Non parametric (Wilcoxon)

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Example Paired samples

• Compare production yield of two types of corn
  seed.
• Type of seed will have influence but others
  things too
• Sun, wind, cropland
• Idea Lets test the two types of seed in the
  same conditions

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Example Paired samples
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Independent samples

• Research question
• Calcium intake lowers blood pressure?
• Material and methods
• Two samples of individuals (independent)
• Experimental (calcium intake)/Placebo
• There must be some difference among means, Can
  they be explained by random chance?
• We choose a statistical test and compute
  significance (p).
• When p is small (plt0,05) we have evidence for
  differences not random Calcium intake have a
  signifficant effect on blood pressure.

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y ahora la inferencia
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Independent samples

• Null hypothesis
• There are no difference among groups
• Two ways of computing signifficance
• Parametric (T- Student)
• Non parametric (Wilcoxon, Mann-Whitney)

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Example Independent samples

• We think that calcium intake decreases blood
  pressure. To test it, we use two groups of
  similar people to do an experiment
• Experimental group 10 individuals, 3 months of
  treatment. We measure the difference (change in
  blood pressure)
• Before After
• Control group 11 individuals, placebo for 3
  months.

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Validity conditions t-test

• Similar dispersion homoskedastics.
• Normality
• Kolmogorov-Smirnov

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Normality condition
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Numerical variable compared in 3 groups

• Research question
• When comparing means if 3groups, can we
  attribute the differences JUST to hazard?
• Generalizes t-test.
• Numerical variable that measures outcome is
  called dependent
• Numerical
• Variable that classifies individuals in groups
  factor
• Qualitative

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3 independent samples

• Null hypothesis
• There are no differences among the groups
• Two ways of computing signifficance
• Parametric One-way ANOVA
• Non parametric Kruskal-Wallis.

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Example 3 independent samples

• Experiment to compare 3 reading methods
• Random assignment
• 22 students in each group
• We measure several variables, before and
  after (pre-test/post test). The outcome is the
  difference (numerical variable)

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Design problems?

• Do they had the same value before?
• No evidence against (p0,436)

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Validity conditions for ANOVA

• Similar variability Levenes test (we want
  pgtgt0,05)
• Normality in each sample (pgt0,05)
• Conditions can be violated if sample sizes are
  big.

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And now the interesing part

• Are the differences significant?

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A posteriori-analysis

• Planned comparisons
• You need to justify them a priori.
• Post-hoc comparisons

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Non parametric version of ANOVA Kruskal Wallis