Odds Ratio (OR)

• Definition: Compares the odds of an event happening in one group to the odds in another group.
• Why to use: Used in case-control studies to assess the strength of association between exposure and outcome.
• Formula:
  
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Relative Risk (RR)

• Definition: The ratio of the risk of an event in the exposed group to the risk in the control group.
• Why to use: Used in cohort, cross-sectional and RCT studies to determine how much more (or less) likely an event is in the exposed group.
• Formula:  

  

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Experimental Event Rate (EER)

• Definition: The proportion of subjects in the experimental group that experience the event of interest.
• Why to use: Useful for measuring the event rate in the treatment group.
• Formula: 

  

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Control Event Rate (CER)

• Definition: The proportion of subjects in the control group that experience the event of interest.
• Why to use: Measures the event rate in the control group for comparison with the experimental group.
• Formula: 

  

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Relative Risk Reduction (RRR)

• Definition: The proportional reduction in risk between the control and treatment groups.
• Why to use: Useful for understanding the relative decrease in risk with an intervention.
• Formula: 

  

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Absolute Risk Reduction (ARR)

• Definition: The absolute difference in event rates between the control and experimental groups.
• Why to use: Provides the actual decrease in risk with treatment.
• Formula: 

  

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Absolute Risk Increase (ARI)

• Definition: The increase in the event rate for an intervention compared to a control, used when the intervention causes harm.
• Why to use: Used to measure the increase in adverse events with treatment.
• Formula: 

  

Number Needed to Treat (NNT)

• Definition: The number of patients that need to be treated to prevent one additional adverse event.
• Why to use: Important in clinical decision-making to assess the effectiveness of treatment.
• Formula: 

  

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Number Needed to Harm (NNH)

• Definition: The number of patients exposed to a risk factor or treatment needed to cause one additional adverse event.
• Why to use: Important in assessing the potential harm of a treatment.
• Formula: 

  

Prevalence

• Definition: The proportion of a population that has a condition at a specific point in time.
• Why to use: Provides an estimate of how widespread a disease or condition is within a population.
• Formula: 

  

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Incidence

• Definition: The rate of new cases of a condition over a given time period.
• Why to use: Measures how quickly new cases of a disease are developing in a population.
• Formula: 

  

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Cumulative Incidence

• Definition: The proportion of people who develop a condition over a specified period of time.
• Why to use: Indicates the risk of developing a disease within a defined time frame.
• Formula: 

  

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Case Fatality Rate (CFR)

• Definition: The proportion of diagnosed cases of a disease that result in death.
• Why to use: Helps understand the lethality of a disease within a given period.
• Formula: 

  

Crude Mortality Rate

• Definition: The total number of deaths from all causes in a population during a specified time period.
• Why to use: Measures the overall risk of death in a population.
• Formula:  
   
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Confidence Interval

• Definition: A range of values that estimate an unknown population parameter, such as the mean, with a certain level of confidence. 
• Why use it: Provide a measure of uncertainty around a sample statistic (e.g., a mean) and help infer the population parameter by accounting for sample variability. They are commonly used to assess the reliability of estimates from sample data.
• Formula: 

   

  x̄  = sample mean
  Z = Z-score corresponding to the confidence level (e.g., 1.96 for 95% confidence)
  σ = population standard deviation
  n = sample size
• Example: Suppose you measure the heights of 100 individuals and find a sample mean height of 170 cm, with a standard deviation of 10 cm. To find a 95% confidence interval for the true population mean: CI = 170 ± (10 /√ 100) = 170 ± 1.96 x 1 = 170 ± 1.96 
• So, the 95% confidence interval is 168.04 cm ≤ μ ≤171.96 cm
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Correlation

• Definition: A measure of the linear relationship between two variables.
• Why use it: To assess the strength and direction of the relationship between variables.
• Formula: (Pearson Correlation Coefficient)

  

  r  = correlation coefficient
  xi = values of the x-variable in a sample
  x̄ = mean of the values of the x-variable
  yi = values of the y-variable in a sample
  ȳ = mean of the values of the y-variable
• Example: A correlation coefficient r=0.8 indicates a strong positive correlation.
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Hazard Ratio (HR)

• Definition: A measure of how often a particular event happens in one group compared to another over time.
• Why use it: Often used in survival analysis to compare the risk of events between groups.
• Formula: 

  

  h1(t) = the hazard in the treatment group
  h0(t) = the hazard in the control group.
• Example: An HR of 0.7 means the treatment group has 30% less risk of the event compared to the control.
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Mean

• Definition: The average of a set of numbers.
• Why use it: To summarise a dataset with a single value representing the centre.
• Formula: 

  

  xi = each data point
  N = number of data points.
• Example: The mean of [10, 12, 8, 14] is (10+12+8+14)/4=11
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Median

• Definition: The middle value in a sorted dataset.
• Why use it: To represent the central tendency, especially when data is skewed.
• Formula: No specific formula; it's the middle value in ordered data.
• Example: In the dataset [5, 7, 9, 10, 15], the median is 9.
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Normal Distribution

• Definition: A probability distribution where data is symmetrically distributed around the mean.
• Why use it: Many statistical methods assume normal distribution for testing hypotheses.
• Formula (Probability Density Function):

  

• μ = the mean
  σ = the standard deviation.
• Example: A normal distribution with μ=0 and σ=1 is the standard normal distribution.
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Percentile

• Definition: A measure indicating the value below which a given percentage of observations fall.
• Why use it: To describe the relative standing of a value in a dataset.
• Formula: No fixed formula, but the percentile rank is typically calculated from sorted data.
• Example: If a test score is in the 90th percentile, 90% of people scored lower.
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p-Value

• Definition: The probability of obtaining test results at least as extreme as the results observed, assuming that the null hypothesis is true.
• Why use it: To determine statistical significance in hypothesis testing.
• Formula: Calculated from statistical tests (e.g., t-test, chi-square).
• Example: A p-value of 0.03 means there is a 3% probability the observed result could occur by random chance if the null hypothesis is true.
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Sample Size

• Definition: The number of observations or data points in a study.
• Why use it: To ensure the study has enough power to detect a statistically significant effect.
• Formula: (Cochran's Formula)

  

   
  Z = Z-value
  p= estimated proportion of the population
  e= desired margin of error (precision)
• Example: n0 = (1.96)^2 .0.5. (1 - 0.5) / (0.05)^2 = 384.16 
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Simple Linear Regression

• Defintion: Used to model the linear relationship between two variables.
• Why use it:  To predict the value of a dependent variable based on the value of an independent variable and to understand the strength and direction of their relationship.
• Formula: 

  
  y = outcome/disease
  a = baseline outcome value when exposure is 0
  b = Beta-coefficent. The effect of the exposure on the outcome.

• Example y = 41.16 + 4.97(6) = 70.98
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Standard Deviation (SD)

• Definition: A measure of the amount of variation or dispersion in a set of values.
• Why use it: To understand how spread out data points are from the mean.
• Formula: 

  

   
  xi = each data point
  x̄ = mean
  N = the number of data points.
• Example: For a dataset [10, 12, 8, 14], the mean x̄= 11. The SD is approximately 2.45.
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Standard Error (SE)

• Definition: The standard deviation of the sample mean distribution.
• Why use it: To estimate the accuracy of a sample mean relative to the population mean.
• Formula: 

  

  SD= Standard deviation
  n= sample size.
• Example: If SD=10 and n=25, SE = 10/√25 =2
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Z-Score

• Definition: The number of standard deviations a data point is from the mean.
• Why use it: To compare data points from different distributions or assess how unusual a data point is.
• Formula:

  

  x = the value
  μ = the mean
  σ = standard deviation.
• Example: For x=85, μ=80, and σ=5, the z-score is (85−80)/5= 1
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