Intermediate Biostat Midterm Terms Flashcards
Poisson Distribution
A probability distribution that models the probability of a certain number of events occurring within a fixed interval of time or space, given that these events occur with a known average rate and independently of the time since the last event. It is often used to assign probabilities to counts of ‘rare’ events over time or space.
Example: Number of deaths from tuberculosis in one year.
Assumptions of the Poisson Distribution
- The probability of observing one event is directly proportional to the length of the time interval (Δt). 2. The rate (λ) is homogeneous over time; the expected number of events per unit time is constant. 3. The occurrence of events in one time subinterval does not influence the occurrence of events in any other time interval.
λ (Lambda)
The rate parameter in the Poisson distribution, representing the expected number of events per unit time or unit area.
μ (Mu)
The expected number of events over a time period t, related to lambda by the formula μ = λt. In cases of events over space, it is μ = λa where a is the total number of spatial units.
Expected Value of a Poisson Distribution
The expected value of a Poisson(μ) distribution is E(X) = μ.
Variance of a Poisson Distribution
The variance of a Poisson distribution is Var(X) = μ. It is the only discrete distribution where the mean and variance are equal.
Point Estimate for Poisson
An unbiased estimator of λ is given by λ̂ = X/T, where X is the observed number of events over person-years (T).
Person-Years
A unit of time defined as 1 person being followed for 1 year.
For example, a study with 10 people that each person is followed up for 2 years has a total of 20 person-years.
Standardized Mortality Ratio (SMR)
A way to compare the mortality rate of a sample with that of the population. The formula is 100% * (observed number of deaths / expected number of deaths). An SMR > 100% implies increased risk in the sample.
One-Sample Poisson Test
A statistical test used when the underlying distribution is Poisson. It can use a critical value or p-value method.
Chi-Square Distribution (𝜒²)
A distribution that arises from squaring a standard normal distribution. If you have n independent and identically distributed (iid) variables that follow a standard normal, then the sum of their squares follows a chi-square distribution with n degrees of freedom.
Degrees of Freedom
A parameter of the chi-square distribution that reflects the amount of information or flexibility in the data. The degrees of freedom are reduced by one for each parameter that is estimated from the data.
One-Sided Confidence Interval
A confidence interval that focuses on one direction of estimation (either an upper or a lower bound) rather than a range around a point estimate. It is used when only interested in one direction, for example, whether a value is better than a standard or worse than a standard.
Reproducible Research
Research where other scientists can investigate the same research question using the same methods and achieve similar results. It is a way to improve scientific rigor and transparency.
Markdown
A plain text formatting syntax that is easy to read and write and can be converted into structural XHTML or HTML. It is used to create reproducible reports by keeping analysis code and report together.
Conditional Probability
The probability of an event (B) occurring given that another event (A) has already occurred, denoted as P(B|A).
Sensitivity
The probability of a test showing positive when the person actually has a disease, denoted as P(Test+|Disease).
Specificity
The probability of a test showing negative when the person does NOT actually have a disease, denoted as P(Test-|No Disease).
Predictive Value Positive (PV+)
The probability of actually having the disease given the test is positive, denoted as P(Disease|Test+).
Predictive Value Negative (PV-)
The probability of not having the disease given the test is negative, denoted as P(No Disease|Test-).
