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The use of log probabilities improves numerical stability, when the probabilities are very small, because of the way in which computers approximate real numbers. [1] Simplicity. Many probability distributions have an exponential form. Taking the log of these distributions eliminates the exponential function, unwrapping the exponent.
An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of event A taking place in the presence of B, and the odds of A in the absence of B. Due to symmetry, odds ratio reciprocally calculates the ratio of the odds of B occurring in the presence of A, and the odds of B in the absence of A.
If p is a probability, then p/(1 − p) is the corresponding odds; the logit of the probability is the logarithm of the odds, i.e.: = = = = (). The base of the logarithm function used is of little importance in the present article, as long as it is greater than 1, but the natural logarithm with base e is the one most often used.
In practice the odds ratio is commonly used for case-control studies, as the relative risk cannot be estimated. [1] In fact, the odds ratio has much more common use in statistics, since logistic regression, often associated with clinical trials, works with the log of the odds ratio, not relative risk. Because the (natural log of the) odds of a ...
The log diagnostic odds ratio can also be used to study the trade-off between sensitivity and specificity [5] [6] by expressing the log diagnostic odds ratio in terms of the logit of the true positive rate (sensitivity) and false positive rate (1 − specificity), and by additionally constructing a measure, :
In statistics, the logistic model (or logit model) is a statistical model that models the log-odds of an event as a linear combination of one or more independent variables. In regression analysis, logistic regression [1] (or logit regression) estimates the parameters of a logistic model (the coefficients in the linear or non linear combinations).
In this case the odds ratio for allele T is A:B (meaning 'A to B', in standard odds terminology) divided by X:Y, which in mathematical notation is simply (A/B)/(X/Y). When the allele frequency in the case group is much higher than in the control group, the odds ratio is higher than 1, and vice versa for lower allele frequency.
A Poisson compounded with Log(p)-distributed random variables has a negative binomial distribution. In other words, if N is a random variable with a Poisson distribution , and X i , i = 1, 2, 3, ... is an infinite sequence of independent identically distributed random variables each having a Log( p ) distribution, then