Calculations - Evidencio
Evidencio Calculations

We want to be fully transparent regarding the underlying calculations for the standard algorithm types that Evidencio supports. This page lists our standard algorithm types and the associated calculations

Linear Regression Algorithms

Linear regression algorithms are used to predict continuous outcomes. The prediction is estimated by:
predicted result `P = \beta_0 + X\beta`

Logistic Regression Algorithms:

Logistic regression algorithms are used to predict probabilities. The prediction is estimated by:
predicted probability `P = e^(X\beta)/(1+e^(X\beta))`

Cox proportional-hazards regression

Cox proportional-hazards algorithms are used to predict the probability `S(t)` that the patient will be free from an event (e.g. biochemical recurrence) at some time point (e.g. 5 years after surgery). For survival analysis the prediction is estimated by: `S(t) = S_0(t)^exp(X\beta)`

Custom calculation

Users can define Custom calculations based on custom mathematical formulas expressed in terms of algorithm variables. Evidencio supports both single and conditional custom formulas. The custom formula(s) used by an Evidencio algorithm can always be viewed in the details section of the respective algorithm, so that algorithm users can exactly identify the underlying algorithm logic.
Example of conditional formulas:

R-Script Algorithms

Evidencio supports the use of R-Script code to define the calculation logic for prediction algorithms and calculators. R-Script algorithms may contain complex and nested functions as long as they produce a single value outcome.

Parameter transformations

Evidencio lets you define variable/parameter transformations for each continuous algorithm variable, for instance to accommodate non linear behaviour. We support both simple transformations as well as conditional (range based) transformations (e.g. cubic splines) to tackle a broad spectrum of non-linear behaviour.

Confidence interval data

You can attribute confidence interval data to your algorithms on Evidencio. Your confidence interval data can be specified in terms of a bootstrap data-set or as covariance matrix. You can simply copy paste your bootstrap or matrix data from e.g. excel or another data-sheet.

Calculation Legend
`\beta_0` Intercept term, denoted by "Intercept"
`\beta_(varN)` Coefficient estimate, associated with a covariate/variable
`\gamma` Scaling parameter in survival regression algorithms, denoted by "Scaling Parameter"
`X\beta` Algorithm linear predictor, estimated by summation of the intercept term and all `\beta` values multiplied by that variable. E.g.: `\beta_0 + \beta_(var1) * var1 + \beta_(var2) * var2 + \beta_(varN) * varN`
`S_0(t)` The baseline survival function, the survival proportion when all covariates are equal to zero (`X\beta = 0`).
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