risk_mod {riskscores}

Fit an Integer Risk Score Model

Description

Fits an optimized integer risk score model using a cyclical coordinate descent algorithm. Returns an object of class "risk_mod".

Usage

risk_mod(
  X,
  y,
  gamma = NULL,
  beta = NULL,
  weights = NULL,
  lambda0 = 0,
  a = -10,
  b = 10,
  max_iters = 100,
  tol = 1e-05,
  shuffle = TRUE,
  seed = NULL
)

Arguments

X

Input covariate matrix with dimension n \times p; every row is an observation.

y

Numeric vector for the (binomial) response variable.

gamma

Starting value to rescale coefficients for prediction (optional).

beta

Starting numeric vector with p coefficients. Default starting coefficients are rounded coefficients from a logistic regression model.

weights

Numeric vector of length n with weights for each observation. Unless otherwise specified, default will give equal weight to each observation.

lambda0

Penalty coefficient for L0 term (default: 0). See cv_risk_mod() for lambda0 tuning.

a

Integer lower bound for coefficients (default: -10).

b

Integer upper bound for coefficients (default: 10).

max_iters

Maximum number of iterations (default: 100).

tol

Tolerance for convergence (default: 1e-5).

shuffle

Whether order of coefficients is shuffled during coordinate descent (default: TRUE).

seed

An integer that is used as argument by set.seed() for offsetting the random number generator. Default is to not set a particular randomization seed.

Details

This function uses a cyclical coordinate descent algorithm to solve the following optimization problem.

\min_{\alpha,\beta} \quad \frac{1}{n} \sum_{i=1}^{n} (\gamma y_i x_i^T \beta - log(1 + exp(\gamma x_i^T \beta))) + \lambda_0 \sum_{j=1}^{p} 1(\beta_{j} \neq 0)

l \le \beta_j \le u \; \; \; \forall j = 1,2,...,p

\beta_j \in \mathbb{Z} \; \; \; \forall j = 1,2,...,p

\beta_0, \gamma \in \mathbb{R}

These constraints ensure that the model will be sparse and include only integer coefficients.

Value

An object of class "risk_mod" with the following attributes:

gamma

Final scalar value.

beta

Vector of integer coefficients.

glm_mod

Logistic regression object of class "glm" (see stats::glm).

X

Input covariate matrix.

y

Input response vector.

weights

Input weights.

lambda0

Imput lambda0 value.

model_card

Dataframe displaying the nonzero integer coefficients (i.e. "points") of the risk score model.

score_map

Dataframe containing a column of possible scores and a column with each score's associated risk probability.

Examples

y <- breastcancer[[1]]
X <- as.matrix(breastcancer[,2:ncol(breastcancer)])

mod1 <- risk_mod(X, y)
mod1$model_card

mod2 <- risk_mod(X, y, lambda0 = 0.01)
mod2$model_card

mod3 <- risk_mod(X, y, lambda0 = 0.01, a = -5, b = 5)
mod3$model_card