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Predict the standard error from a prediction formula using the delta method

Source: R/deltamethod_pred_function.R
deltamethod_pred_function.Rd

Constructs a prediction function that computes model predictions, their standard errors and Wald confidence interval using the delta method for a user-specified prediction formula.

Usage

deltamethod_pred_function(
  prediction_str,
  coefs,
  coef_cov,
  additional_coefs = character(),
  fixed_vars = numeric(),
  logit = FALSE
)

Arguments

prediction_str

Character. A string specifying the prediction formula, which must contain one occurrence of "LP" to be replaced by the linear predictor constructed from the coefficients and covariate values.

coefs

Named numeric vector. The estimated coefficients from the fitted model. The names must correspond to the covariate names used in the model.

coef_cov

Square numeric matrix. The covariance matrix of the estimated coefficients in coefs. The row and column names must match the names of coefs.

additional_coefs

Character vector. Names of coefficients in coefs that are not part of the linear predictor but are required in the prediction formula (default is an empty character vector). An example is the estimated scale from a parametric survival model.

fixed_vars

Named numeric vector. Fixed values for variables used in the prediction formula but not present in the new data (default is an empty numeric vector).

logit

Logical. TRUE, the delta method is used on the logit scale. This ensures CIs are between 0 and 1 (default is TRUE).

Value

A function(df, z = 1.96) that takes a data frame of covariates df and returns a data frame with columns for the prediction prediction, lower lower and upper upper Wald confidence intervals, and standard error se. The function can also take an optional argument z for the z-score used in confidence interval calculation (default is 1.96 for 95% confidence intervals).

Details

This function is intended for use with fitted regression models, including those for survival analysis, and allows flexible specification of the linear predictor, additional coefficients, and fixed covariate values. The resulting function can be applied to new data to obtain predictions, delta method-based standard errors and confidence intervals.

This function is used internally in the package by deltamethod_from_model().

For a prediction function \(g(\theta)\), the standard error is approximated as \[\sqrt{\nabla g(\theta)^\top \Sigma \nabla g(\theta)}\] where \(\Sigma\) is the covariance matrix of the estimated coefficients.

The input prediction_str must contain one occurrence of "LP", which will be replaced by the linear predictor constructed from the provided coefficients and covariate values.

With logit=TRUE the confidence intervals can be calculated on a logit scale, see IPCWJK for more information.

Examples

coefs <- c("(Intercept)" = 0.5, "age" = 0.1, "sex" = -0.2)
coef_cov <- diag(c(0.01, 0.0025, 0.0025))
rownames(coef_cov) <- colnames(coef_cov) <- names(coefs)
pred_fun <- deltamethod_pred_function(
  prediction_str = "1 / (1 + exp(-(LP)))",
  coefs = coefs,
  coef_cov = coef_cov
)
newdata <- data.frame(age = c(50, 60), sex = c(1, 0))
pred_fun(newdata)
#>   prediction     lower    upper          se
#> 1  0.9950332 0.9707925 1.019274 0.012367680
#> 2  0.9984988 0.9896802 1.007317 0.004499284