Interpolate Survival Curve for a Range of Ages — interpolate_survival

This function fits a regression model to interpolate (calculate) the probability of dying for a range of user-specified ages. The fitted model regresses the cumulative hazard rate, which is transformed from the input survival function (curve), on the corresponding age. The cumulative hazard ($H(t)$) is related to the survival function ($S(t)$) by: $$H(t) = -\log(S(t))$$ where $S(t)$ is the survival probability up to time $t$.

Usage

interpolate_survival_curve(
  survival_curve_ages,
  survival_curve,
  target_ages,
  interpolation_model = "gam",
  smr_multiplier = 1
)

Arguments

survival_curve_ages: A numeric vector representing the ages corresponding to the survival probabilities.
survival_curve: A numeric vector of mortality probabilities (the probability of dying) corresponding to `age`.
target_ages: A numeric vector of ages for which the hazard rates are to be predicted.
interpolation_model: A character string specifying the model to use for fitting the log cumulative hazard. Options are "gam" (default) for Generalized Additive Model and "spline" for spline model.
smr_multiplier: A numeric value representing the Standardized Mortality Ratio (SMR) multiplier. The SMR is used to adjust the mortality rates of the population under study compared to a standard population. An SMR of 1 (default) indicates no difference in mortality rates, while an SMR greater than 1 indicates higher mortality in the study population.

Value

A numeric vector of the interpolated survival function (curve). ages.

Examples

if (FALSE) { # \dontrun{
# Define age range and survival probabilities
model_starting_age <- NeuroblastomaPSM::l_psm_parameters$age
df_lifeTable <- NeuroblastomaPSM::df_lifeTable_Jordan
age <- df_lifeTable$`Age Group`
mortality_probs <- df_lifeTable$`Both sexes`
mortality_probs <- mortality_probs[age >= model_starting_age]
age <- age[age >= model_starting_age]

# Calculate the survival curve for the modeled cohort
survival_curve <- NeuroblastomaPSM::get_lifeTable_survival_curve(
   mortality_probs = mortality_probs
)

# Define output ages
target_ages <- seq(model_starting_age, 29, 7/365)

# Interpolate Survival Curve
v_interpolated_curve <- NeuroblastomaPSM::interpolate_survival_curve(
  survival_curve_ages = age,
  survival_curve = survival_curve,
  target_ages = target_ages
)

v_interpolated_curve

# Define output ages
target_ages2 <- seq(min(age), max(age), 7/365)

# Interpolate Survival Curve
set.seed(1)
v_interpolated_curve2 <- NeuroblastomaPSM::interpolate_survival_curve(
  survival_curve_ages = age,
  survival_curve = survival_curve,
  target_ages = target_ages2
)

v_interpolated_curve2

# Compare fitted and observed survival curves
plot(x = age, y = survival_curve, xlab = "Age", ylab = "Survival")
lines(x = target_ages2, y = v_interpolated_curve2, col = "blue")

# Interpolate Survival Curve with a SMR = 5.6
set.seed(1)
v_interpolated_curve3 <- NeuroblastomaPSM::interpolate_survival_curve(
  survival_curve_ages = age,
  survival_curve = survival_curve,
  target_ages = target_ages2,
  smr_multiplier = NeuroblastomaPSM::l_psm_parameters$smr_EFS
)

v_interpolated_curve3

# Compare fitted and observed survival curves
plot(x = age, y = survival_curve, xlab = "Age", ylab = "Survival")
lines(x = target_ages2, y = v_interpolated_curve2, col = "blue")
lines(x = target_ages2, y = v_interpolated_curve3, col = "orange")

# Interpolate Survival Curve with a SMR = 5.6 * 1.9
set.seed(1)
v_interpolated_curve4 <- NeuroblastomaPSM::interpolate_survival_curve(
  survival_curve_ages = age,
  survival_curve = survival_curve,
  target_ages = target_ages2,
  smr_multiplier = NeuroblastomaPSM::l_psm_parameters$smr_PPS
)

v_interpolated_curve4

# Compare fitted and observed survival curves
plot(x = age, y = survival_curve, xlab = "Age", ylab = "Survival")
lines(x = target_ages2, y = v_interpolated_curve2, col = "blue")
lines(x = target_ages2, y = v_interpolated_curve3, col = "orange")
lines(x = target_ages2, y = v_interpolated_curve4, col = "red")
} # }