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Estimating equation for pooled logistic regression

Source: R/ee-survival.R
ee_plogit.Rd

Returns a p-by-n matrix of estimating equation contributions for pooled logistic regression with discrete-time survival data. This implementation does not require creation of a long data set.

Usage

ee_plogit(
  theta,
  X,
  time,
  event,
  S = NULL,
  unique_times = NULL,
  weights = NULL,
  offset = NULL
)

Arguments

theta

Numeric vector of length b + p_s, where b is the number of covariate columns in X. When S is supplied, p_s is ncol(S); when S = NULL, p_s is K, the number of unique event times.

X

Numeric n-by-b design matrix for baseline covariates.

time

Numeric vector of n observed (possibly censored) times.

event

Numeric vector of n event indicators (1 = event, 0 = censored).

S

Optional time design matrix with K rows (one per time step) and p_s columns. Default NULL uses disjoint indicators for unique event times. When supplied, time is modeled over the unit-time intervals from one to the maximum observed time, so K has to be the number of those intervals.

unique_times

Optional numeric vector of unique event times. Default NULL. When S = NULL it names the time steps the disjoint indicators are built for. When S is supplied the grid is the unit-time intervals up to the maximum observed time, and that grid is also the binning of the person-periods the equation is solved on, so unique_times may only agree with it: a value equal to it is accepted and changes nothing, and any other value is an error rather than the silently ignored argument Python Delicatessen documents. plogit_predict() validates it the same way.

weights

Optional numeric vector of n weights, or an n-by-K matrix of time-varying weights with one column per time interval (K must equal the number of unit-time intervals). Default NULL.

offset

Optional numeric vector of n offsets. Default NULL.

Value

A (b + p_s)-by-n matrix.

Examples

# Bladder tumor recurrence, comparing the novel treatment to placebo while
# adjusting for the number and size of the initial tumors.
W <- cbind(
  novel = collett_bladder$treat - 1,
  as.matrix(collett_bladder[, c("init", "size")])
)

# Time is modeled with disjoint indicators, one per distinct event time,
# which ee_plogit builds by default.
k <- length(unique(collett_bladder$time[collett_bladder$delta == 1]))

psi <- function(theta) {
  ee_plogit(
    theta,
    X = W,
    time = collett_bladder$time,
    event = collett_bladder$delta
  )
}
m <- m_estimate(
  stacked_equations = psi,
  init = c(rep(0, ncol(W)), -4, rep(0, k - 1))
)

# The first three parameters are the covariate coefficients, which
# approximate log hazard ratios. The rest describe the baseline hazard over
# time: the first of them is the log-odds of an event at the earliest event
# time, and each one after it is that time's departure from it.
summary(m, subset = 1:3)
#> ── MEstimator Results ──────────────────────────────────────────────────────────
#> Observations: 86
#> Parameters: 24
#> 
#>           Estimate    Std.Err    Z-score    95% LCL    95% UCL    P-value    S-value
#> theta_1    -0.5479     0.3298    -1.6613    -1.1944     0.0985     0.0967     3.3710
#> theta_2     0.2598     0.0824     3.1535     0.0983     0.4213    0.00161     9.2757
#> theta_3     0.0735     0.0931     0.7898    -0.1089     0.2560       0.43     1.2188