Predictions from a panel count model

Usage

# S3 method for class 'pcdfit'
predict(object, newdata, type = c("lp", "mean"), ...)

Arguments

object: A fitted pcdreg() model.
newdata: Data to predict for. Defaults to the data the model was fitted to. For type = "mean" it must also contain the variables in the pcd() response, since the prediction follows each subject's covariate trajectory; the counts themselves are ignored.
type: "lp" returns the linear predictor \(\beta' X(t)\) for each row. "mean" returns the predicted mean number of events at every fitted examination time within each subject's follow-up: \(\int_0^t \exp(\beta' X(s)) \, d\hat\Lambda(s)\) for pcdreg(), and \(\hat\mu(t) \exp(\beta' X(t))\) for pcdreg().
...: Ignored.

Value

For type = "lp", a numeric vector with one element per row of newdata. For type = "mean", a tibble with columns id, time and mean.

Details

The rate model's predicted mean is non-decreasing in \(t\) by construction, because it integrates a positive quantity. The means model's is not: it is a fitted \(\hat\mu(t)\) rescaled by a covariate value that may itself move up and down, so a predicted mean count that falls is possible and is the practical drawback of that model with time-varying covariates.

Examples

set.seed(1)
d <- sim_pcd(60, beta = c(1, -1), lambda = function(t) 8 / (1 + t))
fit <- pcdreg(pcd(id, tstart, tstop, count) ~ x1 + x2, data = d)
head(predict(fit))
#>         1         2         3         4         5         6 
#> 0.4582126 0.4582126 0.4582126 0.5172010 0.4472924 0.4472924 
head(predict(fit, type = "mean"))
#> # A tibble: 6 × 3
#>   id     time     mean
#>   <chr> <dbl>    <dbl>
#> 1 1      0.01 1.60e-45
#> 2 1      0.02 4.76e-43
#> 3 1      0.03 9.91e-41
#> 4 1      0.04 7.85e-20
#> 5 1      0.05 1.57e-19
#> 6 1      0.07 3.61e- 1