Wayne Nelson cumulative hazard estimator with lognormal confidence limits

Compute the Nelson-Aalen cumulative hazard estimate with lognormal confidence limits. Supports weighted events for severity-adjusted analyses of repeated/recurrent events. This is the R equivalent of the SAS nelsonl.sas macro.

Usage

hzr_nelson(time, event, weight = NULL, conf_level = 0.95)

# S3 method for class 'hzr_nelson'
print(x, digits = 4, ...)

Arguments

time

Numeric vector of follow-up times.

event

Numeric event indicator (1 = event, 0 = censored).

weight

Optional numeric vector of event weights (default 1). Weights are applied only to events (censored observations contribute zero weight). Use for severity-weighted repeated events.

conf_level

Confidence level for the interval (default 0.95).

x

An hzr_nelson object.

digits

Number of decimal places for formatting.

...

Additional arguments (ignored).

Value

A data frame with one row per unique event time and columns:

time

Event time.

n_risk

Number at risk.

n_event

Number of events at this time.

weight_sum

Sum of event weights at this time.

cumhaz

Nelson cumulative hazard estimate.

std_err

Standard error.

cl_lower

Lower lognormal confidence limit.

cl_upper

Upper lognormal confidence limit.

hazard

Interval hazard rate.

cum_events

Cumulative (weighted) event count.

Details

Unlike survival::survfit() which uses the Breslow estimator with Greenwood variance, this function uses the Wayne Nelson estimator with lognormal confidence limits that are always non-negative.

See also

hzr_kaplan() for survival estimation.

Examples

data(cabgkul)
nel <- hzr_nelson(cabgkul$int_dead, cabgkul$dead)
head(nel)
#> Nelson cumulative hazard estimate with lognormal CL
#> Events: 69  | Time points: 6 
#> 
#>     time n_risk n_event weight_sum cumhaz std_err cl_lower cl_upper hazard
#>  0.03285   5880      39         39 0.0066   2e-04   0.0063   0.0070 0.2019
#>  0.06571   5841       9          9 0.0082   2e-04   0.0077   0.0087 0.0469
#>  0.09856   5832       3          3 0.0087   3e-04   0.0081   0.0093 0.0157
#>  0.13142   5829       7          7 0.0099   3e-04   0.0092   0.0106 0.0365
#>  0.16427   5822       9          9 0.0114   4e-04   0.0107   0.0122 0.0471
#>  0.19713   5813       2          2 0.0118   4e-04   0.0110   0.0126 0.0105
#>  cum_events
#>          39
#>          48
#>          51
#>          58
#>          67
#>          69