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Wald test for treatment effect using negative binomial model (Mutze et al.)

Source: R/mutze_test.R
mutze_test.Rd

Fits a negative binomial (or Poisson) log-rate model to the aggregated subject-level data produced by cut_data_by_date(). The method matches the Wald test described by Mutze et al. (2019) for comparing treatment arms with recurrent event outcomes. When the maximum likelihood negative binomial fit is unreliable, the test automatically switches to one of two statistically sensible fallbacks: a Poisson Wald test when the data are essentially Poisson, or a method-of-moments (MoM) variance estimate plugged into the same negative binomial information formula when the data are extremely overdispersed or the ML fit fails to converge. The latter avoids the anti-conservative behaviour of a blind Poisson fallback under genuine overdispersion.

Usage

mutze_test(
  data,
  method = c("nb", "poisson"),
  conf_level = 0.95,
  sided = 1,
  poisson_threshold = 50,
  mom_threshold = 20
)

# S3 method for class 'mutze_test'
print(x, ...)

Arguments

data

A data frame with at least the columns treatment, events, and tte (follow-up time). Typically output from cut_data_by_date().

method

Type of model to fit: "nb" (default) uses a negative binomial GLM via MASS::glm.nb(), "poisson" fits a Poisson GLM.

conf_level

Confidence level for the rate ratio interval. Default 0.95.

sided

Number of sides for the test: 1 (default) or 2.

poisson_threshold

Upper threshold (in units of fit$theta, the MASS::glm.nb() shape parameter \(\theta_{\text{NB}} = 1/k\)) above which the data are treated as essentially Poisson and the function falls back to a Poisson Wald test. Default is 50, corresponding to \(\hat{k} < 0.02\), by which point NB and Poisson Wald standard errors are numerically indistinguishable at typical trial sample sizes.

mom_threshold

Lower threshold on fit$theta below which the NB ML fit is considered unreliable (extreme overdispersion). When triggered, or when glm.nb() fails to converge, the function falls back to a method-of-moments NB Wald test: rates and dispersion are re-estimated via estimate_nb_mom() and the Wald variance is computed from the Fisher information formula \(\mathcal{I} = 1/(1/W_1 + 1/W_2)\) with \(W_g = \sum_i \mu_{g,i}/(1 + \hat{k}\mu_{g,i})\). Default is 20, corresponding to \(\hat{k} > 20\). This avoids the anti-conservative variance of a Poisson fallback when the data are truly overdispersed.

x

An object of class mutze_test.

...

Additional arguments (currently ignored).

Value

An object of class mutze_test containing the fitted model summary with elements:

  • method: A string indicating the test method used.

  • estimate: log rate ratio (experimental vs control).

  • se: standard error for the log rate ratio.

  • z: Wald statistic.

  • p_value: one-sided or two-sided p-value.

  • rate_ratio: estimated rate ratio and its confidence interval.

  • dispersion: estimated dispersion. For consistency this is reported on the MASS::glm.nb() scale (\(\theta_{\text{NB}} = 1/k\)), regardless of whether ML, Poisson fallback, or MoM fallback was used. Inf indicates Poisson (\(k=0\)).

  • group_summary: observed subjects/events/exposure per treatment.

  • fallback: character label describing which fit path was used ("ml", "poisson", or "mom").

Invisibly returns the input object.

Methods (by generic)

  • print(mutze_test): Print method for mutze_test objects.

Examples

enroll_rate <- data.frame(rate = 20 / (5 / 12), duration = 5 / 12)
fail_rate <- data.frame(treatment = c("Control", "Experimental"), rate = c(0.5, 0.3))
dropout_rate <- data.frame(
  treatment = c("Control", "Experimental"),
  rate = c(0.1, 0.05), duration = c(100, 100)
)
sim <- nb_sim(enroll_rate, fail_rate, dropout_rate, max_followup = 2, n = 40)
cut <- cut_data_by_date(sim, cut_date = 1.5)
mutze_test(cut)
#> Mutze Test Results
#> ==================
#> 
#> Method:     Poisson Wald (fallback, near-Poisson ML) 
#> Estimate:   -0.1709
#> SE:         0.5175
#> Z:          -0.3302
#> p-value:    0.3706
#> Rate Ratio: 0.8429
#> CI (95%):  [0.3057, 2.3245]
#> Dispersion: Inf
#> 
#> Group Summary:
#>     treatment subjects events exposure
#>  Experimental       20      7 21.78820
#>       Control       20      8 20.98945