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Wald or score test for treatment effect using negative binomial model

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(). With test_type = "wald" (default), the method matches the Wald test described by Mutze et al. (2019). With test_type = "score", the function fits only the null (no treatment effect) model and computes the score statistic, which evaluates all quantities under \(H_0\) and avoids the finite-sample anti-conservatism of the Wald test.

Usage

mutze_test(
  data,
  method = c("nb", "poisson"),
  test_type = c("wald", "score"),
  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.

test_type

Type of test statistic: "wald" (default) or "score". The Wald test estimates the treatment effect under the alternative and divides by its standard error. The score test fits only the null model and evaluates the derivative of the log-likelihood at \(\theta = 0\), avoiding estimation under the alternative. The score test typically has better finite-sample Type I error control and is faster because it only fits a one-parameter null model.

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. Default is 50, corresponding to \(\hat{k} < 0.02\).

mom_threshold

Lower threshold on fit$theta below which the NB ML fit is considered unreliable (extreme overdispersion). Default is 20, corresponding to \(\hat{k} > 20\).

x

An object of class mutze_test.

...

Additional arguments (currently ignored).

Value

An object of class mutze_test containing:

  • method: A string indicating the test method used.

  • estimate: log rate ratio (experimental vs control). For test_type = "score", this is a plug-in estimate.

  • se: standard error for the log rate ratio.

  • z: test statistic (Wald or score).

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

  • rate_ratio: estimated rate ratio and its confidence interval.

  • dispersion: estimated dispersion on the \(\theta = 1/k\) scale.

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

  • fallback: character label ("ml", "poisson", or "mom").

  • test_type: character label ("wald" or "score").

Invisibly returns the input object.

Details

When the maximum likelihood negative binomial fit is unreliable, the test automatically switches to one of two statistically sensible fallbacks: a Poisson 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.

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
mutze_test(cut, test_type = "score")
#> Mutze Test Results
#> ==================
#> 
#> Method:     Poisson score (fallback, near-Poisson ML) 
#> Estimate:   -0.1709
#> SE:         0.5165
#> Z:          -0.3306
#> p-value:    0.3705
#> Rate Ratio: 0.8429
#> CI (95%):  [0.3063, 2.3197]
#> Dispersion: Inf
#> 
#> Group Summary:
#>     treatment subjects events exposure
#>  Experimental       20      7 21.78820
#>       Control       20      8 20.98945