Calculate blinded statistical information

Estimates the blinded dispersion \(k\) and event rate \(\lambda\) from pooled (blinded) interim data and calculates the observed statistical information \(\mathcal{I}\) for the log rate ratio. The estimation follows the approach of Friede & Schmidli (2010): a single negative binomial model is fit to the pooled data, then the estimated overall rate is split into group-specific rates using the planned rate ratio.

Usage

calculate_blinded_info(
  data,
  ratio = 1,
  lambda1_planning,
  lambda2_planning,
  event_gap = NULL
)

Arguments

data

A data frame containing the blinded interim data. Must include columns events (number of events) and tte (total exposure/follow-up time per subject).

ratio

Planned allocation ratio \(r = n_2/n_1\). Default is 1.

lambda1_planning

Planned event rate \(\lambda_1\) for the control group (used to determine the rate split).

lambda2_planning

Planned event rate \(\lambda_2\) for the experimental group (used to determine the rate split).

event_gap

Optional gap duration (numeric). If provided, planning rates are adjusted to effective rates \(\lambda_{\mathrm{eff}} = \lambda / (1 + \lambda \cdot \mathrm{gap})\) before computing the rate split.

Value

A list containing:

blinded_info

Estimated statistical information \(\mathcal{I}\).

dispersion_blinded

Estimated dispersion parameter \(k\).

lambda_blinded

Estimated overall (pooled) event rate.

lambda1_adjusted

Re-estimated control rate \(\hat\lambda_1\).

lambda2_adjusted

Re-estimated experimental rate \(\hat\lambda_2\).

fallback

Character label describing which estimator was used ("ml" or "mom").

Details

If the ML negative binomial fit fails to converge or produces an unreliable shape estimate, the function falls back to method-of-moments (MoM) estimation via estimate_nb_mom() rather than silently assuming \(k = 0\). This avoids the anti-conservative behaviour that would result from treating overdispersed data as Poisson.

The statistical information is computed as: $$\mathcal{I} = \frac{1}{1/W_1 + 1/W_2}$$ where \(W_g = p_g \sum_i \mu_{g,i} / (1 + k\,\mu_{g,i})\) and \(\mu_{g,i} = \lambda_g t_i\) is the expected count for subject \(i\) if they belonged to group \(g\).

References

Friede, T., & Schmidli, H. (2010). Blinded sample size reestimation with negative binomial counts in superiority and non-inferiority trials. Methods of Information in Medicine, 49(06), 618–624. doi:10.3414/ME09-02-0060

See also

blinded_ssr() for blinded sample size reestimation; sample_size_nbinom() for the underlying sample size formula.

Examples

interim <- data.frame(events = c(1, 2, 1, 3), tte = c(0.8, 1.0, 1.2, 0.9))
calculate_blinded_info(
  interim,
  ratio = 1,
  lambda1_planning = 0.5,
  lambda2_planning = 0.3
)
#> $blinded_info
#> [1] 1.640582
#> 
#> $dispersion_blinded
#> [1] 1.617394e-05
#> 
#> $lambda_blinded
#> (Intercept) 
#>    1.794874 
#> 
#> $lambda1_adjusted
#> (Intercept) 
#>    2.243592 
#> 
#> $lambda2_adjusted
#> (Intercept) 
#>    1.346155 
#> 
#> $fallback
#> [1] "ml"
#>