Improved confidence intervals for a difference of two cause‐specific cumulative incidence functions estimated in the presence of competing risks and random censoring

Abstract

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Cardiovascular safety of mometasone/indacaterol and mometasone/indacaterol/glycopyrronium once-daily fixed-dose combinations in asthma: pooled analysis of phase 3 trials

“…Treatment effect estimates were defined as differences in incidence proportions (treatment minus control) × 100%. Confidence intervals (CIs) for the risk differences were constructed based on the method of Agresti and Caffo [19], which results in valid inference with large or small event counts [19,20].…”

Confidence intervals for exposure‐adjusted rate differences in randomized trials

“…The Agresti-Caffo CI also involves addition of two "pseudo-subjects" to the sample size in each arm (in the beta-binomial model, one pseudo-event and two pseudosubjects per arm result in a Bayesian shrinkage of each estimated proportion to 0.5 and away from the nearest boundary of its parameter space). 5,18,58 There is no equivalent of "pseudo-subjects" in the X M interval because the rate parameter space has no upper bound (shrinkage is always away from the lower bound of 0) and no such "pseudo-subjects" naturally arise in the gamma-Poisson model with a non-informative exponential prior (Appendix S1). Intuitively, addition of any "pseudo-subjects" to person-time would not be appropriate because unlike the sample size in the beta-binomial model, the value of person-time depends on the time units.…”

“…Both intervals involve addition of a “pseudo‐event” to each comparison group for calculation of the CI, although in the case of the Agresti‐Caffo interval this correction can be justified based on the beta‐binomial model with a non‐informative uniform prior, 18 while in the case of the X M it is based on the gamma‐Poisson model with a non‐informative exponential prior (Appendix S1). The Agresti‐Caffo CI also involves addition of two “pseudo‐subjects” to the sample size in each arm (in the beta‐binomial model, one pseudo‐event and two pseudo‐subjects per arm result in a Bayesian shrinkage of each estimated proportion to 0.5 and away from the nearest boundary of its parameter space) 5,18,58 . There is no equivalent of “pseudo‐subjects” in the X M interval because the rate parameter space has no upper bound (shrinkage is always away from the lower bound of 0) and no such “pseudo‐subjects” naturally arise in the gamma‐Poisson model with a non‐informative exponential prior (Appendix S1).…”

“…Exposure‐adjusted rates can be used for comparison of adverse event frequencies in these settings, but interpretation of such comparisons depends on the constant rate assumption. When the design effect on the exposure time is absent, the exposure‐adjusted rate differences and ratios can have a causal interpretation even when the rates do not remain constant over time 5 . In fact, we may notice from the last equality in Equation (1) that each observed rate is just a ratio of the mean event count to the mean exposure time at‐risk.…”

“…When the design effect on the exposure time is absent, the exposure-adjusted rate differences and ratios can have a causal interpretation even when the rates do not remain constant over time. 5 In fact, we may notice from the last equality in Equation (1) that each observed rate is just a ratio of the mean event count to the mean exposure time at-risk. A change in either of these quantities on treatment versus control in the absence of a design effect on the exposure time can represent the treatment effect on the study event and/or the competing events (further details are provided in the Methods section).…”