Reference-based MI for Negative Binomial discrete data – SAS macros

Updated 22 January 2020 and update corrected 6 February 2020

Quick summary

Statistical analyses of recurrent event data have typically been based on the missing at random assumption (MAR) along with constant event rate. These treat the number of events as having a Negative Binomial distribution with an offset term which is the log of the length of time observed. One implication of this is that, if data are collected only when patients are on their randomized treatment, the resulting de jure estimator of treatment effect corresponds to the situation in which the patients adhere to this regime throughout the study. For confirmatory analysis of clinical trials, analyses are required that investigate alternative de facto estimands that depart from this assumption.

The macro described in this section parallels those available elsewhere in this section for continuous data but is based on the assumption of a Gamma-Poisson process underlying the classic Negative Binomial analysis. A detailed description of the methodology is presented in Keene, O.N., Roger, J.H., Hartley, B.F., and Kenward, M.G. (2014). Missing data sensitivity analysis for recurrent event data using controlled imputation. Pharmaceutical Statistics, 13, 4, 258-264. This macro implements the methods described there.


As implemented here the approach assumes that the event rate is constant across time. What it does do is allow for frailty in the event rate across patients. To move away from the assumption of constant event rate one might
a) Extend this approach by breaking up the time period into a series of periods with separate constant rates.
b) Follow a more general time-to-event approach as described by Akacha et al (2015).


List of files/folders that can be downloaded NegBI_PMI_20200206.
1) NegBin_PMI29.SAS: The file containing the macro itself. See the header of this file for details of usage.
2) Demo_NegBinMI_1.SAS: A SAS program file running an example as described by Roger & Akacha at the PSI 2014 conference.
3) Demo_NegBinMI_1.MHT: The output from running this demonstration file.
4) Demo_NegBinMI_1.LOG: The log file from running this demonstration file.
5) PSI2014_6A_Roger_Akacha.pdf: The slides from the PSI meeting which describe the example and outline the two approaches and their connection.

This page was written by James Roger ( ).

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