Charles M. Beasley, Jr., and Roy Tamura: What We Know and Do Not Know by Conventional Statistical Standards AboutWhether a Drug Does or Does Not Cause a Specific Side Effect (Adverse Drug Reaction)

2. Introductory comments


            For several years, Charles Beasley has had an interest in what RCTs that support approval of a potential new treatment tell us, with a robust degree of scientific certainty (“prove”–see Part 1), about possible ADRs associated with treatment and what possible ADRs are not associated with treatment? Current designs and practical limitations on the size and length of time over which an RCT can be conducted influence what an RCT can “prove.” With what incidences must an AE occurin association with an investigational treatment and control treatment to “prove” that the AE is an ADR for the investigational treatment under consideration?  What size would studies need to be conducted to “prove” that a rare AE is an ADR? The sample size requirements for deciding what distinguishes ADRs from among AEs and “proving” either the presence or absence of any given potential ADRis the essence of what we are discussing.

            The hypothetical case on which we focus is that of a highly uncommon ADR with an incidence of 1 per 1,000 persons treated (0.001 or 0.1%), the low boundary of “uncommon” events. If the incidence is1 in 1,001 subjects, the event would be “rare”. However, just because such an ADR is highly uncommon, this does not mean that it will not be experienced by a considerable number of individuals during the commercial life of a widely prescribed drug for disorders common in the general population. As Beasley said in his earlier response to Blackwell (2018), if some 20,000,000 individual sare treated with adrug (and that number might be higher by several multiples), the ADR with an incidence of 1 per 1,000 would occur in 20,000 persons. The successful drug will become generic and more people would be treated with more persons experiencing the ADR.

            The majority of what we say below about complexities deals with simple incidence (events/person) for the 0.1% of individuals who experience the hypothetical ADR. However, the distribution of time to experience the ADR can have a substantial impact on the extent to which a specific study design, sample size, and analysis can influence the “proof” of the presence or absence of an ADR.Even rare ADRs, with enough individuals treated, might show three patterns of distribution of time to occurrence (temporal patterns of occurrence):

1)      early in treatment (acute toxicity) – a curve of the cumulative incidence over time would rise rapidly and then taper off (sigmoidal / Gompertz function pattern);

2)      later in treatment – with increasing incidence in later epochs of time (delayed toxicity with increasing exposure [can be due to drug exposure accumulation or a lag between acute exposure that is toxic and the manifestation of the toxicity,e.g., myocardial infarction and ischemic stroke due to acceleration of atherosclerosis])– a curve of the cumulative incidence over time would reflect an initiallinear rise followed by exponential rise after some lag time;and

3)      random occurrence with equal distribution across time of treatment – a curve of the cumulative incidence over time would be linear with a slope dependent on incidence during the period of observation.

            The rate of occurrence (event/person-time [e.g., numberof ADRs / 100-patient-years of treatment]) and the temporal pattern ofoccurrence are two of the multiple factors that complicate “proving” the presence or absence of an ADR. These two related factors would be important considerations in discussing limitations of attempts at such “proof”. In Installments 4 and 5 we discuss sample sizes required for “proving” that an observed AE is or is not an ADR.  These sample sizes for “proving” that an AE is an ADR apply best to temporal pattern of occurrence #1 above (especially if there is a short lag time between initiation of treatment and first occurrence of the ADR) for the AE of interest. An ADR with temporal pattern of occurrence of #2 above would generally result in the requirement for longer periods of observation (a longer RCT) than temporal pattern #1 and therefore require additional subjects to begin a definitive RCT in order to account for subjects discontinuing the RCT/observation prior to the planned end of observation and the more frequent occurrence of the ADR. A relative infrequent or rare ADR, occurring with temporal pattern #3 would also require a longer period of observation in a definitive RCT. Therefore, the sample sizes discussed in Installment 4 that focus on “proving” that an AE is an ADR should be considered conservative estimates for ADRs that would only be observed late in treatment, with an accelerating rate of occurrence after some relatively lengthy period of observation or in a random pattern over time but very infrequently overall. Additionally, any pattern of occurrence that is a change as a function of time might require special statistical techniques (beyond comparing incidences or assessing the ratio of incidences) to “prove” presence or absence of the ADR. Therefore, RCTs required to address the complexity of changes in the rate of occurrence of an ADR over time are likely to requirelarger numbers of subjects beginning such anRCT (because humans ubjects discontinue participation). There is one final caveat regarding patterns over time: as events become rarer, they generally appear to be randomly distributed over time, and there are never a sufficient number of cases observed to discern a temporal pattern within RCTs of practical size, even if a pattern exists. Rare AE occurrences, of which the majority are ADR occurrences,  will generally appear with temporal pattern #3 unless sufficiently large number of subjects are observed to discern temporal pattern #2 when that is the pattern of occurrence.


December 27, 2018