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

Hector Warnes’ comments


         Charles Beasley and Roy Tamura wrote an inciive elaboration of "the sample sizes required to infer with reasonable certainty that some adverse medical event is caused by a drug.” By statistical method they "illustrated the sample sizes required to infer with reasonable medical certainty that some adverse medical events while possible observed during the administration of a drug is not caused by the drug" being tested. They further pointed out the temporal pattern of occurrence as a key factor in identifying an adverse medical event and undoubtedly the adverse effect might be etiologically related to the drug being tested or have other etiology. I would dare to say that one third to one half of the hundreds of adverse side effects attributed to the tested drug which are printed in the complete prospectus may not present "reasonable evidence."

         Another confounding finding in drug research is the fact that often the conclusions are published based on positive outcome and a high percentage of research findings which have negative outcome are not published. Positive outcome would imply that the p-value of < 0.05 is statistically significant difference of the probability of occurrence of the given event while P>0.05 is not significant.

         We are all aware that there is a consensus that an adverse side effect is considered very common when it occurs in more than 10% of the patient population receiving the drug; common or frequent when it occurs in less than 1%; uncommon or infrequent when occurs in 1/1000; rare when it occurs in 1/10,000; and very rare when it occurs in more than 1/10,000.

         The authors, using the Fisher Exact Test, reached the conclusion that the treatment group would have a 51% power should the events be estimated at 0.08 events with the control group and 1.67 events with the test drug. It would have 80% power if it was found 0.17 events with the control group and 3.33 with the experimental drug. It would require 7.905 patients for the treatment group to validate the results.

         It is widely known that post-marketing drug prescription may detect a higher incidence of adverse side effects not previously detected during the research studies of up to 3,000 patients with a control group or using a double-blind-cross over design. At times, the post-marketing side effect is not reported. It is possible that the adverse effect is due to drug interaction because rarely is a patient only taking one drug. It is considered that the doctor should weight the benefits versus the risks. Apparently one out of 5,000-10,000 compounds that enter preclinical testing are approved. Every year some drugs are withdrawn from the market because of frequent side effects which may cause harm to the patient.

         I recognize my limitations of the statistical methods and, like the authors, came to the conclusion that it is not an exact science which would drive us to the latest trend of a personalized medicine (tailoring pharmacotherapy to individual phenotypes)

         I found through Google a synthesis of the limitations of the conventional statistical methods written by Pooja Mehta, MD, entitled “8 Main limitations of Statistics – explained,” posted on  the “Pooja Mehta Economics Discussion website”.  According to Mehta:

  1. The statistical methods do not study the nature of phenomenon which cannot be expressed in quantitative terms. They need conversion of qualitative data into quantitative data.
  2. They do not deal with individual items. They consist of aggregates of facts or items placed in relation to each other.
  3. They do not depict the entire story of phenomenon; when phenomena do happen there may be several causes involved that cannot be expressed in terms of data.
  4. The data may have been collected by inexperienced persons or they may have been dishonest or biased.
  5. Laws are not exact, e.g., the law of inertia of large numbers and the law of statistical regularity are usually approximations.
  6. Results are true only on average. Statistics largely deal with averages and these averages may be made up of individual items radically different from each other.
  7. When several statistical methods are used the results vary with each method used. Although we use many laws and formulae in statistics, the results achieved are not final and conclusive.
  8. Statistical results are not always beyond doubt. They deal only with measurable aspects of things and, therefore, can seldom provide the complete solution to the problem. They provide a basis for a judgement but not the whole judgement.

         Of course, we all agree that the efficacy of the compound being tested and its potential harm to the patient is of the utmost significance. Adverse side effects to the point of lethality are frequently seen in hospital wards (Ernst and Grizzle 2001).

         Xiaodong Feng and Hong-Guang Xie  published an excellent survey, Applying Pharmacogenomics in Therapeutics, in which Cong Liu, Weiguo Chen and Wei Zhang pointed out: “The majority of the Adverse Drug Reactions are due to genetic polymorphism of the enzymes which metabolize the drugs and may be as well due to polymorphism of the transporter of the psychotropic  compound: e.g., SERT for serotonin, HLA-B 1502 for carbamazepine; CYP2D6 for venlafaxine, CYP2C9- 19 y D6, etc. Drug toxicity and positive drug response are often related to the Cytochrome P450.” Human error, age, ethnicity, weight, co-morbidity, diet, gender and polypharmacy must also be taken into account” (Feng and Xie 2016; Liu, Chen and Zhuang 2016).

         The question of responders and non-responders to psychotropic drugs has also raised controversies.



Ernst FR, Grizzle AJ. Drug-related morbidity and mortality: Updating the cost-of illness model. J Am Pharm Assoc 2001; 41: 192-9.

Feng  X and Xie H-G. Applying Pharmacogenomicss in Therapeutics. Boca Raton: CRC Press (Taylor  and Francis Group); 2016.

Liu C, Chen W, Zhang W. Essential pharmacogenomic biomarkers in clinical practice. In: Feng X, and Xie H-G, editors.  Applying Pharmacogenomics in Therapeutics. Boca Raton: CRC Press (Taylor and Francis Group); 2016.


July 11, 2019