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)Overview

Charles M. Beasley’s response to  Barry Blackwell’s response to Charles Beasley’s reply to Edward Shorter’s comment on his (Beasley’s)  Introductory Comments


        First, I thank Barry Blackwell for accepting the suggestion of Ned Shorter and Tom Ban that he provide a response to my reply to Edward (Ned) Shorter’s comment. Tom and INHN have received fewer than expected comments on the e-book by Beasley and Tamura (Beasley and Tamura 2019).  Writing a comment such as Barry’s requires significant effort and, again, I want to thank Barry for expending the effort.

        Now, it might be useful to those that read this reply to review the evolution of interchanges that have led up to what I am writing here.  Barry wrote his “Corporate Corruption in the Psychopharmaceutical Industry” (Blackwell 2016) and a subsequent revised version (Blackwell 2017).  Tom Ban suggested that I write a commentary regarding this work by Barry, which I did (Beasley 2017).  Barry and I continue to exchange comments and replies regarding his original posting concerning corporate corruption.

        As part of this progressive interchange with Barry (Beasley 2018), I included the sample sizes resulting from several sample size calculations, based on the sample sizes required for a study with 80% power. The hypothetical study would definitively address the question as to whether an adverse event (AE) that is observed rarely to very infrequently is an adverse drug reaction (ADR) or a coincidental, background AE not caused by the drug being studied.  These sample size calculations considered the situations where the background incidence of a non-drug-related AE is virtually 0 and the background incidence of a non-drug-related AE  is relatively high compared to the incidence of the same medical event that is an ADR.

        Having written this short piece regarding sample sizes, after discussion with Tom Ban, I decided to write a longer piece (with the collaboration of my statistical colleague, Roy Tamura). The intent of this longer work was the explanation of the limitations on definitive assessment as to whether any given AE is or is not (two very different questions that cannot be addressed properly by the same statistical methods) an ADR.  This work appeared as a series of nine postings (outline plus eight separate sections) in INHN with a collated version posted on November 21, 2019 (Beasley and Tamura 2019).  A postscript was posted as well (Beasley 2019b).  For me, there were two stimuli for the writing of this longer work.  First, for transparent full disclosure, I wanted to make it clear that the sample sizes based on 80% power in the posting 2018 (Beasley 2018) responding to Barry were larger than would be necessary to achieve a statistically significant finding (“proving” a given AE to be an ADR) if the designer of the hypothetical study estimated perfectly or underestimated the incidence of the medical event that would be observed with the experimental drug and did not overestimate this incidence with the control treatment.  With perfect estimates of the observed incidences, sample sizes that result in a study of only ~50-51% power will lead to significant findings based on the conventional definition of significance (p≤0.05).

        The second stimulus was that the matters discussed had been interests of mine during most of my career at Eli Lilly and writing the series of postings allowed me to formalize my thinking and share my thoughts on concepts I believe to be important for medical professionals and other relevant parties, i.e., legislators, plaintiffs and defense attorneys involved in product liability litigation, the public in general, who will have occasion to receive a prescription medication.

        The series of postings has generated several comments to which I have written responses, with some posted and some not yet posted.  Ned offered a comment (Shorter 2019), wondering if I might comment on Lilly’s work on understanding the relationship between olanzapine and diabetes mellitus.  The exact contents of Ned’s comment are important and I quote them in entirety below:

        “Readers of this website will look forward with special interest to the comments of Charles Beasley, in particular on the issue of side effects and their measurement, given that in his long tenure at Eli Lilly he often confronted these issues on an almost daily basis.  In the late 1990s there was an intense in-house discussion about possible hyperglycaemia, weight gain and diabetes associated with olanzapine and much of this correspondence has, in connection with discovery in litigation, now become part of the public record.  In these exchanges, Alan Breier and Dr. Beasley come across very much as the in-house investigators committed to the high road of science and one hopes that in the coming instalments (sic) of this thread, Dr. Beasley might illustrate his points with references to some of this material.”

        Ned was partially correct regarding internal Lilly correspondence and other documents relevant to the investigation of olanzapine and glycemic dysregulation.  Documents that had been obtained as part of discovery by the plaintiffs’ attorneys had been posted on the web, but the postings were illegal and the documents were successfully removed (at least from websites on the conventional web accessible from US IP addresses and from the conventional web from IP addresses appearing to be in Eastern Europe).  Ned might have preferred my response to his comment to discuss the material contained in the posted documents, but these were not available to me.

        As our series of postings (Beasley and Tamura 2019) addressed what can be considered high-quality “proof” that an observed AE is or is not an ADR, Ned’s comment allowed me to briefly review the sequential analyses that had been performed with laboratory analyte data relevant to glycemic control collected in olanzapine Phase 3-4 clinical trials and then turn to a detailed discussion of both hyperglycemic glucose clamp studies (evaluating pancreatic insulin production) and euglycemic-hyperinsulinemic glucose clamp studies (evaluating the effectiveness of insulin in disposing of glucose [causing glucose to be taken up by the body’s cells]).  For a host of reasons, glucose values observed in patients with schizophrenia during mostly outpatient clinical trials (with few patients treated for extended periods) are highly variable.  My discussion of these data in my response to Ned (Beasley 2019a) hopefully illustrated this point clearly.  I reviewed placebo-controlled clamp studies (human and animal) in great detail because as I read the literature,  the combination of both clamp studies in a reasonable sample size of human subjects stands the greatest potential likelihood of addressing the questions as to whether diabetes is likely to be an ADR associated with a drug. 

        There are two confounders with this pair of studies that must be addressed.  First, experts in diabetes and these studies must come to a consensus regarding study methods and analyses that address pancreatic function and the efficiency of insulin action on muscle, liver and the entire body.  My view from the studies reviewed is that such a consensus does not yet exist.  Second, if the drug of interest is associated with weight gain, then methods that would likely be expensive and perhaps difficult to implement would be necessary to isolate any direct diabetogenic effect from an indirect effect due to weight gain.  I am not convinced that statistical analysis methods that would adjust for weight gain would be sufficient to definitively separate a direct effect from a secondary effect in this domain.

        Besides analyses of the laboratory data from well-controlled clinical trials and the conduct of three clamp studies, Lilly undertook other lines of research to address this important clinical question.  I did not review these in response to Ned (Beasley 2019a) as I do not consider them to be as definitive as analyses of clinical trial data and clamp studies might be in assessing diabetes as an ADR.  However, as Barry in his comment to Ned mentions, an epidemiological study conducted using a large database found an excess risk of diabetes with olanzapine.   I will briefly describe the results of this study cited by Barry and two additional studies conducted during the same period using that same database, one study conducted by Lilly.

        Two matters in Barry’s comment require clarification.   The first of these matters is my academic training and functional responsibilities while an employee of Lilly.  The second of these matters are the circumstances surrounding my transitioning from working primarily with olanzapine to other primary responsibilities within Lilly in 2001 (not 2002). 

        In his comment on Ned’s comment (Blackwell 2019), Barry states: “In that context I posted a critical essay on ‘Corporate Corruption in the Pharmaceutical Industry’ in which Charles Beasley spent a distinguished career as the lead biostatistician for Eli Lilly.  Charles was working on Olanzapine and its side effects until 2002 when higher authority ordered him to cease.”  

        My work within Lilly was not as a biostatistician but as a Research Physician (my medical specialty training was as a psychiatrist and I  joined Lilly directly from completing my residency in 1987).  I did have extensive training in computer science and had worked in artificial intelligence research and the development of a database and some analyses methods for an evoked potential laboratory (two separate work experiences) before beginning medical school in 1979.  While I had some statistics and research design training and have maintained a keen interest in the interface among statistical methods, research design and data analyses, I should not be considered a statistician.  I performed all of the initial programming and sample size computations for our posting “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)” posting (Beasley and Tamura 2019).  My statistical colleague Roy Tamura (biostatistics faculty member at a US university medical school) reviewed and checked my work and suggested important revisions for the final posting. 

        Barry is quite correct that I transitioned from a role that reported directly to the President of the Neurosciences Business Unit that involved, for the most part, the in-depth review of the safety of olanzapine to an alternative role.  That alternative role was Medical Director for the Tadalafil (Cialis™) Product Development Team.  The change in primary responsibilities occurred in July 2001.  Barry’s comment implies that Lilly senior management was dissatisfied with my work on olanzapine and perhaps my suggestions for studies, analyses and dissemination of information.  I cannot affirm that Barry’s implication is incorrect.  I will address the reasons that I understand lead to the request that I make this transition.  However, I did not ask senior management if, in addition to the reasons I understood for this request, other reasons were at play as well.  If Barry is correct in his implication, then senior management would have been unlikely to be honest with me if I had asked about other reasons.  I was asked to make this transition shortly after tadalafil had been submitted for review for marketing approval to the FDA and the European Union (EMEA) review body.  The Medical Director for that team had abruptly resigned from Lilly shortly after the submissions and this was a critical juncture in the development of a new drug.  Also important, while tadalafil was being developed by Lilly, it was owned by another company at that time, Icos.  The loss of a Medical Director at that point in its development would not enhance the working relationship between partners in such a joint venture.  I had extensive and recent successful experience in working with FDA, EMEA and the Japanese regulatory authority on several complex matters and, at the risk of being immodest, agreed that I was the best physician within Lilly at the time to step into this role.  Although the tadalafil role was intensive, I continued to be consulted on several matters related to olanzapine through December 2002.  I transitioned back to work in the Neuroscience Business Unit as a special consultant in January 2003 with work completed and tadalafil positioned for US and European approval, the expressed goals for my movement to the Tadalafil Team.

        I now turn back to the work that Lilly and other researchers performed to assess the relationship between olanzapine and glycemic dysregulation.  In the response to Ned’s comment (Beasley 2019a) I explained my rationale for the narrow focus on Lilly clinical trials data (illustrates many of the problems with such data when addressing an adverse event that is relatively infrequent to rare, has a high background incidence and has delayed onset) and glucose clamp studies (if conducted properly, probably the best way of addressing the question of drug impact on glycemic dysregulation).  Lilly conducted other studies as well, including two epidemiological studies for which I advocated.  One of these was US-based (Buse, Cavazzoni, Hornbuckle et al. 2003), and the other was UK based (Carlson, Hornbuckle, DeLisle et al. 2006).  The latter used the same database, the GPRD database, used by the study cited by Barry (Koro, Fedder, L’Italien et al. 2002).  These two Lilly epidemiological studies using large databases were planned to be performed before my transition to my work with tadalafil in 2001 and I cannot address the timing of their publication as I was not involved with these publications as an author.

        The Buse, Cavazzoni, Hornbuckle et al. study (2003) found a greater hazard ratio (hazard ratio from a Cox proportion regression model adjusting for age, gender and duration of exposure - relative to persons not treated with antipsychotics) for new diabetes diagnoses to be associated with: 1) all conventional antipsychotics combined; 2) two conventional antipsychotics that were analyzed separately (haloperidol, thioridazine); 3) all atypical antipsychotics combined; and 4) all atypical antipsychotics analyzed separately (clozapine, risperidone, olanzapine, quetiapine).  The diagnosis of new cases with the four atypical agents was compared to the diagnoses of new cases with haloperidol.  Significantly higher hazard ratios were found only with clozapine and risperidone.  The hazard ratio for olanzapine was numerically higher (1.09).  The hazard ratio for quetiapine was significantly lower (0.67).

        The Carlson, Hornbuckle, DeLisle et al. study (2006), using methods comparable to those in the Buse, Cavazzoni, Hornbuckle et al. study but adjusting for obesity and not length of exposure, found greater hazard ratios with combined conventional antipsychotics and, separately, combined atypical antipsychotics, for thioridazine alone, for both olanzapine and risperidone and olanzapine alone (the only two atypical agents analyzed separately), but not fluopenthixol (sic - flupenthixol), trifluoperazine, chlorpromazine or haloperidol analyzed separately.

        There are notable differences in both the findings and methods of the Carlson, Hornbuckle, DeLisle et al. study (2006) and the Koro, Fedder, L’Italien et al. study (2003) cited by Barry, although both were conducted using the GPRD database.  The Carlson, Hornbuckle, DeLisle et al. study used all patients treated with antipsychotics without a preexisting diagnosis of diabetes and all patients not treated with antipsychotics without a preexisting diagnosis of diabetes as controls.  There were 59,089 patients treated with conventional antipsychotics and 9,059 patients treated with atypical antipsychotics (5,213 with risperidone and 2,374 with olanzapine) included in the Carlson, Hornbuckle, DeLisle et al. analyses.   The Koro, Fedder, L’Italien et al. study limited the investigational cohort to patients with a diagnosis of schizophrenia.  There were only 19,637 patients treated with any antipsychotic, 1,683 risperidone-treated patients and 970 olanzapine-treated patients included in the Koro, Fedder, L’Italien et al. study.  The study was of case-control design with six controls matched to each case.  Controls were matched to cases by sex, age, length of follow-up and date of being eligible as a control.

        The model adjusted odds ratio was significantly greater for the use of conventional antipsychotics and olanzapine, but not for the use of risperidone compared to no antipsychotic treatment.  The model adjusted odds ratio was significantly greater for the use of olanzapine but not for the use of risperidone compared to the use of conventional antipsychotics. 

        While a case-control design restricted to patients with a diagnosis of schizophrenia could be expected to reduce the potential for unknown differences between groups being compared biasing the outcome of the analysis compared to the design of the Carlson, Hornbuckle, DeLisle et al. study, the Koro, Fedder, L’Italien et al. study included smaller comparative sample sizes.  Nonetheless, the results of the two studies agreed except for findings for risperidone.  There were only seven new cases of diabetes in the risperidone group in the Koro, Fedder, L’Italien et al. study.

        Another, earlier, case-control study (Kornegay, Vasilakis-Scaramozza and Jick 2002) was conducted using the GPRD database and this study was conducted by FDA staff.  This study found the adjusted odds ratio for current (emphasis added) use of both conventional antipsychotics and atypical antipsychotics (separately) to be significantly higher than for non-use during the preceding year.  The adjusted odds ratio (1.0) for recent(emphasis added) use of conventional antipsychotics compared to non-use within the preceding year, however, was not significant.  The adjusted odds ratio for recent (emphasis added) use of atypical antipsychotics compared to non-use in the preceding year could not be computed as no subject had this type of exposure as defined by the investigators (use within the seven to twelve months before the index date of diagnosis).

        The Kornegay, Vasilakis-Scaramozza and Jick study included patients with information recorded in the GPRD database on drug treatment between January 1994 and December 1998 (publication approximately four years after the data cut-off date).  The Koro, Fedder, L’Italien et al. study included patients with a diagnosis of schizophrenia and information on drug treatment recorded in the GPRD database between June 1987 and September 2000 (publication approximately three years after data cut-off date).  The Carlson, Hornbuckle, DeLisle et al. study included patients with information recorded in the GPRD database on drug treatment between January 1, 1994, and December 31, 2001 (publication approximately five years after data cut-off date).  Based on the earliest to latest end dates for patient inclusion in these retrospective epidemiological analyses, they were conducted in the order in which they were described in the preceding three sentences.  With each subsequent study, more data for atypical antipsychotics would come available.  The differences in analysis results demonstrate what are likely the impact of both increasing data (especially for the atypical antipsychotics) and methodological differences in the analyses.  These methodological differences were the result of slightly different questions that the three groups of researchers hoped to answer with their studies.

        Not only did other groups publish the results of analyses strongly supporting the hypothesis that olanzapine has an association with a risk of incident cases of diabetes, but Lilly also conducted such research and published the results (Carlson, Hornbuckle, DeLisle et al. 2006).  However, Lilly’s work found conventional antipsychotics as a group and atypical antipsychotics as a separate group to also be associated with this risk.  FDA analysis (Kornegay, Vasilakis-Scaramozza and Jick 2002) resulted in similar findings for both conventional and atypical antipsychotics as separate groups when considering the diagnosis of diabetes while being actively treated with an antipsychotic.

        To me, the epidemiological study findings with olanzapine are not surprising.  That olanzapine is associated with substantial weight gain has been well understood since the five registration trials for the drug were conducted and documented in the initial Product Information for the drug in the US and other regulatory venues.  Any medical professional licensed to treat patients with pharmaceutical products (physicians, advanced nurse practitioners, physician assistants, clinical psychologists in some licensing venues) should have a clear understanding that weight gain, especially weight gain primarily in the form of visceral adipose tissue, is a major risk factor for the development of Type II diabetes mellitus.  

        What was surprising to me was that the results of the analyses designed by my statistical colleagues and me, executed by these statistical colleagues in the late 1990s and presented in multiple, public scientific forums (e.g., Beasley 2000) failed to demonstrate that glycemic dysregulation and diabetes was an ADR with olanzapine.  These analyses demonstrated two important things.  The analyses first demonstrated the magnitude of variability or “noise” in what are intended to be fasting glucose concentration values obtained from patients with schizophrenia (also mentioned above) and therefore the great difficulty in using such data to find evidence of impaired glucose regulation or diabetes in such a patient population.  Second, these analyses demonstrated that there was no “smoking gun” in the clinical trial data.  Even with an additional four years of clinical trial data acquired since the completion of the registration studies, there was no evidence demonstrating an association between olanzapine and glucose dysregulation or diabetes.  “Noisy” data collected from too few patients over a too short a time for cases of an ADR to develop where the time of onset might require months to years from treatment initiation to occurrence of the ADR is unlikely to offer “proof” that a drug is or is not associated with such an ADR. The difficulty with clinical trial data used for the assessment of such possible ADRs is exacerbated by a high background incidence of the medical event that might be an ADR, as is the case with diabetes.  This matter was discussed at length, with examples in Beasley and Tamura (2019).

        The interpretation of the results of our late 1990s (Beasley 2000) studies should be highly limited.  These analyses were conducted with the null hypothesis of olanzapine being equivalent to placebo and haloperidol (haloperidol being important for long-term comparisons) and this null hypothesis could not be rejected.  As stated above, this was important because the analyses then demonstrated that there was no “smoking-gun” within the existing clinical trial data demonstrating that olanzapine was causally related to diabetes.  The results of these analyses underscored the need for additional research using alternative methods (e.g., glycemic clamp studies, epidemiological studies in ‘big-data’ databases).  Lilly and others undertook and published such work.

        It is important to underscore that while the analyses (Beasley 2000) failed to “prove” a diabetic effect, the results of the analyses most assuredly and unequivocally did not prove the absence of a diabetic effect associated with olanzapine. As Paul Leber, Director of the Division of Neuro-Pharmacological Drug Products within the FDA from 1981 through 1999, said, “Absence of evidence is not evidence of absence.”  Stated alternatively, failure to reject the null hypothesis does not allow acceptance of the null hypothesis as correct.  I would consider any use of the results of these analyses to suggest that they demonstrated that olanzapine was not associated with a diabetic effect to be a grossly inappropriate use.  If such use resulted from a lack of understanding of the principals of interpreting statistical analyses, then such use could be attributed to ignorance.  If such use did not result from a lack of understanding of these fundamental principals of interpretation, then such use could be considered malignant.

        I will conclude this response to Barry with a return to the matter of weight gain and the question as to whether the diabetic ADR with olanzapine is a direct effect, an indirect effect mediated through visceral adipose tissue gain or a combination of both.  While others might substantially disagree, I do not believe this question has been adequately addressed (Beasley 2019a).  Furthermore, I believe the question to be very important in determining which antipsychotics to use with a given patient, how to assess individual patient risk-benefit and when to switch antipsychotics, if necessary.  Weight gain is easily followed.  For olanzapine, substantial long-term weight gain can be predicted with as few as 2-3 weeks of treatment (Lipkovich, Jacobson, Caldwell et al. 2009).  If this weight gain (likely most if not all adipose tissue) is the primary but indirect etiology of glycemic dysregulation, some ~50% or more of patients who will experience substantial weight gain during longer term olanzapine treatment (not all of whom would develop diabetes) can be identified and alternative medication considered in terms of individual risk-benefit assessment.  In this case, olanzapine is easy to use with respect to this specific risk assessment

        However, if there is a potentially abrupt and yet unpredictable direct diabetogenic effect of olanzapine and other antipsychotics, then the individual risk of glycemic dysregulation is unpredictable.  In this case, olanzapine and other such antipsychotics become exceedingly difficult to use with respect to this individual risk assessment.  Both robust response and compliance with frequent follow-up in patients judged to be at significant risk of consequent morbidity if glycemic dysregulation developed (i.e., diabetes due to a direct diabetogenic effect) would be required for me to consider olanzapine as the first choice for such an individual patient.  Not all patients would be at significant and imminent risk of severe morbidity if new-onset diabetes were not detected very soon after the development of diabetes.  However, for those at such risk (e.g., patients with preexisting atherosclerotic coronary artery and/or carotid artery disease, patients with hypertension, patients with dyslipidemia), I would personally view substantial efficacy and capacity on the part of the patient to participate in frequent follow-up examinations to be present to consider olanzapine (or any drug with a direct diabetogenic effect) as a first-choice treatment for such a patient.

        Again, we thank Barry for his comments.



Beasley C, Berg P, Dananberg J, Kwong K, Taylor C, Breier A.  Incidence and rate of treatment-emergent potential impaired glucose tolerance and potential diabetes with olanzapine compared to other antipsychotic agents and placebo.  Annual Meeting of the American College of Neuropsychopharmacology.  San Juan, PR, Dec. 11, 2000.

Beasley CM. Commentary – corporate corruption in the psychopharmaceutical industry.  March 23, 2017.

Beasley CM. Charles J. Beasley, Jr’s response to Barry Blackwell’s reply (Barry Blackwell: Corporate corruption in the psychopharmaceutical industry). 11, 2018. 

Beasley CM.  Charles M. Beasley Jr.: Reply to Edward Shorter’s comments. Olanzapine and Diabetes Mellitus, Evolution of Data – Illustrating the Difficulties in Identification of Adverse Drug Reactions (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] Outline).  July 4, 2019 (2019a).

Beasley CM.  A Post-Script (Charles Beasley 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]).  October 24, 2019 (2019b).

Beasley CM, Tamura R.  Full Text (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]).  November 21, 2019.

Blackwell B.   Corporate corruption in the psychopharmaceutical industry. September 1, 2016.

Blackwell B.   Corporate corruption in the psychopharmaceutical industry (revised). March 16, 2017.

Blackwell B. Barry Blackwell’s comments on Charles Beasley’s reply to Edward Shorter’s comment. Olanzapine and diabetes mellitus; evolving data illustrating the difficulties in identification of adverse drug reactions. Background (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]).  November 28, 2019.

Buse JB, Cavazzoni P, Hornbuckle K, Hitchins D, Breier A, Jovanovic L.  A retrospective cohort study of diabetes mellitus and antipsychotic treatment in the United States.  J Clin Epidemiol 2003; 56:164-70.

Carlson C, Hornbuckle K, DeLisle F, Kryzhanovskaya L, Breier A, Cavazzoni P.  Diabetes mellitus and antipsychotic treatment in the United Kingdom.  Eu Neuropsychopharmacol 2006; 16:366-75.

Kornegay CJ, Vasilakis-Scaramozza C, Jick H.  Incident diabetes associated with antipsychotic use in the United Kingdom General Practice Research Database.  J Clin Psychiatry  2002; 63:758-62.

Koro CE, Fedder DO, L’Italien GJ, Weiss SS, Magder LS, Kreyenbuhl J, Revicki DA, Buchanan RW.  Assessment of independent effect of olanzapine and risperidone among patients with schizophrenia: population based nested case-control study.  BMJ 2002; 325:243-7.

Lipkovich I, Jacobson JG, Caldwell C, Hoffman VP, Kryzhanovskaya L, Beasley CM.
Early predictors of weight gain risk during treatment with olanzapine: analysis of pooled data from 58 clinical trials.  Psychopharm Bull 2009; 42:23-39.

Shorter E.  Edward Shorter’s comment on Outline (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).  April 25, 2019.


May 14, 2020