1 Boring Old Man

Discrepancies Between Prespecified and Reported Outcomes

Annals of Internal Medicine

by Eirion Slade; Henry Drysdale; Ben Goldacre, on behalf of the COMPare Team

December 22, 2015

[online]

TO THE EDITOR: Gepner and colleagues’ article reports outcomes that differ from those initially registered. One prespecified primary outcome was reported incorrectly as a secondary outcome. In addition, the article reports 5 “primary outcomes” and 9 secondary outcomes that were not prespecified without flagging them as such. One prespecified secondary outcome also was not reported anywhere in the article.

Annals of Internal Medicine endorses the CONSORT [Consolidated Standards of Reporting Trials] guidelines on best practice in trial reporting. To reduce the risk for selective outcome reporting, CONSORT includes a commitment that all prespecified primary and secondary outcomes should be reported and that, where new outcomes are reported, it should be made clear that these were added at a later date, and when and why this was done should be explained.

The Centre for Evidence-Based Medicine Outcome Monitoring Project [COMPare] aims to review all trials published going forward in a sample of top journals, including Annals. When outcomes have been incorrectly reported, we are writing letters to correct the record and audit the extent of this problem in the hopes of reducing its prevalence. This trial has been published and is being used to inform decision making, and this comment is a brief correction on a matter of fact obtained by comparing 2 pieces of published literature. We are maintaining a Web site [www.COMPare-Trials.org] where we will post the submission and publication dates of this comment alongside a summary of the data on each trial that we have assessed.

Discrepancies Between Prespecified and Reported Outcomes

Annals of Internal Medicine

by the Editors

December 22, 2015

[online]

… According to COMPare’s protocol, abstractors are to look first for a protocol that has been published before a trial’s start date. If they find no such publication, they are supposed to review the initial trial registry data. Thus, COMPare’s review excludes most protocols published after the start of a trial and unpublished protocols or their amendments and ignores amendments or updates to the registry after a trial’s start date. The initial trial registry data, which often include outdated, vague, or erroneous entries, serve as COMPare’s “gold standard.”

Our review indicates problems with COMPare’s methods. For 1 trial, the group apparently considered the protocol published well after data collection ended. However, they did not consider the protocol published 2 years before MacPherson and associates’ primary trial was published. That protocol was more specific in describing the timing of the primary outcome [assessment of neck pain at 12 months] than the registry [assessment of neck pain at 3, 6, and 12 months], yet COMPare deemed the authors’ presentation of the 12-month assessment as primary in the published trial to be “incorrect.” Similarly, the group’s assessment of Gepner and colleagues’ trial included an erroneous assumption about one of the prespecified primary outcomes, glycemic control, which the authors had operationalized differently from the abstractors. Furthermore, the protocol for that trial clearly listed the secondary outcomes that the group deemed as being not prespecified.

On the basis of our long experience reviewing research articles, we have learned that prespecified outcomes or analytic methods can be suboptimal or wrong. Regardless of prespecification, we sometimes require the published article to improve on the prespecified methods or not emphasize an end point that misrepresents the health effect of an intervention. Although prespecification is important in science, it is not an altar at which to worship. Prespecification can be misused to sanctify both inappropriate end points, such as biomarkers, when actual health outcomes are available and methods that are demonstrably inferior.

The Centre for Evidence-Based Medicine Outcome Monitoring Project’s assessments seem to be based on the premise that trials are or can be perfectly designed at the outset, the initial trial registry fully represents the critical aspects of trial conduct, all primary and secondary end points are reported in a single trial publication, and any changes that investigators make to a trial protocol or analytic procedures after the trial start date indicate bad science. In reality, many trial protocols or reports are changed for justifiable reasons: institutional review board recommendations, advances in statistical methods, low event or accrual rates, problems with data collection, and changes requested during peer review. The Centre for Evidence-Based Medicine Outcome Monitoring Project’s rigid evaluations and the labeling of any discrepancies as possible evidence of research misconduct may have the undesired effect of undermining the work of responsible investigators, peer reviewers, and journal editors to improve both the conduct and reporting of science…

The Hidden Harm of Antidepressants

An in-depth analysis of clinical trials reveals widespread underreporting of negative side effects, including suicide attempts and aggressive behavior

Scientific American

By Diana Kwon

February 3, 2016

Antidepressants are some of the most commonly prescribed medications out there. More than one out of 10 Americans over age 12 — roughly 11 percent — take these drugs, according to a 2011 report by the National Center for Health Statistics. And yet, recent reports have revealed that important data about the safety of these drugs — especially their risks for children and adolescents — has been withheld from the medical community and the public.

In the latest and most comprehensive analysis, published last week in BMJ [the British Medical Journal], a group of researchers at the Nordic Cochrane Center in Copenhagen showed that pharmaceutical companies were not presenting the full extent of serious harm in clinical study reports, which are detailed documents sent to regulatory authorities such as the U.S. Food and Drug Administration and the European Medicines Agency [EMA] when applying for approval of a new drug. The researchers examined documents from 70 double-blind, placebo-controlled trials of two common types of antidepressants — selective serotonin reuptake inhibitors [SSRI] and serotonin and norepinephrine reuptake inhibitors [SNRI] — and found that the occurrence of suicidal thoughts and aggressive behavior doubled in children and adolescents who used these medications.

This paper comes on the heels of disturbing charges about conflicts of interest in reports on antidepressant trials. Last September a study published in the Journal of Clinical Epidemiology revealed that a third of meta-analyses of antidepressant studies were written by pharma employees and that these were 22 times less likely than other meta-studies to include negative statements about the drug. That same month another research group reported that after reanalyzing the data from Study 329, a 2001 clinical trial of Paxil funded by GlaxoSmithKline, they uncovered exaggerated efficacy and undisclosed harm to adolescents.

Because of the selective reporting of negative outcomes in journal articles, the researchers in the most recent BMJ study turned to clinical trial reports, which include more detailed information about the trials. They discovered that some of most the useful information was in individual patient listings buried in the appendices. For example, they uncovered suicide attempts that were passed off as “emotional liability” or “worsening depression” in the report itself. This information, however, was only available for 32 out of the 70 trials. “We found that a lot of the appendices were often only available upon request to the authorities, and the authorities had never requested them,” says Tarang Sharma, a PhD student at Cochrane and lead author of the study. “I’m actually kind of scared about how bad the actual situation would be if we had the complete data”…

I was a late comer to what this Scientific American article is about, in my later sixties, retired from a psychotherapy practice that had been more out of the mainstream than I knew at the time. In retirement, I had started volunteering in some general clinics and was struck with a couple of things. First, the patients were almost universally taking a lot of medications in odd combinations unfamiliar to me. But even more striking, they came with expectations from the medications that were well beyond any possibilities I knew. To borrow a book title, I felt like a stranger in a strange land. About that time, I read in the New York Times that the chairman of the department I had been affiliated with for over thirty years was under investigation for unreported income from pharmaceutical companies [Top Psychiatrist Didn’t Report Drug Makers’ Pay]. And somewhere in there, I had prescribed an SSRI to a 17 year old young man who became confused, agitated, and suicidal within days – all thankfully clearing as fast as they came when the medication was discontinued. At the time, I didn’t know that could happen.

I’m surprised at how much the disillusionment I felt affected me. I had experienced my share of such things before, but this one was different. Reading back over the blogs I’ve written since then, I’ve bounced from place to place in how I understood [or didn’t understand] it all. I was lucky. I had a strong hard science background from a former career and could look into the science involved. And I’ve met a number of like minded people along the way who brought a wealth of experience and wisdom my way – helping me answer questions I didn’t even know were there to be asked. But there were two concrete experiences that helped me with my own uncomfortable disillusionment. The first was going to the Allen Jones TMAP Trial in Austin in January 2012 where I watched any number of regular people caught up in some little piece of the drama without allowing themselves to see the whole picture. The second was being involved in the research for one of those articles up there and seeing the details – another example of people neither stepping back far enough to see the big picture nor getting close enough to see what they were involved in. In both instances the main problems were at the top, and had to do with unnecessary secrecy.

Medical advances have often been accompanied by high hopes and enthusiasm [illusion] followed by the more accurate reality that comes with clinical experience [dis·illusionment]. This sequence has been eroded at both ends. The Clinical Trials that are meant to be a simplistic starting place have been jury-rigged and given an undeserved enduring authority. Meanwhile, academic medical departments and journals have not only become engaged in the hype, but have also failed in their traditional role as watchdogs and skeptics. In the process, the appropriate disillusionment that comes with clinical experience with medications is being replaced with a disillusionment with medicine itself – an unacceptable trade-off.

I signed up for STAT on the Boston Globe because Pharmalot moved there. But the new additions to the morning emails these last several days have given me pause. We could use an explanation…

Hi Mickey,

They’re simply sponsors for the newsletter — they’re paid advertisements that come from the business end of the publication. I have nothing to do with them, don’t interact with them, and they have no bearing on my content whatsoever. They started showing up because the newsletter has been rolling for a few months now, and in order to pay for the journalism we do, the business team needs to create revenue through advertisements like all other publications.

Thanks,
Megan

Revisiting the Commercial–Academic Interface

by Jeffrey M. Drazen, M.D.

New England Journal of Medicine. 2015 372:1853-1854.

Reconnecting the Dots — Reinterpreting Industry–Physician Relations

by Lisa Rosenbaum, M.D.

New England Journal of Medicine. 2015 372:1860-1864.

Understanding Bias — The Case for Careful Study

by Lisa Rosenbaum, M.D.

New England Journal of Medicine. 2015; 372:1959-1963.

Beyond Moral Outrage — Weighing the Trade-Offs of COI Regulation

by Lisa Rosenbaum, M.D.

New England Journal of Medicine. 2015; 372:2064-2068.

In order to make that argument, they have to ignore the numerous examples of "experts" using review articles to push some product they had personal connections with – one of the more egregious versions being Dr. Nemeroff et al’s review of the vagal nerve stimulator in depression [VNS Therapy in Treatment-Resistant Depression: Clinical Evidence and Putative Neurobiological Mechanisms] that cost him his own editorship at Neuropsychopharmacology. That was an unacknowledged COI, but there are many other examples to choose from where acknowledgement doesn’t mitigate the glaring bias.

Data Sharing

by Dan L. Longo, and Jeffrey M. Drazen

New England Journal of Medicine. 2016  374:276-277.

[full text on-line]

Confluence, Not Conflict of Interest: Name Change Necessary

by Anne Cappola and Garret FitzGerald

JAMA. 2015 314[17]:1791-1792.

… Confluence of interest represents a complex ecosystem that requires development of a uniform approach to minimize bias in clinical research across the academic sector. Such a policy must be at once simple and accessible, capturing the complexity of the relationships while being sufficiently flexible at the individual level not to intrude on the process of innovation.

JAMA JUMPS THE SHARK

Health Care Renewal

by Bernard Carroll

January 24, 2016

"… the authors, presuming to speak for investigators generally, were offended by the increasing regulations for managing COI. Those developments have occurred at the Federal, institutional, and publication levels. Worse, the authors ignored the reality of recent corruption that led to those new regulations. That uncomfortable fact was airbrushed out of their discussion."

Top journal editors resist transparency

HEALTHNEWSREVIEW

by Susan Molchan

January 25, 2016

It’s difficult to make a case for hiding or obscuring information about health and the medicines we take, but it seems the editors of two top medical journals are doing just that. The decisions of these editors substantially affect the quality of medical research studies reported, what public relations officials communicate about those studies, and what news stories eventually say about the research to patients and the public…

Discrepancies Between Prespecified and Reported Outcomes

Annals of Internal Medicine

December 22, 2015

[online]

… The Centre for Evidence-Based Medicine Outcome Monitoring Project’s assessments seem to be based on the premise that trials are or can be perfectly designed at the outset, the initial trial registry fully represents the critical aspects of trial conduct, all primary and secondary end points are reported in a single trial publication, and any changes that investigators make to a trial protocol or analytic procedures after the trial start date indicate bad science. In reality, many trial protocols or reports are changed for justifiable reasons: institutional review board recommendations, advances in statistical methods, low event or accrual rates, problems with data collection, and changes requested during peer review. The Centre for Evidence-Based Medicine Outcome Monitoring Project’s rigid evaluations and the labeling of any discrepancies as possible evidence of research misconduct may have the undesired effect of undermining the work of responsible investigators, peer reviewers, and journal editors to improve both the conduct and reporting of science.

Harry Stack Sullivan was from the days before psychopharmacology, and he was nobody’s fool. He was objecting to the "un" in Freud’s "unconscious." Things people either don’t or don’t want to think about don’t just go away. The mind becomes selectively inattentive, but it shows. They get some kind of fidgety when the unwanted mental content is nearby. They may start doing odd things that gamblers call "tells." If the wires are hooked up to a polygraph, the needles on the graph begin to wiggle. They may change the subject, or ask why you’re asking, or get hostile, or be defensive, or maybe sarcastic, or go silent. There’s a subtle disturbance in the force. Such things don’t tell you what’s being selectively unattended – only that you’re in the neighborhood of something that matters.

Data Sharing

by Dan L. Longo, and Jeffrey M. Drazen

New England Journal of Medicine. 2016  374:276-277.

[full text on-line]

The aerial view of the concept of data sharing is beautiful. What could be better than having high-quality information carefully reexamined for the possibility that new nuggets of useful data are lying there, previously unseen? The potential for leveraging existing results for even more benefit pays appropriate increased tribute to the patients who put themselves at risk to generate the data. The moral imperative to honor their collective sacrifice is the trump card that takes this trick.

But in this first paragraph, Drazen also sets the stage for another agenda – one heavily promoted by the pharmaceutical industry. When the clamor about distorted clinical trial reports reached a pitch that could no longer be ignored, they reframed the real intent of the move for Data Transparency. Instead of that being a reform move to allow independent reanalysis to keep them honest [because they hadn’t been], they spoke of it as Data Sharing for the reasons Drazen presents in his opening gambit – a generous act in the service of scientific progress.

However, many of us who have actually conducted clinical research, managed clinical studies and data collection and analysis, and curated data sets have concerns about the details. The first concern is that someone not involved in the generation and collection of the data may not understand the choices made in defining the parameters. Special problems arise if data are to be combined from independent studies and considered comparable. How heterogeneous were the study populations? Were the eligibility criteria the same? Can it be assumed that the differences in study populations, data collection and analysis, and treatments, both protocol-specified and unspecified, can be ignored?

A second concern held by some is that a new class of research person will emerge — people who had nothing to do with the design and execution of the study but use another group’s data for their own ends, possibly stealing from the research productivity planned by the data gatherers, or even use the data to try to disprove what the original investigators had posited. There is concern among some front-line researchers that the system will be taken over by what some researchers have characterized as “research parasites”…

How would data sharing work best? We think it should happen symbiotically, not parasitically. Start with a novel idea, one that is not an obvious extension of the reported work. Second, identify potential collaborators whose collected data may be useful in assessing the hypothesis and propose a collaboration. Third, work together to test the new hypothesis. Fourth, report the new findings with relevant coauthorship to acknowledge both the group that proposed the new idea and the investigative group that accrued the data that allowed it to be tested. What is learned may be beautiful even when seen from close up.

I don’t personally see running industry-funded Phase III Clinical Trials as Research, I think of it as Product Testing. There’s an enormous financial coloring to the whole enterprise, billions of dollars riding on the outcome of some of these Clinical Trials that say yes or no to the investment put into any given drug. But the trials are primarily about the safety and efficacy of the drugs themselves, not about the financial health and fortunes of the company that developed them, nor the academic departments and faculty that involve themselves in this process. There’s an epithet coined to describe people who are skeptical about clinical trials – pharmascolds – implying that they are biased against all drugs. Such people exist for sure, but I’m not one of them, nor are most of us who look into the data from Sponsored drug trials. We’re physicians and science minded others who don’t like being gamed by our own scientific literature, depriving us of a vital source of information about how to treat our patients.

Frankly, I’m a reluctant parasite. I’ve had to revive skills from a previous career here in my retirement. I had some other plans that were pushed to the side in order to do that. But I think it’s vitally important for the medical·scientific community to have watchdogs, particularly in today’s climate. Certainly the scientific literature in psychiatry for the last twenty plus years begs for serious oversight. Our group’s work was unfunded and difficult [in part because of the way we had to access the data]. Our paper was extensively reviewed and only accepted after the seventh submission, though in a way, the thorough and comprehensive nature of the peer review was confirming [if only that original paper had been subjected to that kind of rigor…].

^{hat tip to Ferrell…}  

Antidepressants Appear To Be Much More Dangerous For Kids, Teens Than Reported In Medical Journals, Review Finds.

HealthDay reports, “Antidepressants appear to be much more dangerous for children and teens than reported in medical journals, because initial published results from clinical trials did not accurately note instances of suicide and aggression,” a review published Jan. 27 in the BMJ suggests. Researchers arrived at that conclusion after analyzing data from “68 clinical study reports from 70 drug trials that involved more than 18,500 patients.” The clinical studies “involved five specific antidepressants: duloxetine [Cymbalta], fluoxetine [Prozac], paroxetine [Paxil], sertraline [Zoloft] and venlafaxine [Effexor].”

According to Medical Daily, “the limitations in both design and reporting of clinical trials may have led to ‘serious under-estimation of the harms.’” The study authors concluded, “The true risk for serious harms is still uncertain.” The Telegraph [UK] also covers the story.

Suicidality and aggression during antidepressant treatment: systematic review and meta-analyses based on clinical study reports

by Tarang Sharma, Louise Schow Guski, Nanna Freund, and Peter C. Gøtzsche

British Medical Journal. 2016 352:i65

[full text on-line]

Objective: To study serious harms associated with selective serotonin and serotonin-norepinephrine reuptake inhibitors.

Design: Systematic review and meta-analysis.

Main outcome measures: Mortality and suicidality. Secondary outcomes were aggressive behaviour and akathisia.

Data sources: Clinical study reports for duloxetine, fluoxetine, paroxetine, sertraline, and venlafaxine obtained from the European and UK drug regulators, and summary trial reports for duloxetine and fluoxetine from Eli Lilly’s website.

Eligibility criteria for study selection: Double blind placebo controlled trials that contained any patient narratives or individual patient listings of harms.

Data extraction and analysis: Two researchers extracted data independently; the outcomes were meta-analysed by Peto’s exact method [fixed effect model].

Results: We included 70 trials [64 381 pages of clinical study reports] with 18 526 patients. These trials had limitations in the study design and discrepancies in reporting, which may have led to serious under-reporting of harms. For example, some outcomes appeared only in individual patient listings in appendices, which we had for only 32 trials, and we did not have case report forms for any of the trials. Differences in mortality [all deaths were in adults, odds ratio 1.28, 95% confidence interval 0.40 to 4.06], suicidality [1.21, 0.84 to 1.74], and akathisia [2.04, 0.93 to 4.48] were not significant, whereas patients taking antidepressants displayed more aggressive behaviour [1.93, 1.26 to 2.95]. For adults, the odds ratios were 0.81 [0.51 to 1.28] for suicidality, 1.09 [0.55 to 2.14] for aggression, and 2.00 [0.79 to 5.04] for akathisia. The corresponding values for children and adolescents were 2.39 [1.31 to 4.33], 2.79 [1.62 to 4.81], and 2.15 [0.48 to 9.65]. In the summary trial reports on Eli Lilly’s website, almost all deaths were noted, but all suicidal ideation events were missing, and the information on the remaining outcomes was incomplete.

Conclusions: Because of the shortcomings identified and having only partial access to appendices with no access to case report forms, the harms could not be estimated accurately. In adults there was no significant increase in all four outcomes, but in children and adolescents the risk of suicidality and aggression doubled. To elucidate the harms reliably, access to anonymised individual patient data is needed.

• The reference came from a primary care newsletter. Non-psychiatrist physicians prescribe the majority of the SSRIs, and that’s where this information about harms belongs. Hopefully the news is finally spreading.
• The heavy lifting in this article was done by students working with Dr. Gøtzsche at the Nordic Cochrane Center. We desperately need for this kind of critical evaluation of Clinical Trials to be coming from the world of young researchers and physicians rather than just from us old guys.
• They did this meta-analysis using a large number of Complete Study Reports[ CSRs] they got from the European Medicines Agency [EMA]. Again, great news that they could get them. And there was more, they got to see the wide variability in what was in those reports and how variable they were with raw data – clarifying that in lobbying for Data Transparency, we need to specify that they have actual data.
• They emphasize the point that that the CSRs are not enough to evaluate harms. We absolutely need to have access to the Case Report Forms [CRFs] where the data was originally transcribed. We couldn’t have done our Paxil Study 329 article without them.
• Their findings mirrored ours from Paxil Study 329, but they had information from many more studies than just our one source. It is a more general commentary.
• It’s always great to hear from an old friend from the time when the world was young [among many other things, ironically, we were lab partners in pharmacology lab a little over 50 years ago]…

I did want to jump in and thank PsychPractice for mentioning my jaunt into statistics [in the land of sometimes… 1, 2, 3, 4, and 5 & john henry’s hammer… 1, 2, 3, 4, and 5] and for giving it a test drive [DIY Study Evaluation]. I’m not a statistician, and I’ll be glad to hear when I get things wrong. But I’ve decided that a lot of the reason people are not reading these clinical trials critically is that all the modern talk of statistical modelling and linear regression etc puts people off. Either they don’t understand the analytic methodology or worse – it’s presented in a deliberately obfuscating way to keep the reader from looking behind all the fancy talk. What I’m proposing is that the average medical reader can easily learn how to use a few simple tools to quickly decide if one is being served a plate of science or dish of something else. At least in my specialty, psychiatry, the industry generated clinical trial reports have been heavily weighted on the south side of something else. There are more statistical things to say before I’m done.

Don’t be alarmed. This isn’t one of those long boring posts with formulas and numbers. The graphic below is just window dressing to make one simple point:

I’ve been writing a mini-tutorial for evaluating Clinical Trials, and this spreadsheet will generate the needed information in the absence of Data Transparency. All we need for the Continuous Variables is the MEAN, the Standard Deviation or the Standard Error of the Mean, and the Number of Subjects for the control [placebo] and the drug groups. And for the Categorical Variables, we need even less – just the tally of yeses and nos for both. Those are not esoteric numbers – a basic minimum of information.

In defending their claim that the raw data from these Clinical Trials is proprietary and can be kept from scrutiny, the pharmaceutical industry makes two arguments: protecting their subject’s privacy and withholding commercially confidential information [CCI in slang]. But neither argument pertains to the simple information to plug into that spreadsheet. And yet one is surprised with how often that data isn’t available in an article. The graphic is meant to demonstrate how minimal the request – three numbers for each group in the Continuous Variables and only two numbers for the Categorical Variables in each group.

The Categorical Variables just get one post. It’s not because they aren’t important. It’s because I’ve already said what I’m up to in this series. And because they’re easy…

I thought it would be easiest to start with the spreadsheet itself this time because the column headings make it easy to discuss the output. This spreadsheet has been added below the one discussed in john henry’s hammer: continuous variables I…, downloadable here. It’s shown above with the MADRS efficacy data from the two recent Brexpiprazole Augmentation-in-Treatment-Resistant-Depression studies [see a story: the beginning of the end…].

Categorical Variables show up in almost every Clinical Drug Trial. They are derived variables that hold binary [yes/no] data based on some specified criteria. They’re often named, though the criteria for the names vary from study to study. So RESPONSE might be «final HAM-D score < 50% of the baseline» or «final HAM-D score < 50% of the baseline OR final HAM-D score < 8». In this case, the data is usually reported in the articles – the tally of the yeses and nos. Unlike the Continuous Variables, defining the dataset with Summary Data requires no mathematical manipulations [MEAN, Standard Deviation, Standard Error of the Mean], all you have to do is count.

The classic statistical test for significance is ChiSquare, discussed in in the land of sometimes^[2]…. The spreadsheet supplies two measurements of EFFECT SIZE. The first, Number Needed to Treat [NNT], is the more intuitive. It’s exactly what its name says, how many patients you have to treat to get one that beats what you would’ve gotten with placebo. The second EFFECT SIZE index is the ODDS RATIO [OR]. It is a quantitative measure frequently reported in meta-analyses where multiple studies are compared. One thing to note, unlike Cohen’s d, the Odds Ratio is not centered between the the 95% Confidence Intervals, so it is often charted on a logarithmic scale [which "centers" the OR]. For the mathematically inclined, the formulas for these column are:

    if a=control_[yes], b=control_[no], c=drug_[yes], & d=drug_[no], then:
Control Response% = a÷(a+b)
Drug Response% = c÷(c+d)
ChiSquare = ((a×d-b×c)²×(a+b+c+d))÷((a+b)×(c+d)×(a+c)×(b+d))  [1df]
NNT = 1÷(c÷(c+d)-a÷(a+b))
OR = (c÷d)÷(a÷b)
OR_[95%CI] = Exp(Ln(OR)±1.96x√((1÷a)+(1÷b)+(1÷c)+(1÷d)))
    ^{Ln is the natural log value and Exp means raise to the power of e [take the antilog]}

In this case, the Internet Calculators are all over the place. For the Chi Square calculations, I use the one at VassarStats because it gives the classic Pearson’s Chi Square, but it also calculates the Chi Square with the Yates correction. In addition, it computes the Fisher Exact Probability Test. These refinements are used in articles occasionally and the VassarStats page gives those results and links to an explanation of each [see Chapter 8 in their Web Textbook] so I don’t have to try and explain. And as for the Odds Ratio and its 95% Confidence Intervals, Why not stick with a winner – VassarStats? This version of their Internet Calculator does both the Chi Square and the Odds Ratio with its 95% Confidence Intervals. One stop shopping! As for the NNT, there are Internet Calculators around, but frankly it’s almost easier to do it in your head or using the calculator in your computer. Subtract the %yes of the control  from the %yes of the drug and divide the result into 100. That’s all there is to it. So 23.5%-14.7%=8.8% then 100÷8.8=11.27.