Computing Confidence Interval for Poisson Mean

For Poisson distribution, there are many different ways for calculating the confidence interval. The paper by Patil and Kulkarni discusses 19 different ways to calculate a confidence interval for the mean of a Poisson distribution.

The most commonly used method is the normal approximation (for large sample size) and the exact method (for small sample size)

Normal Approximation:

For Poisson, the mean and the variance are both lambda (λ).
The standard error is calculated as: sqrt(λ /n) where λ is Poisson mean and n is sample size or total exposure (total person years, total time observed,…)

The confidence interval can be calculated as:

                  λ ±z(α/2)*sqrt(λ/n).

The 95-percent confidence interval is calculated as: λ ±1.96*sqrt(λ/n).

The 99-percent confidence interval is calculated as: λ ±2.58*sqrt(λ/n).

  

EXACT method:

Refer to the following paper for the description of this method: 

• Garwood, F. 1936. Fiducial limits for the Poisson distribution. Biometrika. 28(3/4):437-442
• Ulm K. A simple method to calculate the confidence interval of a standardized mortality ratio. American Journal of Epidemiology 1990;131(2):373-375.

The confidence interval for event X is calculated as: 

           (qchisq(α/2, 2*x)/2, qchisq(1-α/2, 2*(x+1))/2 )

Where x is the number of events occurred under Poisson distribution.

In order to calculate the exact confidence interval for Poisson mean, the obtained confidence interval for the number of events need to be converted to the confidence interval for Poisson mean.

Here are two examples from the internet:

Example 1:

Would like to know how confident I can be in my λ. Anyone know of a way to set upper and lower confidence levels for a Poisson distribution?

• Observations (n) = 88

• Sample mean (λ) = 47.18182

what would the 95% confidence look like for this?

With Normal Approximation, the 95% confidence interval is calculated as:

                47.18182 +/- 1.96* sqrt(47.18182/88)

This gives 45.7467, 48.617

With Exact method, we first need to calculate x (# of events):

                X = n * λ = 88 * 48.18182 = 4152

The compute the 95% confidence interval for X = 4152. This will give the 95% confidence interval for X as (4026.66, 4280.25)

The 95% confidence interval for mean (λ) is therefore:

lower bound = 4026.66 / 88 = 45.7575

upper bound = 4280.25 /88 = 48.6392

  

Example 2

Say that 14 events are observed in 200 people studied for 1 year and 100 people studies for 2 years. Calculate the 95% confidence interval for Poisson mean

In this example, the number of events (X) is given, the Poisson rate (λ) or mean needs to be calculated.

First step is to calculate the person year:

The person time at risk is 200 + 100 x 2 = 400 person years

The poisson rate / poisson mean (λ) is :

• Events observed = 14
• Time at risk of event = 400
• Poisson (e.g. incidence) rate estimate = 14/400 = 0.035

Normal Approximation: 95% confidence interval is calculated as: 

                0.035 +/- 1.96* sqrt(0.035/400)

This will give the 95% confidence interval of (0.0167, 0.0533)

Exact approach:  Calculate the 95% confidence interval for the number of events (X) using: 

(qchisq(0.025, 2*x)/2, qchisq(0.975, 2*(x+1))/2 )

and the result is: [7.65, 23.49]

Exact 95% confidence interval for Poisson mean is:

         Lower bound = 7.65 / 400 =0.019135 for lower bound and

         Upper bound = 23.49 / 400 = 0.058724 for upper bound

We will then say the Poisson mean is 0.035 with 95% confidence interval of (0.019, 0.059).

The following SAS programs can illustrate the calculations above: 

data normal;

  input lambda n ;

  lower = lambda - probit(0.975)*sqrt(lambda/n);

  upper = lambda + probit(0.975)*sqrt(lambda/n);

  datalines;

  47.18182 88

  0.035       400

;

proc print data=normal;

  title 'Normal Approximation for 95% confidence interval for Poisson mean';

run;

data exact;

  input X;

  lower = quantile('CHISQ',.025,2*x)/2;

  upper = quantile('CHISQ',.975,2*(x+1))/2;

  datalines;

 4152

 14

;

proc print data=exact;

  title 'Exact method for 95% confidence interval for Poisson mean';

run;

Intra-Subject Coefficient of Variation (CV%) for Sample Size Estimation for Crossover Design

To calculate the sample size for a crossover design for bioequivalence study, a key assumption is the intra-subject variation. The intra-subject variation is usually expressed with coefficient of variation (COV).

In sample size calculation software ‘PASS’, “Equivalence Test for Two Means in 2x2 Crossover Design - Specify Using Ratio” procedure requires COV (Coefficient of Variation) as the following:

COV (COEFFICENT OF VARIATION):“...For log-normal data, the following relationship exists: COV(Y) = SQR(Exp(SX*SX)-1) where SX is the square root of the within mean square error in the ANOVA table of the log-transformed values.” 

 In Sample size calculation software Nquery, “T-tests (TOST) of equivalence in ratio of means for crossover design (natural log scale)” procedure specifies that

“the square root of the mean square error is needed, the square root of the mean squared error can be obtained from the crossover ANOVA computed using the natural log scale. sqrt(MSE) is equal to s_d/sqrt(2), where s_d is the standard deviation of the period difference computed using the natural log scale. To compare results from this table to those in the Diletti, E., et al (1991) paper note that CV = sqrt(exp(s^2-1)”

Suppose we analyze the data using Proc Mixed as following:

proc mixed data=pk ;

    class sequence period treatment subject;

    model logauc = sequence period treatment;

    random subject(sequence);

    lsmeans treatment/pdiff cl alpha=0.1;

run;

Covariance parameter estimates in the SAS outputs will provide the information for calculating intra-subject coeffiicient. 

                                                                The Mixed Procedure
[...] 
           

Covariance Parameter Estimates
Cov Parm	Estimate
SUBJECT(SEQUENCE)	0.06800
Residual	0.1856

[...]

Here, Subject(Sequence) is the inter-subject variability s²_inter and residual the within-subject (or intra-subject) variability s²_within.

If we need to design a new study with crossover design, we will convert the intra-subject variability to CV for sample size calculation. CV_intra can be calculated with the formula CV=100*sqrt(exp(S²_within)-1) or CV=100*sqrt(exp(Residual)-1). From the table above, s²_within=0.1856, CV can be calculated as 45.16%

If we use Proc GLM (for a balanced study with no missing data) as specified below, the within-subject (or intra-subject) variability s²_within is the Mean Square Error (0.1856) – identical to the residual in Proc Mixed. Intra-subject CV is then calculated using CV=100*sqrt(exp(MSE)-1).

PROC GLM data=pk;

 CLASS trtsEQ period trtgrp patno;

 MODEL lauc = trtSEQ patno(trtSEQ) period TRtgrp; * TRtgrp*PERIOD;

 LSMEANS TRTgrp / PDIFF CL alpha=0.1;

RUN;

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	23	6.93036415	0.30132018	1.62	0.1387
Error	20	3.71219721	0.18560986
Corrected Total	43	10.64256136

Further Reading:

• Steven A. Julious (2004) TUTORIAL IN BIOSTATISTICS Sample sizes for clinical trials with Normal data
• Diletti et al (1991) Sample size determination for bioequivalence assessment by means of confidence intervals
• Helmut Schutz “Sample Size Calculation for BE Studies”
• Bioequivalence and Bioavailability Forum Intra subject CV%
• Intra-subject variation calculation
• Sample Size Estimation for (Bio)equivalence Testing Between Two Treatments
•  Statistical Terms

Analysis of 2x2x2 crossover design data: Proc Mixed or Proc GLM

In an early article "Cookbook SAS Codes for Bioequivalence Test in 2x2x2 Crossover Design", I provided the analysis using Proc Mixed model. There is a question about the necessity of using Proc Mixed while the Proc GLM can be used for analyzing the data from a 2x2x2 crossover design. As a matter of fact, FDA guidance  "Statistical Approaches to Establishing Bioequivalence” indeed mentioned the use of Proc GLM for analyzing the non-replicated Crossover Design:

b. Nonreplicated Crossover Designs

For nonreplicated crossover designs, this guidance recommends parametric (normal-theory) procedures to analyze log-transformed BA measures. General linear model procedures available in PROC GLM in SAS or equivalent software are preferred, although linear mixed-effects model procedures can also be indicated for analysis of nonreplicated crossover studies. For example, for a conventional two-treatment, two-period, two-sequence (2 x2) randomized crossover design, the statistical model typically includes factors accounting for the following sources of variation: sequence, subjects nested in sequences, period, and treatment. The Estimate statement in SAS PROC GLM, or equivalent statement in other software, should be used to obtain estimates for the adjusted differences between treatment means and the standard error associated with these differences.

Put it into the SAS statements, the SAS codes will be something like the following:

 PROC GLM data=pk;
    CLASS SEQUENCE PERIOD TREATMENT PATIENT;
    MODEL LogAUC = SEQUENCE PATIENT(SEQUENCE) PERIOD TREATMENT; 
    LSMEANS TREATMENT / PDIFF CL ALPHA=0.1;
RUN;

The SAS output below will provide the mean difference and its 90% confidence interval. Since the data is in log scale, anti-log of the mean difference (1.076) is the ratio of the geometric mean and anti-log of the 90% confidence interval is our 90% confidence interval for the geometric mean ratio (0.860, 1.346). 

Least Squares Means for Effect TREATMENT
i	j	Difference Between Means	90% Confidence Limits for LSMean(i)-LSMean(j)
1	2	0.073113	-0.150925	0.297152

If it is balanced design (i.e., there is no missing value) and all subjects have data available for period 1 and period 2, the results from the Proc GLM will be identical to teh results obtained from Proc Mixed as described in my previous article "Cookbook SAS Codes for Bioequivalence Test in 2x2x2 Crossover Design".

However, it is very often, there is possibility of missing data in one of the periods. In this case, if Proc GLM is used, the entire subject will be excluded from the analysis. If Proc Mixed is used, the subject who contributes only the data for one of the two periods will still be included in the analysis. 

Sending emails through SAS

I am not sure if there is any practical use for sending emails through SAS. But this SAS micro was picked up from RTP SAS User Group Email List and it works very well. The credit goes to Mr Ping Ling. 

 

 

 %macro sendemail(to=,cc=,subj=,msg1=,msg2=,msg3=,msg4=,msg5=,msg6=,msg7=,msg8=,attach=);
         FILENAME mail EMAIL (&to.)
         EMAILID='Microsoft Outlook'
         SUBJECT="&subj."
         %if &cc. ne %then %do;
           cc="&cc."
         %end;
         %if &attach. ne %then %do;
           attach="&attach."
         %end;
;
         %let today=%sysfunc(date(),date9.);

         DATA _NULL_;
           FILE mail;
           PUT "&today.";
           PUT;
           PUT "&msg1.";
           %do i=2 %to 8;
             %if &&msg&i. ne %then %do;
               %if %sysfunc(compress("&&msg&i."))="/n" %then %do; put; %end;
               %else %do; PUT "&&msg&i. "; %end;
             %end;
           %end;
           put;
         run;
%mend;

/*Example for using the macro
     %sendemail(to=%str('abc123@hotmail.com','xxx@gmail.com'),
                subj=%str(Sending email with SAS),
                msg1=%str(This is a test.),
                msg2=%str(/n),
                msg6=%str(xxxx)
                );

*/

Conference in Research Triangle Park, NC: TRENDS AND INNOVATIONS IN CLINICAL TRIAL STATISTICS (2014)

The research triangle area in North Carolina is one of the area with the concentrated talents in statistics and biostatistics. All three big universities (University of North Carolina, North Carolina State University, and Duke University) have great training programs in statistics and biostatistics. There are also many statisticians working in the pharmaceutical companies, biotech companies, CROs, and medical centers. Correspondingly, there should have been more conferences in clinical trial statistics.

The following conference is one that will be held at April 21-23, 2014 in Durham, North Carolina - the heart of the Research Triangle Park. 

Trends and Innovations in Clinical Trial Statistics (2014)

Link to the event homepage: http://biopharmnet.com/wiki/TICTS_2014 Link to the conference agenda: http://www.biopharmnet.com/doc/ticts2014.pdf Link to the event registration form: https://www.regonline.com/TICTS2014

FDA Guidance Webinar Series

FDA's Guidance Webinar series aims to foster collaboration and transparency in the development of guidance documents through direct outreach to affected stakeholders. The webinar series are free to the public and the past webinars are achieved for free access. These webinars are presented by senior FDA officers and the author/coauthor of the issued FDA guidance.

FDA's Guidance Webinar series

Since 2011, the following webinars have been conducted:

• CDER Small Business Webinar on Stability Guidance for ANDAs, and draft Questions and Answers guidance – considerations – November 4, 2013
• FDA Webinar: 60-Day Draft GFI On Antibacterial Therapies For Patients With Unmet Medical Need For The Treatment Of Serious Bacterial Diseases – September 27, 2013
• FDA Webinar: Draft GFI On Expedited Programs For Serious Conditions Drugs And Biologics - August 5, 2013
• FDA Webinar: Webinar Draft GFI on Human Immunodeficiency Virus-1 Infection: Developing Antiretroviral Drugs for Treatment; Availability - July 25, 2013
• FDA Webinar: Webinar Draft GFI On Rheumatoid Arthritis - Developing Drug Products For Treatment; Availability – July 25, 2013
• FDA Webinar: Draft Guidance For Industry On Alzheimer’s Disease: Developing Drugs For The Treatment Of Early Stage Disease; Availability - March 28, 2013
• FDA Webinar: Webinar Draft GFI On Enrichment Strategies For Clinical Trials To Support Approval Of Human Drugs And Biological Products – March 25, 2013
• FDA Webinar: New Draft Guidance on "FDA Guidance for Industry Webinar on Draft Guidance Vaginal Microbicides: Development for the Prevention of HIV Infection" - January 22, 2013
• FDA Webinar: 60-Day Draft Guidance on Using an Endpoint to Support Accelerated Approval of Drugs to Treat Early-Stage Breast Cancer - June 28, 2012
• FDA Webinar: New Draft Guidance on Safety Data Collection - March 27, 2012
• Guidance Webinar: Oversight of Clinical Investigations--A Risk-Based Approach to Monitoring - October 24, 2011

Overrunning Issue In Adaptive Design Clinical Trials

Adaptive designs have been more and more commonly used from early phase clinical trials to late phase pivotal clinical trials and from the limited therapeutic areas (such as oncology) to broad therapeutic areas. While adaptive design can have different forms (group sequential design,  seamless phase II/III design, sample size re-estimation, futility design,…), it all requires formal interim analyses with results to be reviewed by the independent Data Monitoring Committee. The rule for adaptation is pre-specified and the decision for adaptation is based on the interim analysis results.

In the phased clinical trials, the period between the analysis of phase II data and recruitment of phase III patients, is called “white space”. During the “white space” period, the results from early phase studies are digested and the additional time is needed for the study start up including regulatory submissions. The common perception is that with adaptive design such as seamless phase II/III design, the ‘white space’ can be eliminated – that is why the term ‘seamless’ is used in the first place. However, with adaptive design, the ‘white space’ may be shortened, not be eliminated. In studies with adaptive designs, there is usually no break in patient enrollment between the phases or stages or no break while preparing for the interim analysis. This brings in another issue – overrunning issue.

During the period while waiting for the endpoint data available for interim analysis, If the treatment duration is too long, too many patients would be randomized during the transition period – so called ‘overrunning’, which could result in inefficiencies and losing the benefits of the adaptive design. 

Recruitment rate relative to treatment data availability is the critical factor for overrunning. According to a paper by Judith Quinlan and Michael Krams (Implementing adaptive designs: logistical and operational considerations, the ideal ratio of recruitment / treatment duration is 4.

“As a rule of thumb we propose to establish whether the overall recruitment duration is at least four times the observational period required before the primary endpoint reads out in any one patient.  For example, in a stroke trial where each patient is observed over a period of 3 months, an adaptive design could be considered if the trial is open for recruitment for 12 months or longer.  This view may need to be modified, should there be a good early predictor of final outcome, allowing for the deployment of a longitudinal model.  For example, in acute stroke it might be possible to use early measurements of the stroke scale to predict final outcome (Grieve and Krams, 2005).  Should the early observation be a good predictor of the final outcome, we may consider using it in our assessment of weighing recruitment speed versus time needed before endpoint readout.  To formally establish the “optimal” recruitment speed, we propose to conduct clinical trial simulations, mimicking the potential real life environment of the trial and exploring the impact of longitudinal models.”

The overrunning issue was not discussed in FDA’s guidance “Adaptive Design Clinical Trials for Drugs and Biologicals”, however, it is discussed in EMA guidance “Reflection Paper In Methodological Issues in Confirmatory Clinical Trials Planned With an Adaptive Design”. Section 4.1.3 of this guidance has specific discussions about the overrunning issue. 

"4.1.3 Overrunning
In many clinical trials the primary endpoint is not observed immediately for each patient (e.g. survival or time to event data). Furthermore, in trials with a complex organisational structure, additional patients are likely to be randomised or some even followed to the primary endpoint before the results of a pre-planned interim analysis are known. If a trial is to be terminated as a result of an interim analysis it is always important to carry out an additional analysis including all of these further patients that did not contribute to the interim analysis. It may be that when this analysis is carried out, the null hypothesis can no longer be rejected and apparently decision making may depend on whether or not these so called overrunning patients are included or excluded from the analysis. In such a situation, it is accepted regulatory practice to base decision making on the final results of the trial (not the interim analysis). This is also in accordance with the intention to treat principle that all randomised patients should be analysed. Obviously, overrunning patients need to be treated and observed according to the protocol and due attention should be given to this at the planning stage of the trial.

A full discussion of the results of a trial should be based on estimates of the treatment effect rather  than simply on P-values alone. If the estimate of the treatment effect including the overrunning patients is not very different from that excluding them, then a small increase in the P-value might not be regarded as a concern. An important reduction in the size of the point estimate might, in contrast, lead to reluctance to accept the overall result as “positive”, especially as, unless a trial is stopped very early, the proportion of overrunning patients will usually be sufficiently small such that the estimate of the treatment effect should not be substantially altered. In all cases, results including and excluding the overrunning patients should be presented and differences between these two analyses should be discussed.”

The overrunning issue is discussed in many adaptive clinical trial implementations. Here are some of them:

•  Introduction to Adaptive Designs by Werner Brannath
• Pitfalls in Clinical Trials Using Adaptive Design by Thomas Zwingers
• Monitoring Continuous Long-Term Outcomes in Adaptive Designs by Kirsten Wust & Meinhard Kieser
• On the efficiency of adaptive designs for flexible interim decisions in clinical trials by Werner Brannath et al

Archives of Webcast and Presentation Slides for Public Workshop on Complex Issues in Developing Drug and Biological Products for Rare Diseases

To meet the requirements by PDUFA V and FDASIA, FDA organized a public workshop on "Complex Issues in Developing Drug and Biological Products for Rare Diseases".

The webcast and presentation slides for this public workshop are accessible to the public for free.

To access the Webcase and presentation slides for this workshop, please follow the link below:

Complex Issues in Developing Drug and Biological Products for Rare Diseases

Free Webinar by FDA on the final guidance for industry Electronic Source Data in Clinical Investigations

On Wednesday, January 29, 2014, from 2:00PM - 3:00PM EST, FDA will present a webinar on the final guidance for industry Electronic Source Data in Clinical Investigations.

• FINAL GUIDANCE: Electronic Source Data In Clinical Investigations (Procedural) 
• Federal Registration FR NOA 

SUMMARY: The Food and Drug Administration (FDA) has announced the availability of a final guidance for industry titled “Electronic Source Data in Clinical Investigations.” This final guidance provides recommendations to sponsors, Contract Research Organizations (CROs), clinical investigators, and others involved in the capture, review, and retention of electronic source data in FDA-regulated clinical investigations. In an effort to streamline and modernize clinical investigations this guidance promotes capturing source data in electronic form, and it is intended to assist in ensuring the reliability, quality, integrity, and traceability of data from electronic source to electronic regulatory submission.

Guidance Webinar Online-Access Instructions: To access this webinar, follow the link provided below. Audio will broadcast from your computer speakers.

After following the link, enter as a guest and provide your FULL NAME and organization (i.e. "John Smith - FDA/CBER"). The host will then allow you to enter. If you experience technical difficulties email Jeffery.Rexrode@fda.hhs.gov for assistance. Closed captioning will be provided.
Questions/Comments can be submitted live via a Q/A chat window.

Webinar Access link: https://collaboration.fda.gov/guidancewebinars

SPEAKERS:
        Leonard V. Sacks, MD
        Associate Director
        Office of Medical Policy
        Center for Drug Evaluation and Research
        Food and Drug Administration

        Ron Fitzmartin, PhD, MBA
        Office of Strategic Programs
        Center for Drug Evaluation and Research
        Food and Drug Administration

        Jonathan S. Helfgott, MS
        Associate Director for Risk Science (Acting)
        Office of Scientific Investigations
        Center for Drug Evaluation and Research
        Food and Drug Administration

Artistic and Creative Way in Naming a New Drug

We all may have difficulties in remembering the drug names and wonder why many drug names are so awkward and difficult to read. For drug makers, finding a name is more art than science. For a new drug, the proprietary name or brand name needs to reflect certain features.

“Want to sound high-tech? Go for lots of Z's and X's, such as Xanax, Xalatan, Zyban and Zostrix.

Want to sound poetic? Try Lyrica, Truvada and Femara.

Want to suggest what it does? Flonase is an allergy medicine that aims to stop nasal flow. Lunesta, a sleeping drug, implies "luna," the Latin word for moon — a full night's sleep.

Then there's Viagra, the erectile-dysfunction drug made by Pfizer. It uses the prefix "vi" to suggest vigor and vitality. The word rhymes with Niagara, suggesting a mighty flow.”

On the other hand, the proprietary name for a new drug is closely regulated to avoid the similar names that may cause the medical errors. For example, in an article "This Is How Easy It Is to Pick Up the Wrong Prescription Drug", the similar drug names increases the chances for making mistakes in prescribing and in pharmacy. In US, FDA needs to approve the proprietary names of prescription drugs.

“New prescription drugs approved by FDA have both a scientific name, known as the generic (also called the established name), and a name given by the manufacturer, known as the proprietary name (also called the brand name or trade name).  Before a drug is approved by FDA, the Agency will carefully review the proposed proprietary name.  

It is important for safety reasons that the written proprietary name not look like that of another proprietary name nor sound like another proprietary name when spoken.  If there is similarity between the proprietary name of a new prescription drug and the proprietary name of an existing drug, a mix-up could occur in ordering and a patient could receive one drug instead of the other. FDA’s Division of Medication Error Prevention and Analysis is responsible for proprietary name review prior to approval in the Center for Drug Evaluations and Research.  If a company submits a name that is too similar to another name, FDA will require the company to select another name, for safety reasons, as part of the approval process. “

See the following links for more discussion:

• Drug name confusion: FDA regulations and pharma create bizarre new names
• How FDA review Proposed Drug Names?
• FDA guidance: Contents of a Complete Submission for the Evaluation of Proprietary Names
• PhRMA demands an overhaul of FDA's regs on drug names

Recently, the United Therapeutics is very creative in naming their new drug. They simply used their CEO’s name (backward) for their new drug in treating the pulmonary hypertension. The new drug name Orenitram is Martine Ro. backward. And that would be the name of Martine Rothblatt, United Therapeutics’ founder/CEO and one of the most captivating people in the biotechnology industry.

• This Drug Company CEO Just Named Her New Drug After Herself
• Drugmaker Names Pill After CEO Who Sought Daughter's Cure
• CEO of drug company in RTP names new drug after herself

Quantification of Risk – Breaking down adverse reaction into common and uncommon categories

When we conduct a clinical trial using an approved product, we may run into the requests for the list of common, very common adverse events. This may be especially true when the clinical trials are conducted in European countries. The requests may come from the IRB (institutional review board) or EC (ethics committee).

Breaking down the AEs into very common, common, uncommon, rare, and very rare categories is part of the requirements for SmPC (product label in EU countries). The requirements are included in various EC or EMA guidelines

A GUIDELINE ON SUMMARY OF PRODUCT CHARACTERISTICS (2005) stated:

Within each system organ class, the ADRs should be ranked under headings of frequency, most frequent reactions first, using the following convention:
 Very common (greater than and equal to 1/10); common (greater than and equal to 1/100 to less than 1/10); uncommon (greater than and equal to 1/1,000 to less than 1/100); rare  (greater than and equal to 1/10,000 to less than 1/1,000); very rare (less than and equal to 1/10,000), not known (cannot be estimated form the available data).

A GUIDELINE ON SUMMARY OF PRODUCT CHARACTERISTICS  (SmPC) 2009 stated:

Within each system organ class, the adverse reactions should be ranked under headings of frequency, most frequent reactions first. Within each frequency grouping, adverse reactions should be presented in the order of decreasing seriousness. The names used to describe each of the frequency groupings should follow standard terms established in each official language using the following convention: Very common (≥1/10); common (≥1/100 to <1/10); uncommon (≥1/1,000 to <1/100); rare (≥1/10,000 to <1/1,000); very rare (<1/10,000). 

An EMA presentation specifically discussed what the Section 4.8: Undesirable effects should include in terms of quantifying the adverse drug reactions.

There are plenty of examples for showing how the adverse drug reaction tables in Summary of Product Characteristics should be presented.

• Cimzia 200 mg solution for injection
• Avastin 25 mg/ml concentrate for solution for infusion.
• Example SmPC - European Medicines Agency - Europa

In the recent issued EMA guidance for Fibrin Sealant, it also requires to breakdown the AEs into the following categories:

Tabulated list of adverse reactions

The table presented below is according to the MedDRA system organ classification (SOC and Preferred 265 Term Level).  

Frequencies have been evaluated according to the following convention: Very common (greater than and equal to 1/10); common (greater than and equal to 1/100 to less than 1/10); uncommon (greater than and equal to 1/1,000 to less than 1/100); rare (greater than and equal to 1/10,000 to less than 1/1,000); very rare (less than 1/10,000), not known (cannot be estimated from the available data).

The source for the quantification of risk for adverse reactions is the CIOMS. For example, Benefit-Risk Balance for Marketed Drugs: Evaluating Safety Signals Report of CIOMS Working Group IV has a section for “quantification of risk”

5. Quantification of Risk Incidence of the reaction

To put the newly identified risk into perspective, it is important to quantify it in terms of incidence. Precise quantification will usually be difficult in the post-marketing environment, in which most new safety signals arise from spontaneous reporting, with its associated uncertainties as to numerators (reported cases) and denominators (patient exposures). However, risk can often be approximated in terms of magnitudes of 10, as suggested in the CIOMS III report: greater than 1% (common or frequent); greater than 1 per 1000 but less than 1 per cent (uncommon or infrequent); greater than 1 per 10,000 but less than 1 per 1000 (rare); less than 1 per 10,000 (very rare). 

When possible, attempts should be made to determine whether the incidence is affected by the existence of any apparent high-risk groups. These might be defined by, for example, dose or duration of treatment, use of other drugs (e.g., drug interactions), presence of other diseases (e.g., renal failure), or special populations defined by demographics or ethnicity. In principle, one of the most important functions of risk evaluation is to identify individual patients at increased risk of serious adverse reactions. Although some mechanisms are fairly well understood (enzyme inhibition processes; drug interactions), the pharmacological and biological basis of drug-induced diseases (e.g., role of pharmacogenetics) is relatively unexplored. Work in this area is needed and should be encouraged.

In US, when we prepare the summary tables for adverse events or adverse drug reactions, we typically don’t include a table to break down the frequency into very common, common, uncommon, rare and very rare categories. The drug label did not require to include the quantification of risk using these categories. However, for drug to be approved in European countries, it is a good idea to include a summary table with these quantification categories. 

Pharmacokinetic studies when endogenous compounds exist and pre-dose concentrations are not zero

This Monday, FDA issued a new guidance titled “ Bioequivalence Studies with Pharmacokinetic Endpoints for Drugs Submitted Under an ANDA”. While the guidance is more for bioequivalence studies for generic drugs, a paragraph on Endogenous Compounds caught my eyes:

E. Endogenous Compounds
 Endogenous compounds are drugs that are already present in the body either because the body produces them or they are present in the normal diet. Because these compounds are identical to the drug that is being administered, determining the amount of drug released from the dosage form and absorbed by each subject can be difficult. We recommend that applicants measure and approximate the baseline endogenous levels in blood (plasma) and subtract these levels from the total concentrations measured from each subject after the drug product has been administered. In this way, you can achieve an estimate of the actual drug availability from the drug product. Depending on whether the endogenous compound is naturally produced by the body or is present in the diet, the recommended approaches for determining BE differ as follows:  When the body produces the compound, we recommend that you measure multiple baseline concentrations in the time period before administration of the study drug and subtract the baseline in an appropriate manner consistent with the pharmacokinetic properties of the drug.
  When there is dietary intake of the compound, we recommend that you strictly
control the intake both before and during the study. Subjects should be housed at a
clinic before the study and served standardized meals containing an amount of the
compound similar to that in the meals to be served on the pharmacokinetic sampling day.
 For both of the approaches above, we recommend that you determine baseline concentrations for each dosing period that are period specific. If a baseline correction results in a negative plasma concentration value, the value should be set equal to 0 before calculating the baseline-corrected AUC. Pharmacokinetic and statistical analysis should be performed on both uncorrected and corrected data. Determination of BE should be based on the baseline-corrected data.

When we study the therapeutic proteins, we often need to deal with the endogenous concentration issue. Studies using human plasma derived products (proteins) will always involve in the endogenous concentration issue since these therapeutic proteins are naturally occurring substances and are already present in the body. The pharmacology studies for these therapeutic proteins need to consider both the endogenous (already in the body) and exogenous (through augmentation) concentrations. In a book “Clinical pharmacology of therapeutic proteins” by Dr Mahmood, three approaches are discussed to deal with this issue:

1. subtract the pre-dose concentration – baseline-corrected pharmacokinetic analysis
2. using the sum of exogenous and endogenous proteins following the administration of exogenous protein – uncorrected pharmacokinetic analysis;
3. the use of radio-labeled proteins to differentiate the exogenous proteins from the endogenous proteins.

For a bioequivalence study, it is easier to show the bioequivalence with approach #2 above.

When using baseline-corrected pharmacokinetic analyses, the accurate measure of the pre-dose concentration is important. If all possible, there should be multiple measures at pre-dose and then mean value of the pre-dose measuresments can be used as the baseline for correction.

In FDA’s Draft Guidance on Progesterone, it has the following comments regarding the baseline-correction.

 Please measure baseline progesterone levels at -1.0, -0.5, and 0 hours before dosing. The mean of the pre-dose progesterone levels should be used for the baseline adjustment of the post-dose levels. Baseline concentrations should be determined for each dosing period, and baseline corrections should be period specific. If a negative plasma concentration value results after baseline correction, this should be set to 0 prior to calculating the baseline-corrected AUC. Please analyze the data using both uncorrected and corrected data.

  

In a clinical pharmacology review document for a Factor XIII Concentrate, the sponsor presented the pharmacokinetic parameters based on baseline adjusted FXIII activity (Berichrom assay) and  also the pharmacokinetic parameters based on un-adjusted FXIII activity.

In summary, while both baseline-adjusted and unadjusted PK analyses are viable approaches in dealing with the existence of endogenous concentrations, the baseline-adjusted PK analyses are the safer approach to go. In this approach, the pre-dose concentration or average pre-dose concentration will be subtracted from all post-dose concentration measures before the PK parameters (for example AUC) are calculated.