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Bio/pharma quarterly journal

Bio/Pharma Quarterly Journal
Volume 10, Issue 4
December, 2004
Division of Bio/Pharmaceutical Sciences Society of Chinese Bioscientists in America (SCBA) Princeton, NJ 08643
Chief Editor

Lu-Hai Wang, Ph.D.
Mount Sinai School of Medicine
E-mail:[email protected]
TEL: (212) 241-3795
FAX: (212) 534-1684
Editors

Flora W. Feng, Esq.
Mintz, Levin, Cohn, Ferris, Glovsky & Popeo, P.C. [email protected] Guanghan Liu, Ph.D. Merck & Co. Inc. [email protected] Yanan Jenny Luo, Ph.D. Hogan & Hartson L.L.P. [email protected] Peng Qu, Ph.D. Forest Laboratories, Inc. [email protected] Mark Tang, Ph.D. World Technology Ventures [email protected] Sunny Tam, Ph.D. Charles River Laboratories Wei Zhang, Ph.D. Harvard Square Consulting, Inc. Production Executives

Lai Shun Chen, Ph.D.
Bristol-Myers Squibb Co. [email protected] Kuoping Chen, Mr. Genzyme Genetics [email protected]
Editorial
Message from Editorial Committee Limited Use of Cox-2 Inhibitors Drug Approved for Treating Mucositis Temporary Artificial Heart Approved Vaccine Clinical Trials – A Statistical Primer Message from the Editorial Committee
This issue of the Quarterly features a specialized article on " Vaccine Clinical Trials – A Statistical Primer " by Devan V. Mehrotra, Ph.D., Merck Research Laboratories. Dr. Mehrotra clearly and concisely lays out the statistical issues during the course of different phases of clinical trial for the vaccine development including pre- and post-license stages. The article should be quite informative and useful for those who are involved in the clinical trials of developing vaccines. As always, we are most grateful to the authors who have generously donated their time and efforts in writing the specialized articles for the Quarterly. It is the wish of the editorial
board that through this forum, our readers can be better informed and broadening their vision on
various interesting subjects in biotechnology and pharmaceutical sciences. It is also in this spirit
that the editorial board sincerely calls upon our members' help to further develop and enrich this
territory belonging to all of us. Your input in opinions and contribution of publication materials
for the Quarterly are most appreciated. You can reach any member of the editorial board for
your input. We urgently need volunteers willing to contribute the specialized articles.
******************************************
From Chief Editor
As the chief editor of Quarterly for the past two years, I am hereby announcing to resign from my post after the June 2005 issue. I sincerely call upon your suggestion of candidates for chief editor and members of the editorial committee. What Is New?
Media Inquiries: 301-827-6242 Consumer Inquiries: 888-INFO- December 23, 2004 FDA Issues Public Health Advisory Recommending Limited Use of Cox-2
Inhibitors
Agency Requires Evaluation of Prevention Studies Involving Cox-2 Selective
Agents
The Food and Drug Administration (FDA) today issued a Public Health Advisory summarizing the agency's recent recommendations concerning the use of non-steroidal anti-inflammatory drug products (NSAIDs), including those known as COX-2 selective agents. The public health advisory is an interim measure, pending further review of data that continue to be collected. In addition, FDA today announced that it is requiring evaluation of all prevention studies that involve the Cox-2 selective agents Celebrex (celecoxib) and Bextra (valdecoxib) to ensure that adequate precautions are implemented in the studies and that local Institutional Review Boards reevaluate them in light of the new evidence that these drugs may increase the risk of heart attack and stroke. A prevention trial is one in which healthy people are given medicine to prevent a disease or condition (such as colon polyps or Alzheimer's disease). FDA is issuing an advisory because of recently released data from controlled clinical trials showing that the COX-2 selective agents (Vioxx, Celebrex, and Bextra) may be associated with an increased risk of serious cardiovascular events (heart attack and stroke) especially when they are used for long periods of time or in very high risk settings (immediately after heart surgery). Also, as FDA announced earlier this week, preliminary results from a long-term clinical trial (up to three years) suggest that long-term use of a non-selective NSAID, naproxen (sold as Aleve, Naprosyn and other trade name and generic products), may be associated with an increased cardiovascular (CV) risk compared to placebo. Although the results of these studies are preliminary and conflict with other data from studies of the same drugs, FDA is making the following interim recommendations: Physicians prescribing Celebrex (celecoxib) or Bextra (valdecoxib), should consider this emerging information when weighing the benefits against risks for individual patients. Patients who are at a high risk of gastrointestinal (GI) bleeding, have a history of intolerance to non-selective NSAIDs, or are not doing well on non-selective NSAIDs may be appropriate candidates for Cox-2 selective agents. Individual patient risk for cardiovascular events and other risks commonly associated with NSAIDs should be taken into account for each prescribing situation. Consumers are advised that all over-the-counter (OTC) pain medications, including NSAIDs, should be used in strict accordance with the label directions. If use of an (OTC) NSAID is needed for longer than ten days, a physician should be consulted. Non-selective NSAIDs are widely used in both over-the-counter (OTC) and prescription settings. As prescription drugs, many are approved for short-term use in the treatment of pain and primary dysmenorrhea (menstrual discomfort), and for longer-term use to treat the signs and symptoms of osteoarthritis and rheumatoid arthritis. FDA has previously posted extensive NSAID medication informatio. FDA is collecting and will be analyzing all available information from the most recent studies of Vioxx, Celebrex, Bextra, and naproxen, and other data for COX-2 selective and nonselective NSAID products to determine whether additional regulatory action is needed. An advisory committee meeting is planned for February 2005, which will provide for a full public discussion of these issues. FDA urges health care providers and patients to report adverse event information to FDA via the MedWatch program by phone (1-800-FDA-1088), by fax (1-800-FDA-0178), or by the Internet at . The Public Health Advisory is available . Media Inquiries: 301-827-6242 Consumer Inquiries: 888-INFO- December 15, 2004 New Biotechnology Drug Approved to Treat Mucositis Associated with Cancer
Treatments
The Food and Drug Administration (FDA) today approved a new intravenous biologic product, palifermin (trade-name Kepivance) to help reduce the chance that certain cancer patients, those with blood cancers undergoing chemotherapy and radiation in preparation for bone marrow transplants, will develop mucositis. Palifermin also shortens the duration of the condition. Mucositis (painful sores and ulcers in the lining of the mouth) is a common complication of the high-dose chemotherapy and radiation therapy regimens associated with bone marrow transplant. Patients suffering from mucositis have difficulty eating and swallowing. In the most severe form of the condition, patients cannot eat or drink at all and must receive nutrition and fluid replacement through their veins. Palifermin is a man-made version of a naturally occurring human protein called keratinocyte growth factor (KGF). KGF stimulates the growth of cells in the skin and on the surface layer of the mouth, stomach and colon. Palifermin, like the natural KGF, also stimulates cells on the surface layer of the mouth to grow. This is thought to lead to faster replacement of these cells when killed by the cancer treatments and is believed to speed up the healing process of mouth ulcers. In a study of 212 patients with leukemia or lymphoma who were receiving high doses of chemotherapy and radiation treatments associated with bone marrow transplantation, 98% of the patients who did not receive palifermin developed severe mucositis compared to 63% of those who received the drug. Also, for those who received the drug, severe mucositis lasted an average of three days, compared to nine days for those receiving a placebo. Palifermin was given intravenously for three days before cancer treatment began and three days following the treatment. The most common side effects of palifermin were skin rash, unusual sensations in the mouth, such as tingling, and increases in blood proteins suggesting pancreatic irritation. No serious side effects have been reported related to use of palifermin. Palifermin has not yet been shown to be safe and effective in patients being treated for forms of cancer other than leukemia or lymphoma. Palifermin will be marketed with the trade-name Kepivance and is manufactured by Amgen Inc., Thousand Oaks, Calif. Media Inquiries: 301-827-6242 Consumer Inquiries: 888-INFO- November 3, 2004 FDA Announces Guidance for Generic Drugs
The Food and Drug Administration (FDA) announced today that a Guidance for Industry entitled "Listed Drugs, 30-Month Stays, and Approval of ANDAs and 505(b)(2) Applications Under Hatch-Waxman, as Amended by the Medicare Prescription Drug, Improvement, and Modernization Act of 2003: Questions and Answers" is being made available at The Medicare Prescription Drug, Improvement, and Modernization Act of 2003 (MMA) made significant changes to the generic drug approval process designed to provide more certainty to the generic drug approval process and help get generic drugs to the market more quickly. As indicated in our March 3, 2004, Federal Register notice (69 FR 9982), FDA has been considering what steps to take in light of the passage of the MMA. This guidance is one step. As directed by the MMA, this document provides guidance on the definition of a listed drug. A listed drug is required to be referenced in a generic application and indicates the approved drug the generic company is relying upon for approval of its version of the product. The guidance is intended to clarify when a change to a generic application should reference a different listed drug from the listed drug referenced in the original generic application, and thus be made through the submission of an entirely new application that encompasses the desired change. The document also provides guidance to industry on certain sections of the MMA that significantly change provisions of the Food, Drug, and Cosmetic (FD&C) Act that were originally added by the Drug Price Competition and Patent Term Restoration Act of 1984 (Public Law 98-417) (Hatch-Waxman). These provisions affect the Act's 30-month stay of approval of a generic or section 505(b)(2) application upon the filing of a patent infringement suit and the 180-day exclusivity periods available to the first generic applicants to challenge innovator patents. This guidance clarifies changes made by the MMA with respect to (1) the availability and termination of 30-month stays of approval of generic and section 505(b)(2) applications, (2) requirements for notice of patent certifications (paragraph IV certifications) by generic and section 505(b)(2) applicants, and (3) the 180-day exclusivity for "first" generic applicants. The guidance also explains the various effective dates that apply to the MMA's generic drug provisions. Media Inquiries: 301-827-6242 Consumer Inquiries: 888-INFO- October 18, 2004 FDA Approves Temporary Artificial Heart
The Food and Drug Administration (FDA) has approved a partial artificial heart intended to keep people alive in the hospital while they are awaiting a heart transplant. The product is a pulsating bi-ventricular device that is implanted into the chest to replace the patient's left and right ventricles (the bottom half of the heart). The implanted device is sewn to the patient's remaining atria (the top half of the heart). Hospitalized patients are connected by tubes from the heart through their chest wall to a large power-generating console, which operates and monitors the device. The heart is manufactured by Syncardia Systems Inc., of Tucson, Ariz. It is intended as a "bridge to transplant" for people waiting for a heart transplant who do not respond to other treatments and are at risk of imminent death from non-reversible bi-ventricular failure, i.e. people with both left and right side heart failure, and who are eligible for a heart transplant. FDA approved the Syncardia device based on a review of clinical studies of safety and effectiveness conducted by the firm and on the recommendation of an outside panel of experts convened by FDA to review the device. The firm studied use of the artificial heart in 81 transplant-eligible patients with severe bi-ventricular heart failure at five medical centers in the United States. In the studies, 79 percent of patients implanted with the heart remained alive long enough to receive a donor heart (an average of 79 days), demonstrating that the artificial heart could successfully serve as a bridge to transplant. Complications included infection (72% of patients), bleeding (42%), neurological event such as major or minor stroke (25%) and device malfunctions (18%). Seventeen patients in the study died before a donor heart became available. About 4,000 patients in the United States await heart transplants annually. Only about 2,200 donor hearts typically become available. About 100 of the 4,000 patients awaiting transplants have non-reversible bi-ventricular failure and could be candidates for the new artificial heart. FDA is requiring the firm to conduct a post-approval study to monitor the device's performance in commercial use. Specialized Articles
Vaccine Clinical Trials – A Statistical Primer
Devan V. Mehrotra, Ph.D. Merck Research Laboratories, UN-A102, 785 Jolly Road, Blue Bell, PA 19422 E-mail: [email protected]
1. Introduction
The remarkable success of many vaccines and their impressive safety record, along with the
eradication of smallpox are regarded amongst the greatest public health achievements of the 20th
century. Statisticians have contributed (and continue to contribute) significantly toward the
research and development of vaccines worldwide. In this article, we discuss some of the
statistical issues that arise in all phases of vaccine development, and, where necessary, contrast
drug and vaccine clinical trials. A more detailed treatment of this subject is provided by Chan,
Wang and Heyse [1].
In the past three decades, there has been an incredible transformation in our understanding of the
human immune system and its functions. While statisticians working on vaccine clinical trials
are not expected to keep abreast with the latest advances in cellular and molecular immunology,
understanding of the basics is essential for proper development of design and analysis strategies.
Accordingly, before moving on to statistical issues, we provide a brief review of basic
immunology. For more advanced reading, see Abbas, Lichtman and Pober [2].
There are two forms of immunity - innate and adaptive. Innate immunity, the principal
components of which include blood proteins and phagocytic cells, provides the first line of
defense against microbes (bacteria, viruses, parasites, fungi, etc.). The pathogenicity of microbes
is related to their ability to defeat the soldiers of innate immunity. The other form of immunity is
called adaptive (or specific) immunity, and evolves as a response to infection. There are two
types of adaptive immunity: humoral and cellular. Until the 1970s, only humoral immunity had
been well understood. It is mediated by antibodies that primarily defend against extracellular
microbes. Specifically, recognition of microbes triggers white blood cells called B cells to
multiply and secrete antibodies that destroy microbes before they infect host cells. In 1996, two
microbiologists (Peter Doherty and Rolf Zinkernagel) won a Nobel Prize for deciphering how
the cellular immune system works. It is mediated by white blood cells called T cells that defend
against intracellular microbes. Specifically, T cells (mostly CD8+ T cells) seek out and destroy
cells that have already become infected with the specific microbe. T cells can detect the
presence of intracellular microbes because infected cells display on their surfaces peptide
fragments derived from the pathogen's proteins. The foreign proteins are delivered to the cell
surface by specialized host cell glycoproteins called MHC or HLA molecules. The adaptive
immune system "remembers" each encounter with a specific microbe, through the establishment
of memory B and/or T cells. Subsequent microbe-specific encounters stimulate increasingly
effective defense mechanisms, and this immunological memory serves as the basis of protective
vaccination against microbes.
Virtually all vaccines in use today have been licensed using antibody-based endpoints. More
recently, research has intensified on developing vaccines that stimulate cellular immunity (or
both). But regardless of whether the vaccine is intended to induce humoral or cellular immunity, the operational goal of vaccination is the same: to simulate a microbe-specific exposure so that the host's immune system will generate a pool of memory B and/or T cells to protect against potential real exposures later on. The simulation is accomplished via inoculation of the host by a vaccine that contains either a weakened version of the microbe, or a DNA plasmid or viral vector encoding certain gene(s) of the microbe, and so on. Understanding the "mechanism of action" of the vaccine is critical for identifying appropriate study endpoints and statistical analyses in clinical trials. For example, several T cell mediated immunity-based vaccines targeted against HIV-1 are currently being developed worldwide. Such vaccines may not prevent acquisition of HIV-1 infection, but will hopefully prevent or significantly delay the progression to AIDS among subjects who become infected despite vaccination. From a statistical perspective, this poses a plethora of challenges for the design and analysis of current HIV-1 vaccine trials, including the selection of study endpoints. In the following sections, we provide an overview of the key statistical issues in each phase of vaccine development. 2. Preclinical phase
Before a vaccine can be tested in humans, it undergoes extensive testing in animals. This is
similar to what is done in the preclinical phase for drugs. However, for vaccines there is
additional emphasis on the development and validation of bioassays to measure the
immunogenicity of the vaccine, i.e., the ability of the vaccine to induce specific immune
responses. The statistical characteristics of an ideal assay include accuracy, unbiasedness,
reliability, reproducibility, precision, and ruggedness. In addition, a good assay should have high
levels of specificity and sensitivity for the hypothesized biomarker of interest (antibody level, T
cell response, etc.). Standard statistical tools used in assay development and validation include
classic design of experiments (e.g., D-optimal factorial designs), linear and non-linear regression,
the four parameter logistic model, concordance correlation, and variance component models.
Schofield [3,4] provides an excellent overview of this topic.
An important by-product of the assay validation process is identification of what constitutes a
positive (or perhaps more accurately, a non-negative) response to vaccination for each biomarker
of interest. The positivity criterion is often (but not always) one dimensional, such as the 99.9th
percentile of the estimated distribution of biomarker responses in the absence of vaccination. In
such a case, the vaccine is considered minimally immunogenic for a given subject if his or her
biomarker response is greater than the positivity cut-off. Note that this does not necessarily
imply that the vaccine will subsequently provide protection from infection and/or disease for that
subject. Often times, the response has to be notably higher than the positivity immunogenicity
cut-off for the vaccine to induce a protective effect; we revisit this issue in section 4.
Vaccines are advanced to phase I clinical testing if they are deemed to be generally safe in
animals, and for which an adequate proportion of animals exhibit a minimally immunogenic
post-vaccination response.
3. Phase I (clinical safety and immunogenicity)
Phase I vaccine clinical trials are small, typically enrolling 30 to 100 human volunteers across multiple investigational centers. They are usually double-blind, placebo controlled trials that study different doses and/or vaccination schedules of the experimental vaccine. The primary focus is on safety and tolerability, but the trials are designed to also provide preliminary assessments of immunogenicity. Note that drug trials typically enroll healthy subjects in phase I, but move to the target population (patients requiring treatment) in phase II and beyond. In contrast, vaccine trials, not surprisingly, involve healthy volunteers in all phases of development. Exceptions include so-called "therapeutic vaccination" studies, which are not discussed here. The statistical challenges there are even greater, since it is difficult to quantify and conclusively demonstrate the benefits of vaccination in subjects that are already infected with the microbe of interest. Safety in phase I is commonly summarized using the incidence of serious vaccine-related adverse events (if any), along with data on injection-site reactions, body temperatures, systemic adverse events, and laboratory measures. The sparseness of safety data from an individual phase I trial make them more suited for descriptive rather than formal inferential statistical analyses. The decision to proceed to a subsequent trial is therefore based primarily on sound clinical judgment, with input from a safety evaluation committee (if necessary), and regulatory agencies such as the Center for Biologics Evaluation and Research (CBER) for US-based trials. While statisticians may have a smaller role for safety analyses in phase I, they play a pivotal role in the analysis of immunogenicity. Two types of immunogenicity summaries are reported for the biomarker(s) of interest: the proportion of subjects with a post-vaccination response above the predefined positivity cut-off ("responders"), and the (geometric) mean post-vaccination biomarker response. The small sample sizes in phase I trials pose a multitude of statistical challenges for analyzing immunogenicity. Some of these are readily tackled using a prudent selection of methods from the statistician's existing tool kit. Others present opportunities for innovative analytical solutions and further methodological research. Some of the key statistical issues encountered in phase I analyses of immunogenicity are discussed below under subheadings. Cross-validation of "positivity" criterion As mentioned earlier, what represents a "positive" response to vaccination is determined before phase I clinical trials are begun, in conjunction with the assay validation for the biomarker of interest. It is important to use the accumulating immunogenicity data to either confirm the validity of the positivity criterion, or modify it if necessary. For example, Mogg et al [5] used baseline (pre-vaccination) responses from 559 subjects to cross-validate the two dimensional positivity criterion for the HIV-1 gag specific ELISPOT assay that had been established before phase I clinical trials began. Specifically, they used binomial score intervals, robust parametric methods, and non-parametric density estimates with bootstrap-based confidence intervals to estimate the proportion of "non-responders" that are incorrectly classified as "responders". All three methods converged to a common conclusion, namely that the false positive rate associated with the ELISPOT positivity criterion used by Merck Research Laboratories is estimated to be less than 1% with high confidence. Stratification Stratification is often used in vaccine clinical trials; either pre-stratification at the enrollment stage, or post-stratification at the time of analysis. Interestingly, investigational center is rarely used as a stratification factor in phase I because of the small (sometimes zero) sample size per treatment group at each center. Instead, stratification is limited to one or two key prognostic factors that are likely to influence the response to vaccination in a systematic way. For example, it is well-known that the ability of a vaccine to induce an antibody-based immune response diminishes with increasing age. Failure to incorporate this important information at either the design or analysis stage can result in a biased and/or inefficient statistical analysis, particularly for small trials! The summary table below reinforces this point. In this hypothetical phase I trial, vaccine A is observed to be more immunogenic than vaccine B for both younger (18-45 years) and older (> 45 years) subjects. However, a naïve "pooling" of the results, i.e., failing to adjust for an age effect, yields a result which paradoxically suggests that vaccine B is better! Hypothetical Data (% Responders) An overview of stratification issues in clinical trials, including references to some recently developed analytic strategies, is provided elsewhere (Mehrotra [6], [7]). The key point here is that stratification-based adjustment for prognostic factors is important for phase I vaccine trials, particularly since the sample sizes are quite small. Minimum effective dose As mentioned earlier, phase I vaccine trials often involve multiple dose levels of a vaccine. Interest lies in quantifying the dose-response association, and in identifying the smallest dose that provides adequate immunogenicity. It is usually (but not always) expected that, within the range of doses studied, a higher dose of the vaccine will be at least as immunogenic as a lower dose. Given the small sample sizes in phase I, it is important to use statistical methods that capitalize on this additional biological information to help identify the minimum effective dose. For example, consider the analysis of response proportions. A simple way to proceed is to compare each dose group with placebo using an exact score test for two independent binomials (Suissa and Shuster [8]), and assess the resulting p-values for statistical significance after a multiplicity adjustment (Dunnett [9], Hochberg [10], etc.). However, a more efficient way is to use a step-up trend testing strategy, such as an exact Cochran-Armitage trend test [11-12] embedded within the NOSTATSOT closed-testing procedure (Tukey, Ciminera and Heyse [13]). The gains in statistical efficiency using a trend testing approach over the pairwise approach can be considerable, especially when there are three or more dose levels in a small study (Shirley [14]). This is of particular relevance for phase I vaccine trials. The reason is that larger doses of a vaccine can be substantially more costly to manufacture compared with lower doses. As a result, use of a suboptimal statistical approach can have negative economic ramifications if it contributes to a selection of doses for further study that are considerably larger than the truly minimum effective dose. "Missing" immunogenicity data
Most vaccine regimens include a sequence of one or more "priming" inoculations followed by a
"booster" shot later. In phase I trials, blood samples are collected at one or more time points
after each inoculation and assayed for immune activity. The primary analysis focuses on
statistical estimation and inference involving the mean post-boost response of the biomarker of
interest (µ), and the true proportion of post-boost responders (p). However, the post-boost
response is occasionally "missing" for some subjects at the time of analysis. This happens
because subjects either drop out of the study prior to the booster or, more commonly, the analysis
is an interim look at the data when the subjects in question have received priming inoculations
but not yet been boosted.
This situation is similar to the incomplete longitudinal data problem for drug trials. However,
there are two key differences. First, while the missing data resulting from dropouts in vaccine
trials are typically missing completely at random (MCAR), they are more likely to be either
missing at random (MAR) or non-ignorably missing (NM) for drug trials. The reason is that
patients often drop out from drug trials because they are not responding favorably to their
assigned treatment (e.g., high blood pressure not declining); this concept is generally not
applicable for vaccine trials! The second key difference is that the ability to predict or impute
the missing data at, say, the last scheduled visit may be better for vaccine trials compared with
drug trials. This happens because subjects in vaccine trials are inherently less heterogeneous that
patients in drug trials. Moreover, basic immunology tells us that successful priming bodes well
for successful boosting, i.e., if the post-prime immune responses are positive, they will almost
always be positive post-boost.
So, how should we estimate µ and p? A simple (and common) way is to use a "complete case
analysis", i.e., exclude subjects with missing post-boost data. This approach is unbiased under
MCAR, but it is also inefficient because it fails to utilize the rich post-prime information of the
excluded subjects. A better alternative is to use principled methods for longitudinal data analysis
like restricted maximum likelihood (REML), generalized estimating equations (GEE), or
multiple imputation, all of which are readily available in standard software. The gains in
efficiency of the latter approaches over the complete case analysis can be significant when the
amount of missing data is large (say >20%), as illustrated by Li, Mehrotra and Barnard [15].
4. Phase II/III (clinical immunogenicity, efficacy and safety)
After phase I, there is continued assessment of the immunogenicity and safety of the one or two
doses of the vaccine selected for further study. However, the primary focus shifts towards
evaluation of vaccine efficacy, and to determine if the biomarker(s) used to advance the vaccine
beyond phase I are correlated with efficacy. In this section, we discuss the key statistical issues
encountered in phase II/III. Interestingly, for drug clinical trials there is usually a clear
demarkation between phase II and phase III, but this is less common for vaccine trials.
Assessing Vaccine Efficacy
After a candidate vaccine has been demonstrated to be immunogenic and generally safe and well
tolerated in phase I, controlled clinical trials are conducted to evaluate vaccine efficacy (VE).
The "efficacy" of a vaccine refers to its ability to either prevent infection (e.g., for an antibody-
based prophylactic vaccine) or reduce the incidence and/or severity of the associated disease in
the target population (e.g., for a T cell immunity-based vaccine). Two types of strategies are used in practice. In the first, a "small" phase II proof-of-concept efficacy trial is conducted to get preliminary evidence of vaccine efficacy before moving to a "large" phase III confirmatory trial. In the second, researchers proceed directly to a large pivotal trial (phase II/III combined). The sample sizes required to demonstrate vaccine efficacy trials depend on a multitude of factors, and can range from several hundred subjects to tens of thousands of subjects. O'Neill [16], and Chan and Bohidar [17] describe methodology for sample size estimation to establish vaccine efficacy. A commonly used measure of efficacy for a vaccine designed to prevent infection is given by VE = 1 − (λ ÷ λ ), where λ and λ denote the true incidence or hazard rates for the vaccine and control arms, respectively. A vaccine is 100% efficacious if VE = 1. Since a licensed
vaccine could ultimately be administered to millions of healthy subjects, it is usually insufficient
to demonstrate that the vaccine efficacy is merely greater than zero. Instead, there is a
requirement of "super efficacy", i.e., a need to demonstrate with high confidence that the true
vaccine efficacy is greater than some pre-specified non-zero lower bound, say VE*. The choice
of VE* is influenced by several factors, both statistical and non-statistical; this is analogous to
the choice of the non-inferiority or equivalence bound for drug trials. The statistical tools used
to quantify vaccine efficacy are context dependent, and include time-to-event analyses based on
the Cox model, and conditional and unconditional tests for incidence ratios (Chan [18], Ewell
[19]). Interestingly, as is the case for drug trials, there is often a debate on whether the primary
analysis should be an "intent-to-treat" analysis or a "per protocol" analysis (Horne et al [20]).
Fortunately, the two sets of analyses in vaccine efficacy trials have historically yielded very
similar results.
Defining and demonstrating efficacy for a vaccine that is designed to attenuate disease but not
necessarily prevent infection is a difficult issue that is beyond the scope of this article. Some
progress has been made in this area, for example, by Gilbert et al [21] and Mehrotra et al [22] for
evaluation of T cell immunity-based HIV-1 vaccines, but more work remains to be done. Other
statistical tools that appear promising for the evaluation of such vaccines include the "burden-of-
illness" approach (Chang et al [23]) and the "two part model" (Lachenbruch [24]), both of which
provide for a composite evaluation of incidence and severity of disease.
It should be noted that the above discussion of vaccine efficacy has implicitly focused on the
direct effects of the vaccine. In addition to direct effects, vaccines often confer indirect effects
through "herd immunity". Related statistical issues are discussed by several authors (e.g., Haber
et al [25]), and omitted here for brevity.

Surrogate Markers or "Correlates of Protection"
Vaccine efficacy trials provide valuable data for determining whether the immune biomarker
(e.g., antibody or T-cell response) used to assess immunogenicity can also serve as a surrogate
marker for vaccine efficacy. For example, suppose that the vaccine is observed to have no
efficacy in subjects with low biomarker responses, but has near perfect efficacy in those with
high responses (e.g., at a level that is much higher than the positivity cut-off discussed earlier).
In this case, use of the Prentice criterion [26] and related approaches [27-28] will easily help
formally establish the validity of the biomarker as a surrogate for vaccine efficacy. In contrast, it
is very difficult to establish the biomarker as a valid surrogate for vaccine efficacy if the vaccine is highly immunogenic in all subjects, or if the vaccine efficacy is close to 1, for obvious reasons. This was indeed the case for Wyeth-Lederle's PREVNAR®, a seven-valent vaccine licensed in February 2000 to protect infants and children from pneumococcal disease. In a large efficacy trial, all protocol-defined cases of disease occurred in the placebo arm. So, the vaccine was 100% efficacious, but a correlation between immune response and protection from disease could not be determined. Vaccine researchers use the term "correlates of protection" to describe surrogate markers of vaccine efficacy. The availability of such surrogates allows for significantly more efficient evaluation of newer (e.g., 2nd generation) vaccines, since vaccine efficacy can be indirectly demonstrated through the surrogate. A detailed discussion of correlates of protection, including other real examples and a useful bibliography is provided by Chan et al [1]. Assessing Vaccine Safety As mentioned earlier, vaccines are developed for potential administration to millions of healthy subjects worldwide. Accordingly, the assessment of safety is of paramount importance, and requires a comprehensive evaluation to ensure that the benefits of vaccination outweigh the potential risks. The methods and measurements chosen to establish the safety of a vaccine depend on many factors, including the type of vaccine and its mechanism of action. Common reactions to vaccines are readily identified in phase I, and continue to be tracked in phases II and III. These include swelling, tenderness, and redness at the injection site (e.g., arm), and are almost always attributable to the vaccine. Systemic reactions, such as fevers or muscle aches, are also fairly common for some types of vaccines (and placebo!) It is important to stress that the large volume of safety data, either for a single phase III trial or an integrated summary of safety across several trials, calls for careful statistical analysis and interpretation. For example, systemic adverse events (AEs) are typically evaluated using between-group p-values for every AE encountered within each of several body systems. If the p-values are interpreted without multiplicity considerations, there is a potential for an excess of false positive findings. This can needlessly complicate the safety profile of the vaccine under study. Mehrotra and Heyse [29] have recently proposed a novel method for taming the multiplicity artifact in such situations. Their method involves a two-step application of adjusted p-values based on the Benjamini and Hochberg [30] false discovery rate methodology. They use real data from three moderate to large vaccine trials to illustrate their proposed "Double FDR" approach, and to reinforce the potential impact of failing to account for multiplicity. Phase II/III vaccine trials are usually well powered for comparative analyses of common but less serious adverse events. However, determining the sample size required to rule out less common but more serious adverse events is a challenging issue that requires context-dependent solutions. For example, Sadoff et al [31] described the study design considerations necessary to detect an increased risk of intussusception in a randomized, placebo-controlled trial of a rotavirus vaccine. They proposed extensive monitoring for intussusception cases through multiple stopping boundaries, and used Monte Carlo simulation methods to justify a study size of at least 60,000 infants. A more detailed discussion of statistical design and analysis issues involving vaccine safety are provided by Ellenberg [32]. Other Pre-Licensure Issues
The licensing application for a new vaccine is called the Biological License Application (BLA);
it is analogous to the New Drug Application (NDA) for a drug. In order for the license to be
approved by a regulatory agency (like CBER in the US), the BLA must provide convincing data
to support the safety and efficacy of the vaccine. In addition, it must demonstrate that the
product meets regulatory standards of purity and potency, and consistency of manufacturing
(Lachenbruch et al [33]). Evidence for the latter is obtained through a "lot consistency" study.
Such studies typically use three lots of vaccine made from the same manufacturing process. The
goal is to demonstrate that the three lots evoke "similar" immune responses. Similarity is
concluded if a pre-specified clinically significant difference between any two pairs of lots can be
ruled out with high confidence, with respect to both the proportion of responders and the
(geometric) mean response for the primary biomarker. Statistical methods for lot consistency
studies are discussed by Wiens and Iglewicz [34].

5. Post-Licensure Issues
Phase IV studies are conducted after licensure to collect additional information on the safety,
immunogenicity, and/or efficacy of the vaccine to meet regulatory commitments or post-
marketing objectives. These include so-called bridging studies, persistence studies, and post-
licensure safety studies. Some of the attendant statistical issues are briefly discussed here. Chan
et al [1] and Halloran [35] provide more detail.
Bridging Study
After the vaccine has been licensed, the manufacturing process, storage conditions, or dosing
schedule may be altered to enhance production yield, vaccine stability, or convenience of
vaccination schedule, respectively. Regulatory requirements mandate that sponsors conduct
studies to demonstrate that such changes have no material impact on vaccine effectiveness. This
is accomplished via immunogenicity bridging trials designed to demonstrate similarity of the
modified vaccine/process to the current vaccine/process in a manner analogous to that for lot
consistency trials. Of note, it is presumed that the biomarker used to establish similarity in a
bridging study is sufficiently correlated with efficacy. Lack of such a correlation makes it harder
to justify the use of the biomarker, since the ultimate goal is to (indirectly) ensure that the
vaccine efficacy is unaffected.
Immunological Persistence Study
It is important to have an understanding of how long vaccine-induced immunity lasts. For
example, if the protective efficacy of a vaccine is known to last for ten years, then giving a
booster shot every ten years might be reasonable. However, such information is rarely available
before the vaccine is licensed. The reason is that the expected duration of vaccine-induced
immunity is usually much longer than the duration of the clinical trials that are included in the
BLA. Accordingly, immunological long-term persistence studies are often conducted post-
licensure. These are typically open label studies in which vaccinated subjects provide blood
samples over time (usually annually) for determination of immune responses. The resulting data
can be analyzed using standard time-to-event methodology. Modeling strategies have also been
proposed to predict the duration of vaccine-induced immunity based on extrapolation of
observed antibody or cellular immune responses from clinical trials [36-37].
Post-licensure safety surveillance
The Food and Drug Administration (FDA) and the Centers for Disease Control (CDC) have
created the Vaccine Adverse Event Reporting System (VAERS) for post-licensure safety
surveillance [38]. This system accepts reports of adverse events that may be associated with
U.S. licensed vaccines from health care providers, manufacturers, and the public. The reports are
continually monitored for any unexpected patterns or changes in rates of adverse events. Post-
marketing safety evaluations are often complicated and contentious, particularly when they are
based on retrospective analyses or involve data collected via potentially biased reporting
systems. Bayesian data mining methods have been proposed by DuMochel [39] and
implemented in practice by Niu et al [40]. See also Brewer and Colditz [41] for an informative
discussion on post-marketing safety issues.
6. Concluding remarks
In this article, we have provided an overview of the key statistical issues that arise in all phases
of vaccine development. We have stressed the importance of understanding the science behind
the numbers, including how the vaccine is intended to work, as well as the bioassays that
measure whether or not the vaccine is immunogenic. Since licensed vaccines are administered to
millions of healthy people, we have highlighted the importance of establishing vaccine safety in
a large number of subjects, and explained the concept of super efficacy studies. Finally, we have
noted the importance of establishing that the vaccine manufacturing process produces vaccine
lots that evoke statistically similar post-vaccination immune responses. Recent advances in
genetic engineering and pharmacogenetics are spawning a new generation of vaccine modalities
to protect against HIV/AIDS, cancer, malaria, anthrax, plague, and so on. Development of such
vaccines will pose additional statistical challenges that will require innovative thought and
creative solutions.
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frequently invited to present seminars at conferences and in academia. He holds adjunct faculty
appointments at the University of Pennsylvania and Villanova University. His other professional
activities include serving as an Associate Editor for the Journal of Biopharmaceutical Statistics
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and consultant to the Center for Scientific Review at the National Institutes of Health.


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