On testing equivalence of three populations

Immunogenicity, safety and tolerability of 3 lots of 13-valent pneumococcal conjugate vaccine given with routine pediatric vaccinations in the United States

BACKGROUND

The 7-valent pneumococcal conjugate vaccine (PCV7; serotypes 4, 6B, 9V, 14, 18C, 19F and 23F) has decreased invasive pneumococcal disease incidence. This study was performed to support licensure of a 13-valent pneumococcal conjugate vaccine (PCV13), which expands serotype coverage to include serotypes 1, 3, 5, 6A, 7F and 19A. This study assessed the immunogenicity, safety and manufacturing consistency of PCV13.

METHODS

Randomized, double-blind, multicenter trial. Healthy United States infants were randomized 2:2:2:1 to receive 1 of 3 lots of PCV13 or PCV7, along with routine US pediatric vaccines at ages 2, 4 and 6 months (infant series), and 12 months (toddler dose).

RESULTS

Among 1709 vaccinated infants, 1 month postinfant series and 1 month posttoddler dose, immunoglobulin G geometric mean concentrations (GMCs) were within 2-fold among the PCV13 lots, meeting equivalence criteria for all 13 serotypes. In a post hoc analysis, based on percent responders at ≥0.35 μg/mL postinfant series and immunoglobulin G GMC ratios postinfant series and posttoddler dose, noninferiority criteria were met for combined PCV13 lots compared with PCV7 for all common serotypes. Posttoddler dose immunoglobulin G GMCs were higher than postinfant series GMCs for all serotypes. Local reactions and fevers were generally mild; incidences of local reactions, systemic events and adverse events were generally similar between groups.

CONCLUSIONS

PCV13 can be manufactured in a manner that elicits consistent immune responses. PCV13 provides increased serotype coverage and immunogenicity that is noninferior to PCV7 and has a safety profile similar to PCV7 when given with routine pediatric vaccines.

Sample size for equivalence trials: a case study from a vaccine lot consistency trial

For some trials, simple but subtle assumptions can have a profound impact on the size of the trial. A case in point is a vaccine lot consistency (or equivalence) trial. Standard sample size formulas used for designing lot consistency trials rely on only one component of variation, namely, the variation in antibody titers within lots. The other component, the variation in the means of titers between lots, is assumed to be equal to zero. In reality, some amount of variation between lots, however small, will be present even under the best manufacturing practices. Using data from a published lot consistency trial, we demonstrate that when the between-lot variation is only 0.5 per cent of the total variation, the increase in the sample size is nearly 300 per cent when compared with the size assuming that the lots are identical. The increase in the sample size is so pronounced that in order to maintain power one is led to consider a less stringent criterion for demonstration of lot consistency. The appropriate sample size formula that is a function of both components of variation is provided. We also discuss the increase in the sample size due to correlated comparisons arising from three pairs of lots as a function of the between-lot variance.

Lot Consistency as an Equivalence Problem

One requirement for licensure of a vaccine in the United States is demonstration by the manufacturer of consistently produced lots of vaccine. Demonstration of consistency of manufacturing can be viewed as a multigroup equivalence problem. The standard statistical procedures for evaluating equivalence assume normally distributed data and define equivalence margins with respect to group means. As an alternative approach, we define a measure of the similarity among group distributions and their nonparametric estimators. Through computer simulations we explore the statistical properties of an equivalence test based on this estimator and compare them to the standard methods. Preliminary work suggests that a test of similarity can be useful in demonstrating equivalence when distributions are not normal or when there are differences in scale or shape. It appears to detect departures from equivalence that are not reflected by differences among group means.

Type I Error and Power in Noninferiority/Equivalence Trials with Correlated Multiple Endpoints: An Example from Vaccine Development Trials

Clinical trials necessary for the development of new treatment often require testing of multiple endpoints for equivalence or noninferiority relative to an existing effective standard therapy. An example is a vaccine study with multiple antibody measurements in sera of subjects receiving a combination vaccine such as a pneumococcal vaccine, which contains many different serotypes of the pneumococcal organism. This article describes testing methods for the demonstration of simultaneous marginal equivalence or noninferiority of two treatments on each component of the response vector that follows a multivariate normal distribution. Systematic simulation studies are conducted to evaluate the performance of the testing method and to examine under what conditions the power is substantially different if the multiple endpoints are assumed to be independent when they are actually strongly correlated. Data from an illustrative example are used to describe how the study power can be evaluated in the design of the trials.

Design of vaccine equivalence/non-inferiority trials with correlated multiple binomial endpoints

Immunogenicity trials that study the immune responses to vaccination are often used in the vaccine development process as alternatives to clinical efficacy trials. The comparisons of immune responses among various treatment groups are conducted in a non-inferiority or equivalence framework. When there exists a level of immune response that correlates with protection against disease, it is of interest to compare the proportion of responders as defined as response above a specific level or as a predefined increase in immune levels for post-vaccination levels above pre-vaccination levels. Since vaccines often contain several antigens, the correlations between the immune responses need to be taken into account in the analysis. In this paper, we describe appropriate testing methods for demonstrating the non-inferioritylequivalence of two treatments on each of the binomial endpoints. We conduct a comprehensive simulation study to shed light on how the Type I error and power are affected and to what extent when correlated multiple binomial endpoints are present in the vaccine trials. We also illustrate the computation of power for assessment of non-inferioritylequivalence in real studies.

Statistical Analysis of Influenza Vaccine Lot Consistency Studies

This paper presents an integrated statistical approach to the analysis of influenza vaccine lot consistency studies in which three lots are compared. The approach ensures that the overall Type I error rate (i.e., the probability of wrongly concluding that the lots are similar) is controlled. It is argued that the optimum efficacy measure is the geometric mean titer. The approach is demonstrated using data from a randomized, double-blind lot consistency study in which three consecutive production lots of Solvay Pharmaceuticals' new, virosomal subunit influenza vaccine Invivac were compared.

Urinary C-peptide excretion in free-living healthy children is related to dietary carbohydrate intake but not to the dietary glycemic index

This study first examined whether urinary C-peptide (UCP), stored at -20 degrees C, remains stable over the long term, and second, whether the dietary glycemic index (GI) and the glycemic load (GL: GI x g carbohydrates) are related to the 24-h UCP excretion of healthy children. Participants in the Dortmund Nutrition and Anthropometric Longitudinally Designed Study with 24-h urine collections and a simultaneously completed weighed dietary record were included. From these, 3 comparable groups of 7- to 8-y-old children (n = 40 each) from 1990, 1996, and 2002 were randomly selected (total n = 120). C-peptide was measured with a 1-site ELISA. A GI value was assigned to all recorded foods containing carbohydrates (CHO). Statistical equivalence tests corroborated that UCP excretion in the 3 sampling periods was equivalent when corrected for body weight and protein intake (P < 0.05). UCP excretion was associated with the GL after adjustment for body weight, protein, and fiber intake [mean UCP (95% CI) in GL tertiles 1-3: 6.19 (5.37, 7.14) vs. 7.82 (6.77, 9.02) vs. 7.76 (6.71, 8.97) nmol/d, P for difference 0.04]. GI was not significantly related to UCP excretion [adjusted means (95% CI): 7.27 (6.28, 8.41) vs. 6.51 (5.64, 7.51) vs. 7.94 (6.86, 9.18), P for difference 0.2]. In conclusion, UCP retrospectively measured with a 1-site ELISA remained stable for up to 12 y (from 1990 until 2002). The observed positive relation of UCP with GL appears to result largely from its association with the amount of CHO, whereas dietary GI may be relevant only at higher intake levels.

Choosing an equivalence limit for noninferiority or equivalence studies

Studies that compare treatments with the purpose of demonstrating that the treatments are similar require an a priori definition of an equivalence limit, how different the treatments can be before the difference is of concern. Defining such an equivalence limit is one of the most difficult aspects of planning the study. Three principles are proposed for setting such limits, depending on the objective of the study: a putative placebo calculation, an approach based on clinically important differences, and methods based on statistical properties. All methods will be useful for many studies, but the study objective should determine the final choice of an equivalence limit. The statistician must play an integral role in determining the final equivalence limit. Advice is offered for helping the statistician participate in the decision on the equivalence limits.

Long-Term stability of 6-hydroxymelatonin sulfate in 24-h urine samples stored at -20 degrees C

The purpose of the present feasibility study was to determine whether the concentration of 6-hydroxymelatonin sulfate (6-OHMS) remains stable in urine samples stored over at least 15 yr. To test this, 117 twenty-four-hour urine samples were analyzed, which were obtained from healthy children ages 8 to 9 yr within the periods of 1985-1987,1991-1993, and 1997-1999. 6-OHMS concentrations were determined by enzyme-linked immunosorbent assay. The statistical analyses clearly indicate that the concentration of 6-OHMS remains stable for at least 15 yr if the urine is stored at -20 degrees C.

Design and analysis of three treatment equivalence trials

We consider design and analysis of clinical trials aimed at demonstrating equivalence of three treatments. We discuss analysis methods that require demonstrating that each pair of treatments has an unimportant difference. The critical values that we provide are smaller than the standard normal critical values, pointing out that the adjustment is counter to the usual multiplicity adjustments. Special issues in demonstrating equivalence of three rather than two treatments are discussed. We propose some conservative criteria for estimating sample size. Procedures for choosing pairs of treatments that are equivalent to each other, even when all three treatments are not shown equivalent, are also discussed along with implications for control of type I errors. We also demonstrate the methods with data from the literature.