Marie Kassapian 1,2 , Toufik Zahaf 3 , Fabian Tibaldi 3 1 University of Hasselt

COMPARISON OF STATISTICAL TESTS IN PRESENCE OF MANY ZEROS DATA: Application IN VACCINE CLINICAL TRIAL Marie Kassapian1,2, Toufik Zahaf3, Fabian Tibaldi3 1 University of Hasselt 2 Frontier Science Foundation Hellas 3 GlaxoSmithKline (GSK) Vaccines Tel Aviv, 22.04.2013

introduction The disease Herpes Zoster • After a varicella (chicken-pox) incident, the virus may be expressed againafter several years. • Basically in ages above 60 yearsold. • Can turn out very severe in terms of pain. Comparison of Statistical Tests in Presence of Many Zeros Data

Zoster Brief Pain Inventory (ZBPI) Questionnaire: • A set of questions to determine the level of pain interfering with functional status & quality of life • Scale from 0 to 10 • Filled in every day during follow-up period (182 days) • Score=0 Non-incident case & Score>0 Incident case • Final score: Sum of worst daily scores (182-1820) Comparison of Statistical Tests in Presence of Many Zeros Data

Problems • The resulted data after the end of the follow-up period contain many zeros. These zeros belong to the scores of those individuals that did not experience zoster. Need for methods capable of handling such datasets. • Important to account both for the reduction in the total number of cases as well as for the reduction in the severity of pain. Comparison of Statistical Tests in Presence of Many Zeros Data

Methods • Burden-of-Illness (BOI) Measure - Chang et al. (1994) Test accounting for: • Disease incidence • Disease severity Assign a score to each patient and create the Burden-of-Illness score by adding them. Comparison of Statistical Tests in Presence of Many Zeros Data

Statistic: • where : • nj represents the total number of pts. in each group. • mi represents the number of infected pts. in each group. • Wji represents the BOI score of the ith patient in the jth group. • For the groups: • 0:placebo group & 1:vaccine group Comparison of Statistical Tests in Presence of Many Zeros Data

Methods • Choplump test - Follmann et al. (2009) • Sort the scores in each group. • Toss out the same number of zeros in both groups. • 1 group with no zeros + 1 group with few zeros. Statistic: • n=number of pts randomized in each group • m=max(m0,m1) • S2m=pooled variance based on the m largest W’s in each group • Calculation of the p-value can be: Exact or Approximate Comparison of Statistical Tests in Presence of Many Zeros Data

objective • Comparison between the test suggested by Chang et al. (1994) and the one suggested by Follmann et al. (2009). Comparison of Statistical Tests in Presence of Many Zeros Data

APPLICATION IN VACCINE CLINICAL TRIAL Comparison of Statistical Tests in Presence of Many Zeros Data

data • No real data • Simulated dataset based on assumptions for the sample size, the incidence rate and the risk reduction. • Number of cases: • Placebo:Incidence rate * N0* years of follow-up • Vaccine: Incidence rate * N1 * Risk * years of • follow-up Comparison of Statistical Tests in Presence of Many Zeros Data

1.Exploratory Data Analysis *W: the Burden-of Illness score of a patient Comparison of Statistical Tests in Presence of Many Zeros Data

Normality tests to observe the distributionof the patients’ BOI scores. • All cases: Z=0 Z=1 p-value<0.01 (both groups) Comparison of Statistical Tests in Presence of Many Zeros Data

Zoster cases only: Z=0 p-value=0.128 (placebo) p-value=0.15 (vaccine) Z=1 Comparison of Statistical Tests in Presence of Many Zeros Data

Area Under the Curve for the two groups based on • the mean daily severity (BOI) scores. Comparison of Statistical Tests in Presence of Many Zeros Data

2.Comparison between Choplump test & method of chang et al. Implementation of Chang et al. method: Findings: • P-value from Chang et al. method much more significant than those yielded for the separate tests. • Both methods (Choplump & Chang) reject H0. Comparison of Statistical Tests in Presence of Many Zeros Data

2.Comparison between Choplump test & method of chang et al. 1st case:Exact p-value H0: No difference in B.O.I. scores between placebo and vaccine group p-value=0.047 Comparison of Statistical Tests in Presence of Many Zeros Data

Conclusion: The treated groups differ in 2 ways: • Difference in the number of incidents per group • Difference in the mean severity scores per group • Note: • N=10 patients and M=5 incident cases: 252 permutations • N=20 patients and M=10 incident cases: 182,756 permutations Comparison of Statistical Tests in Presence of Many Zeros Data

2.Comparison between Choplump test & method of chang et al. 2nd case:Approximate p-value Simulated dataset (RR=70% , Incidence rate=0.7%) : N=16,000 pts. N0=N1=8,000 pts. M=218 cases M0=168 cases M1=50 cases K=15,782 zeros K0=7,732 zeros K1=7,950 zeros H0: No difference in B.O.I. scores between placebo and vaccine group p-value=2.72*10-31 Comparison of Statistical Tests in Presence of Many Zeros Data

Conclusion: Again, the groups differ in 2 ways: • Difference in the number of incidents per group • Difference in the mean severity scores per group Comparison of Statistical Tests in Presence of Many Zeros Data

3.Power analysis (1) Chang method cannot compute very small p-values. • Comparison between the tests not straightforward. • Implementation of power analysis in order to find the most powerful test. Building of different scenarios based on: • Sample size (1,000 , 2,000 , 5,000 , 10,000 , 20,000) • Risk reduction (30% , 50% , 70%) • Severity reduction (Yes , No) • Simulation of 1,000 datasets for each scenario. Comparison of Statistical Tests in Presence of Many Zeros Data

3.Power analysis (2) Ranges for severity scores: Comparison of Statistical Tests in Presence of Many Zeros Data

3.Power analysis (3) • Boxplots of scores under the different hypotheses (N=10,000) Comparison of Statistical Tests in Presence of Many Zeros Data

3.Power analysis (4) Comments based on the summary statistics of the resulted p-values: • The alternative hypotheses that also account for severity reduction, apart from risk reduction, present incredibly small distances between the minimum and the maximum values. • More obvious in the case of the Choplump test. • As N increases, the mean p-values decrease much faster especially for the Choplump test. Comparison of Statistical Tests in Presence of Many Zeros Data

3.Power analysis (5) Estimated type I error probabilities for each test: Estimated power:

CONCLUSIONS • Both tests represent adequate approaches to the issue of handling a lot of zeros. • The Choplump test is dominant over its competitor only in cases when the efficacy of the vaccine is reflected by both risk and severity reduction. Comparison of Statistical Tests in Presence of Many Zeros Data

Thank you Comparison of Statistical Tests in Presence of Many Zeros Data

Marie Kassapian 1,2 , Toufik Zahaf 3 , Fabian Tibaldi 3 1 University of Hasselt