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Marie Kassapian 1,2, Toufik Zahaf 3, Fabian Tibaldi 3 1 University of Hasselt 2 Frontier Science Foundation Hellas 3 GlaxoSmithKline (GSK) Vaccines Tel Aviv, 22.04.2013

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The disease Herpes Zoster After a varicella (chicken-pox) incident, the virus may be expressed again after several years. Basically in ages above 60 years old. Can turn out very severe in terms of pain. 2 Comparison of Statistical Tests in Presence of Many Zeros Data

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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) 3 Comparison of Statistical Tests in Presence of Many Zeros Data

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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. 4 Comparison of Statistical Tests in Presence of Many Zeros Data

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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. 5 Comparison of Statistical Tests in Presence of Many Zeros Data

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6 Statistic: where : n j represents the total number of pts. in each group. m i represents the number of infected pts. in each group. W ji represents the BOI score of the i th patient in the j th group. For the groups: 0:placebo group & 1:vaccine group Comparison of Statistical Tests in Presence of Many Zeros Data

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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: 7 Comparison of Statistical Tests in Presence of Many Zeros Data n=number of pts randomized in each group m=max(m 0,m 1 ) S 2 m =pooled variance based on the m largest W’s in each group Calculation of the p-value can be: Exact or Approximate

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Comparison between the test suggested by Chang et al. (1994) and the one suggested by Follmann et al. (2009). 8 Comparison of Statistical Tests in Presence of Many Zeros Data

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10 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 * N 0 * years of follow-up Vaccine: Incidence rate * N 1 * Risk * years of follow-up Comparison of Statistical Tests in Presence of Many Zeros Data

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11 NMeanStd. Dev.MedianMin.Max. All cases (W* ≥ 0) Placebo (Z=0)8,00028.69195.92001431 Vaccine (Z=1)8,0004.0150.5800690 Zoster cases only (W* > 0) Placebo (Z=0)1681366.2021.60136613201431 Vaccine (Z=1)50641.5421.02641597690 *W: the Burden-of Illness score of a patient Comparison of Statistical Tests in Presence of Many Zeros Data

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Normality tests to observe the distribution of the patients’ BOI scores. All cases: 12 p-value<0.01 (both groups) Z=0Z=1 Comparison of Statistical Tests in Presence of Many Zeros Data

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

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14 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

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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 H 0. 15 TestStatisticp-value Incidence Rate63.87<0.001 Severity score per case209.49 <0.001 Burden-of-illness score11.22<0.0001 Comparison of Statistical Tests in Presence of Many Zeros Data

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1 st case: Exact p-value H 0 : No difference in B.O.I. scores between placebo and vaccine group p-value=0.047 16 Patient ID12345678910 W=score01326136913871374 0000 650 Z=group0000011111 Comparison of Statistical Tests in Presence of Many Zeros Data

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Conclusion: The treated groups differ in 2 ways: Difference in the number of incidents per group Difference in the mean severity scores per group 17 Comparison of Statistical Tests in Presence of Many Zeros Data Note: N=10 patients and M=5 incident cases: 252 permutations N=20 patients and M=10 incident cases: 182,756 permutations

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2 nd case: Approximate p-value Simulated dataset (RR=70%, Incidence rate=0.7%) : N=16,000 pts. N 0 =N 1 =8,000 pts. M=218 cases M 0 =168 cases M 1 =50 cases K=15,782 zeros K 0 =7,732 zeros K 1 =7,950 zeros H 0 : No difference in B.O.I. scores between placebo and vaccine group p-value=2.72*10 -31 18 Comparison of Statistical Tests in Presence of Many Zeros Data

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Conclusion: Again, the groups differ in 2 ways: Difference in the number of incidents per group Difference in the mean severity scores per group 19 Comparison of Statistical Tests in Presence of Many Zeros Data

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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. 20 Comparison of Statistical Tests in Presence of Many Zeros Data

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Hypothesis Sample size Risk Reduction Severity Reduction H0H0 N 0%No H A (1) 30% Yes H A (2) No H A (3) 50% Yes H A (4) No H A (5) 70% Yes H A (6) No Comparison of Statistical Tests in Presence of Many Zeros Data 21 RR=0%RR=30%RR=50%RR=70% Placebo1-104-10 Vaccine1-103-92-81-7 Ranges for severity scores:

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22 Boxplots of scores under the different hypotheses (N=10,000) Comparison of Statistical Tests in Presence of Many Zeros Data

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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. 23 Comparison of Statistical Tests in Presence of Many Zeros Data

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Estimated type I error probabilities for each test: Estimated power: N1,0002,0005,00010,00020,000 Chang0.010.0110.0130.020.026 Choplump0.020.0270.025 0.032 N ChangChoplump 30%50%70%30%50%70% YesNoYesNoYesNoYesNoYesNoYesNo 1,0000.001 0.0030.0010.210.170.090.0030.240.180.350.44 3,0000.0050.0020.250.160.390.310.210.0350.360.240.740.61 5,0000.430.010.580.130.680.560.510.120.650.390.810.77 10,0000.770.660.860.710.910.800.780.540.880.570.930.85 20,0000.930.890.950.910.990.940.950.920.970.940.980.97

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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. 25 Comparison of Statistical Tests in Presence of Many Zeros Data

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Thank you 26 Comparison of Statistical Tests in Presence of Many Zeros Data

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