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Marie Kassapian1,2, Toufik Zahaf3, Fabian Tibaldi3 1 2 University of Hasselt Frontier Science Foundation Hellas 3 GlaxoSmithKline (GSK) Vaccines Tel Aviv, 22.04.2013 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. Comparison of Statistical Tests in Presence of Many Zeros Data 2 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 3 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 4 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-ofIllness score by adding them. Comparison of Statistical Tests in Presence of Many Zeros Data 5 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 & Comparison of Statistical Tests in Presence of Many Zeros Data 1:vaccine group 6 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 7 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 8 Comparison of Statistical Tests in Presence of Many Zeros Data 9 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 10 N Mean Std. Dev. Median Min. Max. All cases (W* ≥ 0) Placebo (Z=0) 8,000 28.69 195.92 0 0 1431 Vaccine (Z=1) 8,000 4.01 50.58 0 0 690 Zoster cases only (W* > 0) Placebo (Z=0) 168 1366.20 21.60 1366 1320 1431 Vaccine (Z=1) 50 641.54 21.02 641 597 690 *W: the Burden-of Illness score of a patient Comparison of Statistical Tests in Presence of Many Zeros Data 11 Normality tests to observe the distribution of 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 12 Zoster cases only: Z=0 p-value=0.128 (placebo) Z=1 p-value=0.15 (vaccine) Comparison of Statistical Tests in Presence of Many Zeros Data 13 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 14 Implementation of Chang et al. method: Test Statistic p-value Incidence Rate 63.87 <0.001 Severity score per case 209.49 <0.001 Burden-of-illness score 11.22 <0.0001 Findings: P-value from Chang et al. method much more significant than those yielded for the separate tests. Both methods (Choplump & Comparison of Statistical Tests in Presence of Many Zeros Data Chang) reject H0. 15 1st case: Exact p-value Patient ID 1 W=score 0 Z=group 0 2 3 4 5 1326 1369 1387 1374 0 0 0 0 6 7 8 9 10 0 0 0 0 650 1 1 1 1 1 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 16 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 17 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 18 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 19 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 20 Hypothesis Risk Reduction 0% Sample size H0 HA(1) Yes 30% HA(2) HA(3) N No Yes 50% HA(4) HA(5) No Yes 70% HA(6) Severity Reduction No No Ranges for severity scores: RR=0% RR=30% RR=50% RR=70% Placebo 1-10 4-10 4-10 4-10 Vaccine 1-10 3-9 2-8 1-7 Comparison of Statistical Tests in Presence of Many Zeros Data 21 Boxplots of scores under the different hypotheses (N=10,000) Comparison of Statistical Tests in Presence of Many Zeros Data 22 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 23 Estimated type I error probabilities for each test: N 1,000 2,000 5,000 10,000 20,000 Chang 0.01 0.011 0.013 0.02 0.026 Choplump 0.02 0.027 0.025 0.025 0.032 Estimated power: Chang 30% N Choplump 50% 70% 30% 50% 70% Yes No Yes No Yes No Yes No Yes No Yes No 1,000 0.001 0.001 0.003 0.001 0.21 0.17 0.09 0.003 0.24 0.18 0.35 0.44 3,000 0.005 0.002 0.25 0.16 0.39 0.31 0.21 0.035 0.36 0.24 0.74 0.61 5,000 0.43 0.01 0.58 0.13 0.68 0.56 0.51 0.12 0.65 0.39 0.81 0.77 10,000 0.77 0.66 0.86 0.71 0.91 0.80 0.78 0.54 0.88 0.57 0.93 0.85 20,000 0.93 0.89 0.95 0.91 0.99 0.94 0.95 0.92 0.97 0.94 0.98 0.97 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 25 Thank you Comparison of Statistical Tests in Presence of Many Zeros Data 26