Marie Kassapian1,2, Toufik Zahaf3, Fabian Tibaldi3

1 University of Hasselt2 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.

2Comparison 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)

3Comparison of Statistical Tests in Presence of Many Zeros Data

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.

4Comparison of Statistical Tests in Presence of Many Zeros Data

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.

5Comparison of Statistical Tests in Presence of Many Zeros Data

6

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

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:

7Comparison of Statistical Tests in Presence of Many Zeros Data

n=number of pts randomized in each group m=max(m0,m1) S2

m=pooled variance based on the m largest W’s in each group

Calculation of the p-value can be: Exact or Approximate

Comparison between the test suggested by Chang et al. (1994) and the one suggested by Follmann et al. (2009).

8Comparison of Statistical Tests in Presence of Many Zeros Data

Comparison of Statistical Tests in Presence of Many Zeros Data 9

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 * N0* years of follow-up Vaccine: Incidence rate * N1 * Risk * years of follow-up

Comparison of Statistical Tests in Presence of Many Zeros Data

11

N MeanStd.

Dev.Median Min. Max.

All cases (W* ≥ 0)

Placebo (Z=0) 8,000 28.69 195.92 0 0 1431Vaccine (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 1431Vaccine (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

Normality tests to observe the distribution of the patients’ BOI scores.

All cases:

12

p-value<0.01 (both groups)

Z=0 Z=1

Comparison of Statistical Tests in Presence of Many Zeros Data

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

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

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.

15

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

Comparison of Statistical Tests in Presence of Many Zeros Data

1st case: Exact p-value

H0: No difference in B.O.I. scores between placebo and vaccine group

p-value=0.047

16

Patient ID 1 2 3 4 5 6 7 8 9 10

W=score 0 1326 1369 1387 1374 0 0 0 0 650

Z=group 0 0 0 0 0 1 1 1 1 1

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

17Comparison 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

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

18Comparison 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

19Comparison of Statistical Tests in Presence of Many Zeros Data

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

Hypothesis Sample sizeRisk

ReductionSeverity

ReductionH0

N

0% No

HA(1)

30%Yes

HA(2)

No

HA(3)

50%Yes

HA(4)

No

HA(5)

70%Yes

HA(6)

No

Comparison of Statistical Tests in Presence of Many Zeros Data 21

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

Ranges for severity scores:

22

Boxplots of scores under the different hypotheses (N=10,000)

Comparison of Statistical Tests in Presence of Many Zeros Data

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.

23Comparison of Statistical Tests in Presence of Many Zeros Data

Estimated type I error probabilities for each test:

Estimated power:

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

N

Chang Choplump

30% 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.

25Comparison of Statistical Tests in Presence of Many Zeros Data

Thank you

26Comparison of Statistical Tests in Presence of Many Zeros Data