Methodological Research and Collaboration

1. Methodological Research and Collaboration Lan Kong Assistant professor Department of Biostatistics June 5, 2014

2. Outline • Introduction • Methodological Research • Survival analysis • Clinical trials • Collaboration • Projects • Motivated problems

3. Introduction • Joined the Biostat dept in August 2003 • PhD in Biostat from UNC-Chapel Hill • In collaboration with critical care medicine dept. • On doctoral exam committee • Courses intend to teach: survival analysis, advanced categorical data analysis, or estimating equation method.

4. Methodological research • Survival analysis • Study design: case-cohort • Model: semiparametric transformation models and accelerated failure time model. • Approach: estimating equation method, inverse of probability weighting technique • Statistical theory: U-statistics, finite population sampling, martingales, empirical/stochastic process

5. Case-cohort design (Prentice, 1986) Full cohort Failures/cases Subcohort Full cohort Complete data available for Subcohort + Additional Cases outside the subcohort

6. Semiparametric Survival Models • Cox model λ(t)=λ0(t)exp(β’Z), λ0(t) unspecified • Transformation models h(T)= -β’Z+εOR g{Sz(t)}=h(t)+β’Z h unknown, ε has known CDF F(.), g-1=1-F. • Accelerated failure time model log(T)= -β’Z+ε, ε has unspecified CDF.

7. Methodological Research (cont.) • Clinical trials • Problem: Multiplicity issues • Example: Multi-dose clinical trials--correlations among multiple comparisons • Statistical concerns: familywise Type I error and power

8. Family-Wise Error (FWE) • Probability that at least one hypothesis is incorrectly declared significant. • Strongly control of FWE: FWE is protected for any composite null hypothesis • Closed testing procedures strongly control the FWE

9. Multiple testing procedures Analysis strategies: • Perform a sequence of tests in a pre-specified order through the closed testing principle : 1. Global assessment of any dose effect 2. Comparisons of doses to Placebo 3. Other comparisons among doses • Manage multiplicity within the respective steps by Hochberg method (BKA, 1988), closed testing procedure.

10. Vaccine trials • Problem: • Inferiority/Equivalence assessment • Multiplicity due to multiple endpoints (immune responses) • Statistical concerns: How correlations among endpoints affect study design of inferiority/EQ trials (power, sample size)?

11. H0 (inf) H1(sup) T-C 0 Hypotheses H0 (inf) H1(noninf) T-C -K 0 H0 (noneq) H1(eq) H0 (noneq) T-C -K 0 K T: treatment group, C: control group

12. Further questions of interest • How to handle multiple endpoints in multi-dose clinical trials? • How to simultaneously assess inferiority/EQ on some endpoints and superiority on the others?

13. Collaboration Projects mainly involved: • Genetic and inflammatory markers of Sepsis (GenIMS) • Economic Analysis of the Pulmonary Artery Catheter Use (EA-PAC) • Prolonged Outcomes of Nitric Oxide for Ventilated Premature Babies (PRONOX)

14. Statistical problems motivated from collaborative projects

15. Genetic data • Explore how the candidate markers interactively affect the outcome (Selection of subset from a list of candidate genetic markers) • Statistical learning method • Pattern recognition approach • Haplotype analysis for survival data to accommodate missing genotypes, case-cohort design

16. Missing and/or truncated data • Examples: inflammatory marker data are below detectable limit, the measurement on the severity of sepsis are heavily missing • Longitudinal analysis of truncated inflammatory marker (extension of Tobit model) • Jointly modeling several truncated inflammatory markers • Testing whether the missing is informative in the non-monotone missing pattern • Jointly modeling the longitudinal outcome and longitudinal covariates

17. Quality of Life and Cost data • Various types of outcomes: survival data, cost data, quality of life data. • Informative censoring • Modeling quality adjusted survival • Jointly modeling QOL with survival data • Cost-effective analysis in presence of repeated measures and missing data

18. Related papers Kong L, Cai J, Sen PK. Weighted estimating equations for semiparametric transformation models with censored data from a case-cohort design. Biometrika 2004; 91(2):305-319. Kong L, Cai J, Sen PK. Asymptotic results for fitting semiparametric transformation models to failure time data from a case-cohort design. Statistica Sinica 2004, in press. Kong L. Analysis of case-cohort data with accelerated failure time model, in preparation

19. Related papers (cont.) Kong L, Kohberger R, Koch G. Type I error and power in non-inferiority/equivalence trials with correlated multiple endpoints: an example from vaccine development trials. Journal of Biopharmaceutical Statistics 2004; 14(4):893-907. Kong L, Koch G, Liu T, Wang H. Performance of some multiple testing procedures to compare three doses of a test drug and placebo. Pharmaceutical Statistics 2004, in press. Kong L, Kohberger R, Koch G. Equivalence/non-inferiority assessment on multiple proportion outcomes. In preparation.