Robust Analysis of Incomplete Longitudinal Data in Clinical Trials

Robust Analysis of Incomplete Longitudinal Data in Clinical Trials Robin Mogg* and Devan V. Mehrotra Merck Research Laboratories ICSA Applied Statistics Symposium Raleigh, NC June 4, 2007 * robin_mogg@merck.com Outline  The need for an HIV Vaccine  Motivating trials: » Two Phase IIa HIV Vaccine Trials  Numerical example  Statistical methods  Simulation results  Concluding remarks  Interactions with CBER June 4, 2007 2007 ICSA Applied Statistics Symposium 2 The Need for an HIV Vaccine  UNAIDS 2005 Estimates: » 38.6 million people living with HIV worldwide; 4.1 million people newly infected (>11,000/day); 2.8 million people died  Antiretroviral therapy (ART): » Dramatically decreased morbidity and mortality in developed countries; treatment regimens complex and costly; globally reaches only 1 of 5 in need.  A safe and effective HIV Vaccine is the best hope for controlling/ending the AIDS epidemic. » Ideal vaccine candidate would be 100% effective in preventing infection among those uninfected. June 4, 2007 2007 ICSA Applied Statistics Symposium 3 Humoral and Cellular Immunity  Immune responses of preventative vaccines are designed to mimic those from natural exposure. » Humoral immunity: mediated by virus-neutralizing antibodies, prevents virus from infecting cells. » Cellular immunity: mediated by T-lymphocytes, target and kill already infected cells.  The immune system “remembers” each encounter; basis of vaccination against infectious diseases.  In natural HIV infection: » Humoral response is not completely effective in preventing virus from infecting cells. » Success of cellular response varies, “better” responses result in lower virus and better clinical outcomes. June 4, 2007 2007 ICSA Applied Statistics Symposium 4 HIV Infection Markers: CD4 count and Viral load June 4, 2007 2007 ICSA Applied Statistics Symposium 5 HIV Vaccination  Merck’s HIV Vaccine is designed to induce a cellmediated immune (CMI) response.  Prophylactic vaccination: » Goal is to induce broad cellular immune responses in HIV uninfected individuals that provides either protection from infection (sterilizing immunity) or protection from disease (low viral load setpoint, slow disease progression).  Therapeutic vaccination: » Goal is to induce broad cellular immune responses in HIV infected individuals that provides protection from disease (low viral load without ART, slow disease progression). June 4, 2007 2007 ICSA Applied Statistics Symposium 6 Prophylactic Proof of Concept (POC) Efficacy Trial  Design: randomized, double-blind, placebo-controlled study in a population at high risk of HIV infection. Motiviating Trial #1:  Two co-primary endpoints: » Infection » Viral load setpoint (among those infected) – vRNA measured at time of diagnosis and at 2, 8, and 12 weeks after diagnosis. – Viral load setpoint = mean of log10(vRNA) at Weeks 8 and 12.  Hypothesis: HIV vaccination will lead to a lower incidence of HIV and/or lower viral load setpoints among infected subjects. June 4, 2007 2007 ICSA Applied Statistics Symposium 7 Motiviating Trial #2: ACTG A5197 Therapeutic POC Efficacy Trial  Design: randomized, double-blind, placebo-controlled study in an HIV-infected population with prolonged (>2 yrs) ART-based suppression of viral load. » After immunization phase, interrupt ART for everyone.  Primary endpoint: » Viral load setpoint – vRNA measured at 1, 2, 4, 6, 8, 12, and 16 weeks after interruption of therapy. – Viral load setpoint = mean of log10(vRNA) at Weeks 12 and 16.  Hypothesis: Therapeutic HIV vaccination will lead to better control of viral replication during ART interruption. June 4, 2007 2007 ICSA Applied Statistics Symposium 8 Motiviating Trial #2 (cont.): ACTG A5197 N # randomized to vaccine N v v== #randomized to vaccine N # randomized to placebo N p p== #randomized to placebo Therapeutic nn (p ) )==##(proportion) wwho interrupt ART on vaccine POC Efficacyho TrialART on vaccine (p (proportion) interrupt v v RANDOMIZATION RANDOMIZATION Immunization Phase Immunization Phase Immunizations at weeks 0, 4, and 26 Immunizations at weeks 0, 4, and 26 STOP RESUME STOP RESUME ART ART* ART ART* Treatment Treatment Interruption Interruption Phase Follow-up Phase Phase Follow-up Phase (p p # (proportion) w ho interrupt ART on placebo nn p(p p) )== #(proportion) w ho interrupt ART on placebo p v v S S 00 44 26 26 38 39 38 39 54 55 54 55 Week Week needed/desired * *IfIfneeded/desired 84 84 Treatment Interruption Phase Treatment Interruption Phase 11 22 (Wk 39) (Wk 39) 44 66 88 12 12 Week Week 16 16 (Wk 54) (Wk 54) Viral Load i Setpoint (VLS): VLS i = Y = mean of log10(vRNA) VLS i = Y i = mean of log10(vRNA) at at Weeks 12 and 16. Weeks 12 and 16 for subject i. June 4, 2007 2007 ICSA Applied Statistics Symposium 9 Challenge: Missing vRNA Data Due to “Drop-Outs” 100,000 90,000 80,000 Start ART (viral failure) HIV Viral Load (RNA copies/ml) 70,000 60,000 50,000 40,000 Complete Data Lost to Follow-up 30,000 20,000 10,000 0 0 1 2 4 6 8 12 16 Weeks Post-Diagnosis or Post-Treatment Interruption June 4, 2007 2007 ICSA Applied Statistics Symposium 10 Numerical Example: Hypothetical Data based on Therapeutic POC Efficacy Trial Patient 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 log10 viral load during the ART interruption phase Wk 1 Wk 2 Wk 4 Wk 6 Wk 8 Wk 12 Wk 16 2.3* 3.8 4.8 4.5 3.5 2.3* 2.3* 2.3* 2.3* 3.6 4.1 4.4 4.3 4.2 2.3* 2.3* 4.7 4.4 3.8 3.4 2.6 3.9 5.5 5.8 . . . . 2.3* 2.3* 4.1 4.7 4.3 5.4 4.9 2.3* 2.3* 4.3 4.1 4.2 3.8 3.9 2.3* 2.3* 2.7 3.2 3.0 2.3* 2.8 2.9 4.6 3.9 3.7 . . . 2.3* 2.3* 3.3 5.2 6.2 6.5 6.4 2.3* 4.0 4.8 5.2 4.6 4.4 4.5 3.6 3.5 4.0 3.9 4.5 4.2 4.7 2.3* 4.0 4.5 5.7 6.0 . . 2.3* 2.3* 4.6 4.7 4.5 4.4 4.4 2.9 4.2 4.9 4.9 4.5 4.5 4.3 2.3* 3.7 . . . . . 2.3* 2.3* 2.9 3.4 4.1 2.3* 3.4 2.3* 4.4 4.7 4.5 4.8 4.4 3.7 2.3* 5.0 6.4 6.2 5.1 5.1 4.8 2.3* 4.0 4.9 5.1 5.1 5.0 4.7 2.3* 2.3* 4.7 4.8 4.9 3.7 4.2 Trt Group Vaccine VLS 2.3 4.3 3.0 ? 5.2 3.8 2.5 ? 6.4 4.5 4.4 ? 4.4 4.4 ? 2.9 4.1 5.0 4.9 4.0 Placebo Subject restarted ART; Subject was lost to follow-up * log10 viral loads < log10(400) = 2.6 were replaced with log10(200)=2.3 June 4, 2007 2007 ICSA Applied Statistics Symposium 11 Numerical Example (cont.): Hypothetical Data Vaccine 1000000 1000000 Placebo HIV Viral Load (RNA copies/ml) Load (RNA copies/ml) HIV Viral Load (RNA copies/ml) 100000 100000 10000 Median VLS = 4.06 10000 Median VLS = 4.36 1000 1000 100 100 1 2 4 6 8 12 16 1 2 4 6 8 12 16 Weeks Post-ART Interruption Post-ART Interruption Weeks Post-ART Interruption Completers: Lost to Follow-up: Restart ART: June 4, 2007 8/10 (80%) 1/10 (10%) 1/10 (10%) 2007 ICSA Applied Statistics Symposium 8/10 (80%) 1/10 (10%) 1/10 (10%) 12 “Standard”, but Ad hoc Statistical Methods  LOCF » Use LOCF to impute missing values after dropout. » Calculate VLS, then use a t-test.  Tied Worst Rank » Assign VLS = 10^10 to all “drop-outs”. » Use Wilcoxon Rank Sum (WRS) test.  Untied Worst Rank » Assign VLS = 10^10 – tlast to all “drop-outs”, where tlast = time of dropout (penalizes earlier dropouts). » Use Wilcoxon Rank Sum (WRS) test. June 4, 2007 2007 ICSA Applied Statistics Symposium 13 Numerical Example: Hypothetical Data using LOCF Trt Group Vaccine Patient 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 log10 viral load during the ART interruption phase Wk 1 Wk 2 Wk 4 Wk 6 Wk 8 Wk 12 Wk 16 2.3* 3.8 4.8 4.5 3.5 2.3* 2.3* 2.3* 2.3* 3.6 4.1 4.4 4.3 4.2 2.3* 2.3* 4.7 4.4 3.8 3.4 2.6 3.9 5.5 5.8 5.8 5.8 5.8 5.8 2.3* 2.3* 4.1 4.7 4.3 5.4 4.9 2.3* 2.3* 4.3 4.1 4.2 3.8 3.9 2.3* 2.3* 2.7 3.2 3.0 2.3* 2.8 2.9 4.6 3.9 3.7 3.7 3.7 3.7 2.3* 2.3* 3.3 5.2 6.2 6.5 6.4 2.3* 4.0 4.8 5.2 4.6 4.4 4.5 3.6 3.5 4.0 3.9 4.5 4.2 4.7 2.3* 4.0 4.5 5.7 6.0 6.0 6.0 2.3* 2.3* 4.6 4.7 4.5 4.4 4.4 2.9 4.2 4.9 4.9 4.5 4.5 4.3 2.3* 3.7 3.7 3.7 3.7 3.7 3.7 2.3* 2.3* 2.9 3.4 4.1 2.3* 3.4 2.3* 4.4 4.7 4.5 4.8 4.4 3.7 2.3* 5.0 6.4 6.2 5.1 5.1 4.8 2.3* 4.0 4.9 5.1 5.1 5.0 4.7 2.3* 2.3* 4.7 4.8 4.9 3.7 4.2 VLS 2.3 4.3 3.0 5.8 5.2 3.8 2.5 3.7 6.4 4.5 4.4 6.0 4.4 4.4 3.7 2.9 4.1 5.0 4.9 4.0 Placebo Subject restarted ART; Subject was lost to follow-up * log10 viral loads < log10(400) = 2.6 were replaced with log10(200)=2.3 June 4, 2007 2007 ICSA Applied Statistics Symposium 14 Numerical Example: Hypothetical Data using Tied Worst Rank Trt Group Vaccine Patient 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 log10 viral load during the ART interruption phase Wk 1 Wk 2 Wk 4 Wk 6 Wk 8 Wk 12 Wk 16 2.3* 3.8 4.8 4.5 3.5 2.3* 2.3* 2.3* 2.3* 3.6 4.1 4.4 4.3 4.2 2.3* 2.3* 4.7 4.4 3.8 3.4 2.6 3.9 5.5 5.8 . . . . 2.3* 2.3* 4.1 4.7 4.3 5.4 4.9 2.3* 2.3* 4.3 4.1 4.2 3.8 3.9 2.3* 2.3* 2.7 3.2 3.0 2.3* 2.8 2.9 4.6 3.9 3.7 . . . 2.3* 2.3* 3.3 5.2 6.2 6.5 6.4 2.3* 4.0 4.8 5.2 4.6 4.4 4.5 3.6 3.5 4.0 3.9 4.5 4.2 4.7 2.3* 4.0 4.5 5.7 6.0 . . 2.3* 2.3* 4.6 4.7 4.5 4.4 4.4 2.9 4.2 4.9 4.9 4.5 4.5 4.3 2.3* 3.7 . . . . . 2.3* 2.3* 2.9 3.4 4.1 2.3* 3.4 2.3* 4.4 4.7 4.5 4.8 4.4 3.7 2.3* 5.0 6.4 6.2 5.1 5.1 4.8 2.3* 4.0 4.9 5.1 5.1 5.0 4.7 2.3* 2.3* 4.7 4.8 4.9 3.7 4.2 VLS 2.3 4.3 3.0 1010 5.2 3.8 2.5 1010 6.4 4.5 4.4 1010 4.4 4.4 1010 2.9 4.1 5.0 4.9 4.0 Placebo Subject restarted ART; Subject was lost to follow-up * log10 viral loads < log10(400) = 2.6 were replaced with log10(200)=2.3 June 4, 2007 2007 ICSA Applied Statistics Symposium 15 Numerical Example: Hypothetical Data using Untied Worst Rank Trt Group Vaccine Patient 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 log10 viral load during the ART interruption phase Wk 1 Wk 2 Wk 4 Wk 6 Wk 8 Wk 12 Wk 16 2.3* 3.8 4.8 4.5 3.5 2.3* 2.3* 2.3* 2.3* 3.6 4.1 4.4 4.3 4.2 2.3* 2.3* 4.7 4.4 3.8 3.4 2.6 3.9 5.5 5.8 . . . . 2.3* 2.3* 4.1 4.7 4.3 5.4 4.9 2.3* 2.3* 4.3 4.1 4.2 3.8 3.9 2.3* 2.3* 2.7 3.2 3.0 2.3* 2.8 2.9 4.6 3.9 3.7 . . . 2.3* 2.3* 3.3 5.2 6.2 6.5 6.4 2.3* 4.0 4.8 5.2 4.6 4.4 4.5 3.6 3.5 4.0 3.9 4.5 4.2 4.7 2.3* 4.0 4.5 5.7 6.0 . . 2.3* 2.3* 4.6 4.7 4.5 4.4 4.4 2.9 4.2 4.9 4.9 4.5 4.5 4.3 2.3* 3.7 . . . . . 2.3* 2.3* 2.9 3.4 4.1 2.3* 3.4 2.3* 4.4 4.7 4.5 4.8 4.4 3.7 2.3* 5.0 6.4 6.2 5.1 5.1 4.8 2.3* 4.0 4.9 5.1 5.1 5.0 4.7 2.3* 2.3* 4.7 4.8 4.9 3.7 4.2 VLS 2.3 4.3 3.0 1010-4 5.2 3.8 2.5 1010-6 6.4 4.5 4.4 1010-8 4.4 4.4 1010-2 2.9 4.1 5.0 4.9 4.0 Placebo Subject restarted ART; Subject was lost to follow-up * log10 viral loads < log10(400) = 2.6 were replaced with log10(200)=2.3 June 4, 2007 2007 ICSA Applied Statistics Symposium 16 Other “Standard” Statistical Methods  REML: Parametric repeated measures analysis (PROC MIXED default). » Assumptions include: multivariate normality, properly modeled covariance matrix, and missing values (if any) are missing at random (MAR).  Weighted GEE: Extension of semiparametric repeated measures analysis (generalized estimating equations) to accommodate non-normality and MAR data. » Assumptions include: correct modeling of the dropout mechanism to estimate weights (inverse probability of response) and missing values are MAR. June 4, 2007 2007 ICSA Applied Statistics Symposium 17 Numerical Example: Hypothetical Data using Weighted GEE Trt Group Patient Vaccine 1 2 3 4 5 6 7 8 9 10 Placebo 1 2 3 4 5 6 7 8 9 10 Wk 1 2.3* (1.0) 2.3* (1.0) 2.3* (1.0) 3.9 (1.0) 2.3* (1.0) 2.3* (1.0) 2.3* (1.0) 2.9 (1.0) 2.3* (1.0) 2.3* (1.0) 3.6 (1.0) 2.3* (1.0) 2.3* (1.0) 2.9 (1.0) 2.3* (1.0) 2.3* (1.0) 2.3* (1.0) 2.3* (1.0) 2.3* (1.0) 2.3* (1.0) log10 viral load during the ART interruption phase Wk 2 Wk 4 Wk 6 Wk 8 Wk 12 3.8 (1.0) 4.8 (1.1) 4.5 (1.2) 3.5 (1.4) 2.3* (1.6) 2.3* (1.0) 3.6 (1.0) 4.1 (1.1) 4.4 (1.3) 4.3 (1.6) 2.3* (1.0) 4.7 (1.0) 4.4 (1.2) 3.8 (1.3) 3.4 (1.6) 5.5 (1.0) 5.8 (1.1) . . . 2.3* (1.0) 4.1 (1.0) 4.7 (1.1) 4.3 (1.3) 5.4 (1.6) 2.3* (1.0) 4.3 (1.0) 4.1 (1.1) 4.2 (1.3) 3.8 (1.6) 2.3* (1.0) 2.7 (1.0) 3.2 (1.1) 3.0 (1.2) 2.3* (1.4) 4.6 (1.0) 3.9 (1.1) 3.7 (1.2) . . 2.3* (1.0) 3.3 (1.0) 5.2 (1.1) 6.2 (1.3) 6.5 (1.9) 4.0 (1.0) 4.8 (1.1) 5.2 (1.2) 4.6 (1.5) 4.4 (1.8) 3.5 (1.0) 4.0 (1.1) 3.9 (1.1) 4.5 (1.3) 4.2 (1.6) 4.0 (1.0) 4.5 (1.1) 5.7 (1.2) 6.0 (1.5) . 2.3* (1.0) 4.6 (1.0) 4.7 (1.2) 4.5 (1.4) 4.4 (1.7) 4.2 (1.0) 4.9 (1.1) 4.9 (1.2) 4.5 (1.4) 4.5 (1.8) 3.7 (1.0) . . . . 2.3* (1.0) 2.9 (1.0) 3.4 (1.1) 4.1 (1.2) 2.3* (1.5) 4.4 (1.0) 4.7 (1.1) 4.5 (1.2) 4.8 (1.4) 4.4 (1.8) 5.0 (1.0) 6.4 (1.1) 6.2 (1.3) 5.1 (1.8) 5.1 (2.3) 4.0 (1.0) 4.9 (1.1) 5.1 (1.2) 5.1 (1.5) 5.0 (1.9) 2.3* (1.0) 4.7 (1.0) 4.8 (1.2) 4.9 (1.4) 3.7 (1.8) Wk 16 2.3* (1.8) 4.2 (1.9) 2.6 (1.9) . 4.9 (2.2) 3.9 (1.9) 2.8 (1.5) . 6.4 (3.0) 4.5 (2.3) 4.7 (2.0) . 4.4 (2.1) 4.3 (2.2) . 3.4 (1.6) 3.7 (2.2) 4.8 (3.0) 4.7 (2.5) 4.2 (2.1) Subject restarted ART; Subject was lost to follow-up * log10 viral loads < log10(400) = 2.6 were replaced with log10(200)=2.3 June 4, 2007 2007 ICSA Applied Statistics Symposium 18 A New Method: Two-step Approach  A rank-based analysis after multiple imputation (Mogg and Mehrotra, 2007).  Step 1: Impute missing values (Rubin, 1987) » Create M (= 20) complete data sets using SAS PROC MI to impute. – Assumptions include multivariate normality and MAR.  Step 2: Rank-based analysis » Calculate the numerator and denominator of a rankbased test statistic for each complete data set. » Combine the M results to get a single p-value for inference. – Valid inference when assumptions above are violated as long as imputations are rank preserving. June 4, 2007 2007 ICSA Applied Statistics Symposium 19 A New Method: Two-step Approach (cont.)  Two options for rank-based test after imputation: 1) WRS test applied to the VLS values. [MI  WRS] 2) Separate WRS tests at last two time points, combined with equal weight. (MI-based extension of Wei-Lachin, 1984.) [MI  WL] – Mann & Whitney (1947) proposed a rank test equivalent to the WRS test: θ  [Pr(Yv  Y ) - Pr(Yv  Y )]  p  - p  p p – In the multivariate setting, Wei and Lachin (1984) present a Tvariate generalization of this test: pt pt vt ˆ  # (Yvt  Y )# (Y  Y )  p - p , (1  t  T) ˆ t  ˆ t θt nvtnpt ˆ ˆ – The vectors θ and W'θ, where W is a vector of weights, are ˆ asymptotically normal with covariance matrices Σ( θ ) and ˆ W' Σ( θ)W. June 4, 2007 2007 ICSA Applied Statistics Symposium 20 Numerical Example (cont.) VLS p-value .174 .198 .198 .410 .354 .354 .328 Method MI  WL MI  WRS REML WGEE Tied Worst Rank Untied Worst Rank LOCF MI = multiple imputation, WL = Wei-Lachin, WRS = Wilcoxon rank sum test SAS PROC MIXED used for REML, SAS PROC GENMOD used for WGEE June 4, 2007 2007 ICSA Applied Statistics Symposium 21 (based on Therapeutic POC Efficacy Trial)   2 groups (P=Placebo, V=Vaccine); 7 time points; Total N = 120 (80 vaccine, 40 placebo) Three data generating distributions: 1. MVN(,) 2. SCN = 0.9MVN(,) + 0.1MVN(,16) [stochastic mix] 3. MVT() with 3 d.f. P = V under H0 std dev. = 0.65, Toeplitz corr. (0.8) Under HA std dev. vaccine = 0.75 Details of Simulation Study    Under H0, VLS = 4.5 for P and V Under HA, VLS = 4.5 for P and VLS = 4.0 for V 10,000 simulations, nominal  = 2.5% (1-tailed) 2007 ICSA Applied Statistics Symposium 22 June 4, 2007 Details of Simulation Study (cont.)  Combination of two monotone missing data mechanisms: » MAR: Data for a subject was set to missing (subject went back on ART) with 90% probability if 2 consecutive vRNA measurements > 150,000 copies/ml. MCAR: On average, 10% of subjects in each treatment group drop-out at a random time point (lost to follow-up). »  % Missing Data by Study Week Week 1 2 4 6 8 12 16 MVN Placebo Vaccine 0% 0% 3% 3% 4% 4% 9% 9% 23% 18% 29% 22% 33% 24% MVT Placebo Vaccine 0% 0% 3% 3% 6% 6% 13% 13% 26% 22% 32% 26% 36% 29% SCN Placebo Vaccine 0% 0% 3% 3% 6% 6% 11% 11% 25% 21% 31% 25% 36% 27% June 4, 2007 2007 ICSA Applied Statistics Symposium 23 Type I Error Rate (=2.5%) VLS Method MI  WL MI  WRS REML WGEE Tied Worst Rank Untied Worst Rank LOCF MVN 2.2 1.7 2.4 (4.5) 2.1 2.0 1.8 SCN 2.0 1.6 2.3 (8.7) 2.8 2.7 2.7 MVT 2.0 1.6 2.7 (9.4) 2.8 2.5 2.6 Simulation Results Result in parentheses if >2.97% (> 3 std. errors above 2.5%); 10,000 simulations MVN = Multivariate Normality; MVT = Multivariate t3;SCN = Symmetric Contaminated Normal For WGEE, weights estimated using logistic regression with categorical time and previous log10(vRNA) as covariates. June 4, 2007 2007 ICSA Applied Statistics Symposium 24 Simulation Results (cont.)  Severely inflated type I error for WGEE.  Agrees with other published reports (Demirtas, 2004 and Preisser et al., 2002). » WGEE performs poorly when drop-out model is not correctly specified. » Even with “reasonable” model for drop-out, WGEE method breaks down here. » Virtually impossible in practice to properly specify missing data model! June 4, 2007 2007 ICSA Applied Statistics Symposium 25 Simulation Results Power VLS Method MI  WL MI  WRS REML WGEE Tied Worst Rank Untied Worst Rank LOCF MVN 92 90 95 (81) 84 84 88 SCN 80 76 71 (54) 72 72 58 MVT 73 69 65 (49) 66 66 53 Result in parentheses if > 2.97% (> 3 std. errors above 2.5%); 10,000 simulations MVN = Multivariate Normality; MVT = Multivariate t3;SCN = Symmetric Contaminated Normal For WGEE, weights estimated using logistic regression with categorical time and previous log10(vRNA) as covariates. June 4, 2007 2007 ICSA Applied Statistics Symposium 26 Simulation Results when Specifying Correct Drop-out Model for WGEE VLS Method MVN SCN MVT Type I error rate (=2.5%) MI  WL WGEE 2.6 3.0 Power MI  WL WGEE 96 91 85 62 81 58 2.4 3.6 2.1 2.6 1,000 simulations; generated and modeled drop-out using logistic regression with categorical time and previous log10(vRNA) as covariates. MVN = Multivariate Normality; MVT = Multivariate t3;SCN = Symmetric Contaminated Normal June 4, 2007 2007 ICSA Applied Statistics Symposium 27 Concluding Remarks  WGEE: type I error can be severely inflated when drop-out model is not correctly specified.  Multiple imputation followed by a rank-based analysis is robust and efficient. We recommend MI  WL, especially for proof-of-concept clinical trials in a variety of therapeutic areas.  LOCF and “worst rank” single imputation methods are (unfortunately) popular, but inefficient!  REML: no imputation is required, but analysis is inefficient with non-normal and censored data.  SAS macro is available upon request. June 4, 2007 2007 ICSA Applied Statistics Symposium 28 Motiviating Trial #2: ACTG A5197 Therapeutic POC Efficacy Trial  Proposed analysis in Statistical Analysis Plan: Untied Worst Rank » Assign VLS = 10^10 – tlast to all “drop-outs”, where tlast = time of dropout (penalizes earlier dropouts). » Use Wilcoxon Rank Sum (WRS) test.  No comments on analysis from CBER.  Analysis targeted to be performed later this year. June 4, 2007 2007 ICSA Applied Statistics Symposium 29 Prophylactic POC Efficacy Trial  Proposed analysis in Statistical Analysis Plan: MI  WRS » Create M (= 20) complete data sets using SAS PROC MI to impute. » Calculate the numerator and denominator of Wilcoxon rank sum test for each complete data set. Motiviating Trial #1: » Combine the M results to get a single p-value for inference.  CBER accepted the proposed strategy for the primary analysis! » Requested a sensitivity analysis using the Worst Rank method: subjects who initiate ART considered “failures”.  First interim analysis targeted to be performed later this year. June 4, 2007 2007 ICSA Applied Statistics Symposium 30 References [1] [2] Emini E and Koff W (2004). Developing an AIDS Vaccine: Need, Uncertainty, Hope, Science, 304, 1913-1914. Demirtas, H (2004). Assessment of Relative Improvement Due to Weights Within Generalized Estimating Equations Framework for Incomplete Clinical Trials Data, Journal of Biopharmaceutical Statistics, 14, 1085-1098. Hogan et al. (2004). Handling drop-out in longitudinal studies, Statistics in Medicine, 23, 1455-1497. [3] [4] [5] [6] [7] [8] [9] Johnston M and Fauci AS (2007). An HIV Vaccine – Evolving Concepts, New England Journal of Medicine, 356, 2073-2081. Liang and Zeger (1986). Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22. Preisser et al. (2002). Performance of weighted estimating equations for longitudinal binary data with drop-outs missing at random, Statistics in Medicine, 21, 3035-3054. Mogg R and Mehrotra DV (2007). Analysis of antiretroviral immunotherapy trials with potentially non-normal and incomplete longitudinal data, Statistics in Medicine, 26, 484-497. Robins et al. (1995). Analysis of Semiparametric Regression Models for Repeated Outcomes in the Presence of Missing Data, Journal of the American Statistical Association, 90, 106-121. Rubin, DB (1987). Multiple Imputation for Non-Response in Surveys, New York: John Wiley and Sons Inc. [10] Thall, PF and Lachin, JM (1988). Analysis of recurrent events: nonparametric methods for random interval count data, Journal of the American Statistical Association, 83, 339-347. [11] Wei, LJ and Lachin, JM (1984). Two-sample Asymptotically Distribution-Free Tests for Incomplete Multivariate Observations, Journal of the American Statistical Association, 79, 653-661. June 4, 2007 2007 ICSA Applied Statistics Symposium 31