# Presentation: 102180

## STATISTICAL CONSIDERATION

**Exploration of Multivariate Failure Time Analysis Method - An approach for Alcohol Treatment Clinical Trials****Sue-Jane Wang, Ph.D.****Senior Mathematical Statistician****wangs@cder.fda.gov****Division of Biometrics II, OB/CDER/FDA****Second Seattle Symposium in Biostatistics: Analysis of Correlated Data**Nov. 20-21, 2000, Seattle, Washington

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## STATISTICAL EXPERIENCE - 1 (Naltrexone)

**Design**
**Randomized and double-blind 12-week study of Naltrexone vs. placebo in conjunction with psychotherapy**
**References:**
**Volpicelli: one psychotherapy was used**
**Archival General Psychiatry Vol. 49, 876-880, 1992**
**O’Malley: two kinds of psychotherapy were used**
**Archival General Psychiatry Vol. 49, 881-887, 1992**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## STATISTICAL EXPERIENCE - 2 (Naltrexone)

**Outcome Measures reported by patients**
**time-to-1st-drink**
**time-to-1st-heavy-drinking-day(e.g., ******** 5 drinks/day)**
**relapse to heavy drinking**
**complete abstinence from drinking**
**number of days on which patients drank or were drunk**
**craving for alcohol**
**Lab measurements**
**blood alcohol**
**liver enzyme levels**
**etc.**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## CLINICAL RESPONSE (Yes/No)  (Volpicelli et al., n=35/arm, Arch. Gen. Psychiatry, 1992) 

**% patients completed, no-relapse  37%(Placebo) vs. 60%(Naltrexone),   p=0.093(exact);  p=0.056(*****X******2*****)**
**% dropout, no-known-relapse            9% (P) vs. 17% (N), p=0.477(exact)**
**% patients with relapse           ****   ****54% (P) vs. 23% (N), p=0.013(exact)**
**Alcohol Relapse: reporting**
**drinking ******** 5 days/week**
****** ****5 drinks per drinking occasion**
**coming to the treatment appointment with a blood alcohol concentration above 100 mg/dL**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## CLINICAL RESPONSE (Yes/No) (O’Malley et al., n=52/arm,* Arch. Gen. Psychiatry, 1992)

**%  patients completed, no-drink     22% (Placebo) vs. 30% (Naltrexone),                       p=0.359 (exact); p=0.319 (*****X******2*****)**
**% dropout, no-known-drinking            6% (P) vs. 24% (N), p=0.019 (exact)**
**% patients w/ ******** 1-drinking               72% (P) vs. 46% (N), p=0.012 (exact)**
**Patients were relatively older            in naltrexone (42.8yrs+/-10.3yrs) than in placebo (38.5yrs+/-8.8yrs) **
*** 97 patients received medication for ******** 1-week (51 placebo; 46 naltrexone)**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## TIME TO FIRST RELAPSE(Volpicelli et al., n=35/arm, Arch. Gen. Psychiatry, 1992) 

**TIME TO FIRST RELAPSE****(Volpicelli et al., n=35/arm, Arch. Gen. Psychiatry, 1992)**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## TIME TO FIRST RELAPSE(O’Malley et al., n=52/arm, Arch. Gen. Psychiatry, 1992)

**Time-to-1st-relapse defined as drinking ********5 for men, ******** 4 for women on an occasion****Comparison of cumulative time to first relapse, p-value =0.007****median relapse: 35days (placebo/supportive); 25 days (placebo/coping)****median relapse: more than 12 weeks (Naltrexone/supportive or Nalrexone/coping)**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## RECURRENT EVENT WITHIN SUBGROUP

**Published literature**
**Implicit concept of analysis of recurrent events**
**Determine: Naltrexone-treated patients drank less once they initiated drinking [e.g., Volpicelli, 50%(8/16) in naltrexone and 95% (19/20) in placebo, p<0.01]**
**Examine: probability of relapse once a person had a drink [e.g., O’Malley, p=0.04, naltrexone/coping therapy was found to be more effective than any of the remaining three groups]**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## CONSIDERATIONS OFALCOHOL TREATMENT TRIALS

**Study population of interest**
**alcoholics**
**nearly alcoholics**
**excessive alcohol users**
**Low to Moderate Dropouts**
**minimize dropouts**
**enforce scheduled visits (schema)**
**retrieved-dropout**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## Treatment effect of primary interest
Time-to-first-event and gap-times between events
Time-to-all-heavy-drinking-days ( 5 drinks/day for male and  4 drinks/day for female)
Quantitative outcome
Number of heavy drinking days
Number of low-risk drinking days (  2 drinks/day for male and  1 drink/day for female)
Binary outcome
% of patients having  1 heavy drinking days
% of patients with low-risk drinking
% abstinence

**Time-to-first-event and gap-times between events**
**Time-to-all-heavy-drinking-days (******** 5 drinks/day for male and ******** 4 drinks/day for female)**
**Quantitative outcome**
**Number of heavy drinking days**
**Number of low-risk drinking days**** ( ******** 2 drinks/day for male and ******** 1 drink/day for female)**
**Binary outcome**
**% of patients having ******** 1 heavy drinking days**
**% of patients with low-risk drinking**
**% abstinence**

**CONSIDERATIONS OF****ALCOHOL TREATMENT TRIALS**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## POTENTIAL HYPOTHESES

**Naltrexone enhances abstinence rates?**
**Naltrexone decreases alcohol drinking overall?**
**Naltrexone reduces rate of any relapse?**
**Naltrexone decreases heavy drinkings?**
**Naltrexone reduces rate of heavy relapse?**
**Some combinations of the above?**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## *

**0****	****1****	****2****	****3****	****4****	****5****	****6****	****7****	****8****	****9****	****10****	****11****	****12**

**(1)**

- Week

**Heavy-Drinking Episode (Events)**

**Improvement ?**

**No-improvement**

**?**

**(2)**

**(3)**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## CONVENTIONAL ANALYSIS METHOD

**Time-to-first event**
**might not be able to distinguish pattern (1) from pattern (2)**
**might consider pattern (3) a more favorable outcome than either pattern (1) or pattern (2)**
**What if treatment effect cannot be distinguished based on time-to-first event ?**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## ALTERNATIVE STATISTICAL APPROACH

**Time-to-recurrent-event analysis methods take into account**
**time-to-each-heavy-drinking-day**
**time-to-overall-heavy-drinking-day **
**number of heavy-drinking-days**
**abstinence from heavy-drinking**
**total time or gap times between heavy-drinking-days**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## *

**0****	****1****	****2****	****3****	****4****	****5****	****6****	****7****	****8****	****9****	****10****	****11****	****12**

- Week

**Heavy-Drinking Episode (Events)**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## RECURRENT EVENTSEXAMPLES

**Cardiovascular trial**
**# of arrhythmias occurring over time in same patient**
**Chemotherapeutic trial **
**repeated infections reported by cancer patients**
**Asthma clinical trial **
**multiple asthma attacks in a patient**
**Seizure study **
**recurrent seizures in a patient during trial period**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## Time-to-first-event show treatment difference

Time-to-recurrent-event may strengthen the evaluation of treatment effect  

**Time-to-recurrent-event may strengthen the evaluation of treatment effect  **

**SCENARIO - 1**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## SCENARIO - 2

**Time-to-first-event fail to show treatment difference statistically**
**Time-to-recurrent-events show treatment difference**
**(Barai and Teoh, 1997) - repeated infections in the growth factor studies (patients with high grade malignant non-Hodgkin’s lymphoma)**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## Better Defined Study Population ?

**Better Defined Study Population ****?**
**Outcome Measure(s) of Primary Interest ****?**
**Time to first heavy drinking**
**Time to all heavy drinking days**
**% patients abstinence during the trial period (e.g., 12-weeks)**
**Number of heavy drinking days**
**Number of low-risk drinking days**
**Time-to-recurrent-event-analysis-method** **?**
**Pre-specification of primary hypothesis or hypotheses**
**Design and power the study accordingly**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium

## ANALYSIS METHODS FOR TIME-TO-RECURRENT-EVENT

**Some References**
**AG model (1982, Annals of Stat)**
**PWP total/gap time model (1981, Biometrika)**
**Marginal Model of WLW (1989, JASA)**
**Lawless and Nadeau (1995, Technometrics)**
**Frailty model (e.g., Clayton&Cuzick (1985), Hougarrd (1986))**
**Power/Design Consideration (Hughes (1997); Cook (1995, 2000), Matsui (1999, 2000), etc.)**
**Software available**
**MULCOX2 (Fortran); Splus; SAS, S macros**

- SJ Wang, 11/20/00-11/21/00 2nd Seattle Biostatistics Symposium