Ketamine for Treatment Resistant Late-Life Depression
Phase: PHASE3
Conditions: Treatment Resistant Depressive Disorder
Sponsor: VA Office of Research and Development

Ketamine for Treatment-Resistant Late-Life Depression (PI: Sanjay Mathew, M.D.) 
Updated Analytic Plan (08/20/18) 
 
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Updated Trial Design and Analysis Plan 
 
The study protocol captures depression severity via the MADRS on a regular basis following 
administration of the pharmacotherapy; however, the MADRS is not obtained daily over the 
initial seven day post-infusion period.  This renders the use of time to relapse problematic as both 
an adaptation criterion and for the final analysis.  Given that we are accruing participants at ~ 1-2 
per month, have currently randomized n = 22 patients, and anticipate initiating the adaptive 
component of the protocol at n = 25, we have elected to update the adaptation and analysis 
criteria to make the conduct of the study logistically feasible.    
 
We will define the response, on which we will base adaptive randomization, as well as the 
final decision-making, as the probability that a condition results in response (i.e. > 50% decrease 
from the baseline MADRS score) at day seven, following the infusion.   The initial design planned 
to allocate a maximum of N = 72 participants to k = 4 conditions (i.e.  midazolam, ketamine 0.10 
mg/kg, 0.25 mg/kg and 0.5 mg/kg). An initial randomization was to assign participants in a 1:3 
ratio to receive midazolam or further, adaptive randomization.  The 75% of participants allocated 
to adaptive randomization will receive midazolam, ketamine 0.10 mg/kg, 0.25 mg/kg or 0.50 
mg/kg (Figure AAA).  The rationale for the initial 1:3 split, which remains in place, was that if 
investigators expectations held true, the adaptive algorithm would rapidly decrease the 
proportion of participants adaptively randomized to midazolam and increase those allocated to 
ketamine. The 1:3 split will guarantee a sufficient control group (i.e. midazolam) with which to 
credibly compare the best performing ketamine condition. Based on our initial estimates, the 
maximum number of participants initially randomized to midazolam or further, adaptive 
randomization would be n = 18 and n = 54 respectively.  Among participants allocated to adaptive 
randomization (n = 54), the minimum number assigned to conditions (i.e. if all conditions stop 
for utility/futility) will be n = 20. Allocation of these initial n = 20 participants will utilize equal, 
random assignment probabilities prior to invocation of any adaptive decision rules.  
 
All of the above procedures remain in place, with the exception that the alteration in the 
adaptation plan will permit a slight reduction in the sample size required for adaptive 
randomization from n = 54 to n = 49 resulting in an overall sample size of N = 67, slightly lower 
than the initially planned N = 72.  
 
Figure AAA.  Trial Design. 
 
 
 
 
 
While we previously focused on the decision-rules that would maximize the time to relapse  we 
now define these decision rules to maximize the probability of responding on day seven, following 
the infusion. Discussion of prior specification for the survival model is detailed in the previous 
version of the protocol.  For the updated adaptation/analysis plan we derive the priors as follows.  
The anticipated times-to relapse were 2, 3, 4 and 7 days for midazolam, ketamine 0.10 mg/kg, 
0.25 mg/kg and 0.50 mg/kg respectively.  Assuming that the survival model curve follows an 
Exponential  Distribution, the probability of remaining a responder at day seven is 0.09, 0.20, 
0.30 and 0.50 for midazolam, ketamine 0.10 mg/kg, 0.25 mg/kg and 0.50 mg/kg respectively.  
Based on extant data and clinical experience we stipulated that the best and worst case 
1:3 Randomization 
Midazolam 
Adaptive 
Randomization 
Midazolam 
Ketamine 0.10 
Ketamine 0.25 
Ketamine 0.50 

Ketamine for Treatment-Resistant Late-Life Depression (PI: Sanjay Mathew, M.D.) 
Updated Analytic Plan (08/20/18) 
 
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probabilities of seven-day response for each of these conditions were (0.1, 0.25), (0.10,0.30), 
(0.20,0.50) and (0.30,0.70) for midazolam, ketamine 0.10 mg/kg, 0.25 mg/kg and 0.50 mg/kg 
respectively. We use these probabilities to define the 2.5th and 97.5th percentiles of the respective 
prior distributions.  Since the use of a binary decision-rule implies a binomial process, we will use 
a Beta-Binomial model for adaptation and decision-making.  Assuming that the probabilities 
above constitute the 2.5th and 97.5th percentiles of a Beta Distribution for each treatment, we can 
calculate the Beta prior distributions as ~Beta(a = 1.797, b = 17.743), ~Beta(a = 10.849, b = 
46.329), ~Beta(a = 12.607, b = 24.268) and ~Beta(a = 11.260, b = 11.260).  These priors 
countenance a range of credible probability values encompassing both optimistic and pessimistic 
estimates of the probability of response at day seven for each treatment. 
 
The randomization and adaptation rules remain similar with a number of exceptions, which we 
will provide in bold text.  Following equal allocation of the first n = 20 participants to the four 
conditions, the adaptive decision-rules will take effect. If the response rate of the best performing 
condition is large enough that the posterior probability is >0.975 that it is better than the next 
best condition, this will trigger a stop to the study, and declaration of superiority for the highest-
performing condition.  Suspension of accrual will occur for any condition that demonstrates a 
response rate so small that the posterior probability is <0.025 that it is better than the best 
performing condition. Further, if data for any condition indicates that a 10% chance of 
responding at day seven has a posterior probability < 0.05, that condition will be 
stopped for futility. Finally, after allocation of all participants, subject to the preceding 
decision-rules, a condition will be declared superior, and a candidate for further outpatient 
testing, clinical trials if the posterior probability that its response rate exceeds that of the next 
best performing condition is > 0.75.  For the purposes of adaptive randomization, any participant 
failing to demonstrate an initial response will be treated as a non-responder at  day seven. 
 
 
 
Updated Simulations and Operating Characteristics. Changes are provided in bold 
text.  The anticipated probability of remaining a responder at day seven is 0.09, 
0.20, 0.30 and 0.50 for midazolam, ketamine 0.10 mg/kg, 0.25 mg/kg and 0.50 
mg/kg respectively. Assuming these effects as well as the previously specified prior 
distributions and decision-rules, K = 10,000 Monte Carlo simulations indicated that 
the preceding decision rules would identify the best condition (i.e. ketamine 0.50 
mg/kg) 95% percent of the time. This estimate corresponds to conventional power 
and exceeds the widely-used value of 80%. While the maximum planned sample size 
for adaptive allocation is N = 49, on average, the adaptive design required allocation 
of n = 42 participants to reach these conclusions.  Specifically, over 10,000 Monte 
Carlo simulations, an average n = 5, 5, 8 and 24 participants were allocated to 
Midazolam, Ketamine 0.10 mg/kg, 0.25 mg/kg and 0.50 mg/kg by adaptive 
randomization.  Clearly, n = 5 adaptively allocated to Midazolam fails to provide a 
credible comparison group for the best performing Ketamine 0.05 mg/kg condition 
(n = 24); hence the required initial randomization step which will augment the 
Midazolam groups with approximately n = 18 participants, and provide a credible 
comparison group (n = 23).  Evaluation of the Type I Error rate requires 
ascertainment of the chance that the adaptive randomization design will identify a 
treatment as best when, in fact, the null hypothesis obtains.  Setting the probability 
of seven-day response to 0.09 for all conditions simulates this scenario. K = 10000 
Monte Carlo simulations indicate that the preceding decision-rules identify a 
condition as best 4.21% of the time. This compares favorably to the 5% Type I Error 
Rate usually implemented in conventional trials.  
 
Comparing these simulation results to the sample sizes required for a 
conventional, between groups approach permits determination of the degree to 
which to Bayesian adaptive approach confers benefit in decision-making about the 
most promising compound/dose for further investigation.  Detection of a difference 
between probabilities of responding of 0.20, 0.30 and 0.50 at seven days post 
infusion (i.e. Ketamine 0.10 mg/kg, 0.25 mg/kg and 0.50 mg/kg) relative to a 
comparison group with a probability of responding of 0.09 (i.e. Midazolam) would 
require samples of n = 344, 124, and 44 respectively to achieve 80% power with a 

Ketamine for Treatment-Resistant Late-Life Depression (PI: Sanjay Mathew, M.D.) 
Updated Analytic Plan (08/20/18) 
 
3 
two-sided alpha = 0.05.  The Bayesian adaptive randomization approach permits flexibility in 
exploring multiple doses while maximizing allocation to more promising conditions. 
 
Final Data Analysis 
Preliminary data analyses will inspect baseline, group differences and compliance variables 
for correlations with specified outcomes. Variables demonstrating baseline group differences, for 
which there is a correlation with outcomes, will be treated as potential confounders.1,2 Two sets of 
analyses will determine the degree to which any group differences might confound conclusions 
regarding treatment:  one including, and one excluding the relevant variable as a covariate.   
Given recommendations that all clinical trials should be analyzed in conventional, 
Frequentist and Bayesian fashion, parallel analyses will implement each approach for evaluation 
of Aims 1 and 2.3 Frequentist results yield the probability of the observed data, or data more 
extreme, given that the null hypothesis holds.  Bayesian results yield to probability that the 
governing parameter for an observed process equals some value or range of values.  This permits 
statements regarding the probability that treatment confers benefit of some magnitude; a critical 
issue in treatment development. Statistical analyses will use R.4  
Broadly, the analytic strategy will use generalized linear modeling.  Continuous, dichotomous 
and time-to-event data will utilize linear, logistic, and proportional hazards regression 
respectively (Proc GENMOD and Proc PHREG; SAS v. 9.3).  Longitudinal analyses will employ 
generalized linear mixed models (Proc GLIMMIX; SAS 9.3). Intention-to-treat analyses will 
evaluate time to relapse as a function of drug condition, collapsing participants initially 
randomized to midazolam with those assigned to the same condition via adaptive randomization.  
For intention-to-treat purposes, participants failing to demonstrate a response to treatment will 
counted as having relapsed on the first day of follow-up.  Per protocol analyses will subsequently 
estimate effects among only those participants who demonstrated an initial response to 
treatment. Multiple imputation and maximum likelihood solutions, which are robust under 
assumptions of missing at random, will address missing data in cross-sectional and longitudinal 
analyses respectively.5 Sensitivity analyses will evaluate robustness of analytic conclusions to 
missing data. Non-ignorable missing data patterns will be addressed through pattern-mixture 
modeling methods.6 
For Bayesian analyses, unless otherwise indicated in the data analytic plan, priors will be 
neutral and diffuse.  For linear, Poisson, and logistic and Cox Proportional Hazards regression, 
priors for coeficients will take the form ~N(mean = 0, var = 1 x 106) in the linear, log, log(odds) 
and log(hazard) scales respectively.  Evaluation of proportions will use beta-binomial 
models with both the previously stated Beta prior as well as with ~Beta(1,1) priors 
for the purposes of reporting.  Priors for error or dispersion terms will use 
~Uniform(1,100), a ~Half-Normal (µ = 0, σ = 100) or a ~Folded T-Distribution(df = 
3, µ = 0, σ = 100).  Sensitivity analysis using optimistic and pessimistic, skeptical priors will 
evaluate prior assumptions.7 Assessing the convergence of Bayesian analyses on the posterior 
distributions via Monte-Carlo Markov chain (MCMC) will use graphical (Trace Plot, 
Autocorrelation Plot) and quantitative (Geweke Diagnostics, Gelman-Rubin Diagnostics, and 
Heidelberger-Welsh Diagnostics) evidence.  Evaluation of posterior distributions will permit 
statements regarding the probability that effects of varying magnitudes exist, given the data. 
 
 
1 Pocock, S. J. & et al. (2002). Subgroup analysis, covariate adjustment and baseline comparisons 
in clinical trial reporting: current practice and problems. Stat.Med, 21, 2917-2930. 
2Assman, S. F. & et al. (2009). Subgroup analysis and other (mis)uses of baseline data in clinical 
trials. Lancet, 355, 1067-1069. 
3 WIjeysundera DN AP, Hux JE, Beattie WS, Laupacis A. Bayesian statistical inference enhances 
the interpretation of contemporary randomized controlled trials. J Clin Epidemiol. 2009;62(1). 
4 http://www.r-project.org . 
5 Enders, C.  (2010) Applied Missing Data Analysis. Guilford Press. 
6 Fitzmaurice, G.M. & Laird, N.M.  (2000).  Generalized linear mixture models for handling 
nonignorable dropouts in longitudinal studies.  Biostatistics.  1(2):  141-156. 
                                               

Ketamine for Treatment-Resistant Late-Life Depression (PI: Sanjay Mathew, M.D.) 
Updated Analytic Plan (08/20/18) 
 
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7 Spiegelhalter, D.J., Abrams, K.R. & Myles, J.P. (2004)  Bayesian Approaches to Clinical Trials 
and Health-Care Evaluation.  John Wiley & Sons Ltd.  West Sussex, England.