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Comparing two strategies for primary analysis of longitudinal trials with missing data. Peter Lane Research Statistics Unit. Acknowledgements. Missing data working group (2001 – ) Fiona Holland (Stats & Prog, Harlow) Byron Jones (RSU Harlow) Mike Kenward (LSHTM)

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comparing two strategies for primary analysis of longitudinal trials with missing data

Comparing two strategies for primary analysis of longitudinal trials with missing data

Peter Lane

Research Statistics Unit

acknowledgements
Acknowledgements
  • Missing data working group (2001– )
    • Fiona Holland (Stats & Prog, Harlow)
    • Byron Jones (RSU Harlow)
    • Mike Kenward (LSHTM)
  • MNLM vs LOCF working group (2004– )
    • Paul McSorley (Psychiatry area leader, RTP)
    • Suzanne Edwards & Wen-Jene Ko (S&P, RTP)
    • Kath Davy, Claire Blackburn, Andrea Machin (S&P, Harlow)

FDA/Industry Workshop 23 September 2004

contents
Contents
  • Outline of the problem
  • Methods of analysis
  • Six clinical trials in GSK
  • Simulation study
    • parameters estimated from trials
    • range of drop-out mechanisms
    • comparison of two methods of analysis
  • Conclusions

FDA/Industry Workshop 23 September 2004

outline of the problem
Outline of the problem
  • Missing values in longitudinal trials are a big issue
    • First aim should be to reduce proportion
    • Ethics dictate that it can’t be avoided
    • Information lost can’t be conjured up
    • There is no magic method to fix it
  • Magnitude of problem varies across areas
    • 8-week depression trial: 25%−50% may drop out by final visit
    • 12-week asthma trial: maybe only 5%−10%
    • Most serious when efficacy evaluated at end

FDA/Industry Workshop 23 September 2004

methods of analysis
Methods of analysis
  • Ignore drop-out
    • CC (complete-case analysis)
  • Single imputation of missing values
    • LOCF (last observation carried forward)
  • Generate small samples from estimated distributions
    • MI (multiple imputation)
  • Fit model for response at all time-points
    • GEE (generalized estimating equations)
    • MNLM (multivariate normal linear model; also referred to as MMRM, or mixed-model repeated measures)
  • Model drop-out as well as response
    • SM (selection models)
    • PMM (pattern-mixture models)

FDA/Industry Workshop 23 September 2004

properties of methods
Properties of methods
  • MCAR: drop-out independent of response
    • CC is valid, though it ignores information
    • LOCF is valid if there are no trends with time
  • MAR: drop-out depends only on observations
    • CC, LOCF, GEE invalid
    • MI, MNLM, weighted GEE valid
  • MNAR: drop-out depends also on unobserved
    • CC, LOCF, GEE, MI, MNLM invalid
    • SM, PMM valid if (uncheckable) assumptions true

FDA/Industry Workshop 23 September 2004

usage of methods
Usage of methods
  • In the past, LOCF has been used widely
    • seen as conservative: not necessarily true
    • gives envelope together with CC: not necessarily true
    • conditional inference: not often interpretable
  • MI was developed to improve imputation
    • concern with repeatability & assumptions
  • MNLM is being increasingly used
    • software available, but lack of understanding
  • SM, PMM recommended for sensitivity analysis
    • looks at some types of MNAR, requiring assumptions

FDA/Industry Workshop 23 September 2004

compare locf and mnlm
Compare LOCF and MNLM
  • Simulation study, based on experience from trials
    • Six trials from a range of psychiatry areas
    • Pattern of treatment means over time
    • Covariance matrix between repeated obs
    • Drop-out rates
  • Set up a range of drop-out mechanisms
  • Generate many datasets and analyse both ways
  • Look at bias of treatment diff. at final time-point
  • Look at power to detect diff.

FDA/Industry Workshop 23 September 2004

slide9

Trial 2

Pick two comparisons

Trials 3, 4, 6

Pick one comparison

Gives seven two-arm scenarios

FDA/Industry Workshop 23 September 2004

covariance matrix from trial 4
Covariance matrix from Trial 4

Week Correlation SD

1 4.6

2 .686.3

3 .57.727.2

4 .52.64.837.3

5 .43.53.70.827.2

6 .39 .50.64.75.857.4

7 .33 .43.60.71.78.897.6

8 .32 .44.59.67.74.84.887.7

1 2 3 4 5 6 7

  • Used estimates from each trial in simulation

FDA/Industry Workshop 23 September 2004

drop out rates from trials 2 6
% drop-out rates from Trials 2 & 6

Week 1 2 3 4 5 6 Total

Treat 1 17 11 15 51158

Treat 2 10 13 14 10149

Treat 3 6 15 8 8 340

Week 1 2 3 4 6 8 Total

Treat 1 3 9 5 6 730

Treat 2 7 7 5 7 936

Treat 3 6 3 2 3 922

  • Used average rate over times and treatments from each trial

FDA/Industry Workshop 23 September 2004

drop out mechanisms
Drop-out mechanisms
  • MCAR – generate drop-out at random
  • MAR – classify responses at Time k by size, and simulate drop-out at Time k+1 with varying probabilities for each class
  • MNAR – as for MAR, but simulate drop-out at Time k, so actual response that influences drop-out is “not observed”
  • Divide all responses at any visit into 9 quantiles, and investigate 3 probability patterns (next slide) for drop-out

FDA/Industry Workshop 23 September 2004

drop out probabilities
Drop-out probabilities

Drop-out probability increases as response increases

These patterns give an average 4% drop-out rate per visit

FDA/Industry Workshop 23 September 2004

trial 1 simulation results
Trial 1, simulation results
  • Large treatment difference: 19
    • average obs. SD: 19
    • patients per arm: 93
  • Example of simulation results
    • MCAR drop-out
    • 1000 simulations

%power_mnlm 99.90

%power_cc 99.90

%power_locf 99.90

%bias_mnlm 0.32

%bias_cc 0.29

%bias_locf –12.17

FDA/Industry Workshop 23 September 2004

trial 1 summary
Trial 1, summary
  • Bias uniformly greater for LOCF
    • average 18% vs 4% for MNLM
    • all negative bias except one for LOCF (MAR extreme)
    • e.g. MNAR linear: 13% bias for LOCF, i.e. treat diff 15 rather than 19; 2% bias for MNLM
    • e.g. MNAR extreme: 24% for LOCF, 18% for MNLM
  • Power nearly all 100%

FDA/Industry Workshop 23 September 2004

trial 2 first comparison
Trial 2, first comparison
  • Medium treatment difference: 13
    • average obs. SD: 19; patients per arm: 75
  • Bias greater for LOCF than MNLM except one (MNAR extreme) with 27% for LOCF, 28% for MNLM
    • average 23% for LOCF, 7% for MNLM
    • all negative bias except one for LOCF (+39% for MAR extreme)
  • Power uniformly higher for LOCF: average 92% vs 67% for MNLM

FDA/Industry Workshop 23 September 2004

trial 3
Trial 3
  • Medium treatment difference: 3
    • average obs. SD: 8.7; patients per arm: 116
  • Similar results to Trial 2 with first comparison, except
    • smaller power difference: 76% for LOCF, 60% for MNLM

FDA/Industry Workshop 23 September 2004

trial 4
Trial 4
  • Small treatment difference: 2
    • average obs. SD: 6.9; patients per arm: 142
  • Bias uniformly greater for LOCF (but small in magnitude as treatment difference is small)
    • average 44% vs 4% for LOCF
    • all negative bias except three for MNLM (+2, 0, 0 for MCAR, MAR light and MAR medium)
  • Power uniformly lower for LOCF
    • average 21% vs 36% for MNLM

FDA/Industry Workshop 23 September 2004

trial 5
Trial 5
  • Small treatment difference: 2
    • average obs SD: 8.9; patients per arm: 121
  • Similar results to Trial 4, except
    • smaller bias difference: 12% for LOCF, 4% for MNLM
    • little power difference: 26% for LOCF, 22% for MNLM

FDA/Industry Workshop 23 September 2004

trial 6
Trial 6
  • Almost no treatment difference: 1
    • average obs. SD: 10.3; patients per arm: 115
  • Bias uniformly greater for LOCF
    • average 28% vs 9% for MNLM
    • negative bias except five for MNLM (+12, +9, +5, +2, +4 for MCAR, MAR and MNAR light)
  • Power virtually the same
    • average 7% for LOCF vs 9% for MNLM

FDA/Industry Workshop 23 September 2004

trial 2 second comparison
Trial 2, second comparison
  • Almost no treatment difference: 1
    • average obs. SD: 19; patients per arm: 75
  • Similar results to Trial 6, except
    • little bias difference: 23% for both

FDA/Industry Workshop 23 September 2004

conclusions
Conclusions

1. MNLM is nearly always superior in terms of reduced bias

  • LOCF is biased even for MCAR with these patterns
  • MNLM has virtually no bias for MCAR and MAR
  • MNLM has less bias than LOCF for moderateMNAR
  • extreme MNAR gives problems for both

2. Bias is usually negative

  • underestimates the effect of a drug
  • is this contributing to the attrition rate of late-phase drugs?

FDA/Industry Workshop 23 September 2004

conclusions continued
Conclusions (continued)

3. LOCF sometimes has more power than MNLM, sometimes less

  • reduced treatment effect can be more than counteracted by artificially increased sample-size
  • against statistical and ethical principles to augment data with invented values

4. MNLM gives very similar results to CC

  • MNLM adjusts CC for non-MCAR effects
  • LOCF adjusts CC in unacceptable ways
  • other methods must be used to investigate non-MAR effects: neither LOCF nor MNLM can address these problems

FDA/Industry Workshop 23 September 2004

actions within gsk
Actions within GSK
  • Continue to propose MNLM for primary analysis of longitudinal trials
  • Prepare clear guides for statisticians, reviewers and clinicians about MNLM
  • Continue to investigate methods for sensitivity analysis to handle MNAR drop-out

FDA/Industry Workshop 23 September 2004

selected references
Selected references
  • Mallinckrodt et al. (2003). Assessing and interpreting treatment effects in longitudinal clinical trials with missing data. Biological Psychiatry53, 754–760.
  • Gueorguieva & Krystal (2004) Move Over ANOVA. Archives of General Psychiatry61, 310–317.
  • Mallinckrodt et al. (2004). Choice of the primary analysis in longitudinal clinical trials. Pharmaceutical Statistics3, 161–169.
  • Molenberghs et al. (2004). Analyzing incomplete longitudinal clinical trial data (with discussion). Biostatistics5, 445–464.
  • Cook, Zeng & Yi (2004). Marginal analysis of incomplete longitudinal binary data: a cautionary note on LOCF imputation. Biometrics60, 820-828.

FDA/Industry Workshop 23 September 2004

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