The Prevention and Treatment of Missing Data in Clinical Trials (2010) / Chapter Skim
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5 Principles and Methods of Sensitivity Analyses
5 Principles and Methods of Sensitivity Analyses
Pages 83-106
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From page 83... ...
We also provide case study illustrations to suggest a format for conducting sensitivity analyses, recognizing that these case studies cannot cover the broad range of types and designs of clinical trials. Because the literature on sensitivity analysis is evolving, the primary objective of this chapter is to assert the importance of conducting some form of sensitivity analysis and to illustrate principles in some simple cases.
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From page 84... ...
One obvious strategy is to consider various dependencies of the missing data process on the outcomes or the covariates. One can choose to supplement an analysis within the selection modeling framework, say, with one or several in the pattern mixture modeling framework, which explicitly models the missing responses at any given time given the previously observed responses.
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From page 85... ...
The paradigm shift to sensitivity analysis is, therefore, welcome. Prior to focused research on sensitivity, many methods used in practice were potentially useful but ad hoc (e.g., comparing several incompatible MNAR models to each other)
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From page 86... ...
As the clinical contexts vary between studies, so too will the specific form of the sensitivity analysis. EXAMPLE: SINGLE OUTCOME, NO AUXILIARY DATA We start with the simple case in which the trial records no baseline covariate data, and the only measurement to be obtained in the study is that of the outcome Y, taken at a specified time after randomization.
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From page 87... ...
ˆ i i Third, this example is the simplest version of a pattern mixture model: the full-data distribution is written as a mixture -- or weighted average -- of the observed and missing data distributions. Under MAR, their means are equal.
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From page 88... ...
Pattern Mixture Model Approach Because we are only interested in the mean of Y, it suffices to make assumptions about how the mean of Y among nonresponders links to the mean of Y among respondents. A simple way to accomplish this is by introducing a sensitivity parameter D that satisfies m0 = m1 +D, or E(Y | R = 0)
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From page 89... ...
. Selection Model Approach A second option for conducting sensitivity analysis is to assume that one knows how the odds of nonresponse change with the values of the outcome Y
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From page 90... ...
With the selection model approach described here we can conduct sensitivity analysis, not just about the mean but about any other component of the distribution of Y, for example, the median of Y Just as in the preceding pattern mixture approach, the data structure in this setting is so simple that we need not worry about postulating type (ii)
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From page 91... ...
(11) Pattern Mixture Model Approach In this and the next section, we demonstrate sensitivity analysis under MNAR.
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From page 92... ...
assumption; it can be critiqued by standard goodness-of-fit procedures using the observed data. Example: Binary Outcome Y If Y is binary, the functional form of g and η will need to be different than in the continuous case.
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From page 93... ...
But when Y0 is continuous, or includes other auxiliary covariates, model choice for η will take on added importance. Inference A sensitivity analysis to examine how inferences are impacted by the choice of D consists of repeating the inference over a set or range of values of Ddeemed to be plausible.
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From page 94... ...
Selection Model Approach In parallel to the first example, with no auxiliary data, another way to postulate type (i) assumptions about the nature of selection bias is by postulating a model for the dependence of the probability of nonresponse on the (possibly missing)
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From page 95... ...
Mean Among Nonresponders Delta Delta Delta (Placebo) FIGURE 5-1 Pattern mixture sensitivity analysis.
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From page 96... ...
EXAMPLE: GENERAL REPEATED MEASURES SETTING As the number of planned measurement occasions increases, the complexity of the sensitivity analysis grows because the number of missing data patterns grows. As a result, there can be limitless ways of specifying models.
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From page 97... ...
FIGURE 5-2 Selection model sensitivity analysis. Left panel: plot of mean outcome among nonrespondents as a function of sensitivity parameter a, where a = 0 corresponds to MAR.
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From page 98... ...
, where L ≤ K − A Pattern Mixture Model Approach As noted above, there are many pattern models that can be specified.
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( T E Y3 (32) This modeling of the observed data distribution comprises our type (i)
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From page 100... ...
A sensitivity analysis consists of estimating m and its standard error repeatedly over a range of plausible values of specified D parameters. For this illustration, setting D = 0 implies MAR.5 Selection Model Another way to posit type (i)
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From page 101... ...
One would make this choice if it is believed that the recorded history Yk− encodes all the predictors of Yk+1 that are associated with missingness. Values of a ≠ 0 reflect residual association of dropping out between visits k and k + 1 and the possibly unobserved outcome Yk+1, after adjusting for previous outcomes, and hence the belief that dropping out cannot be entirely explained by the observed recorded history Yk− .
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From page 102... ...
distribution of Yk+1 among those who drop out between visits k and k + 1 and those who remain through visit k + 1. If one believes that the association between dropping out and future outcomes depends solely on the current outcome but varies according to the recorded history, one can replace a with a known function of Yk− .
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From page 103... ...
examine the appropriateness of existing models and in particular the potential pitfalls of assuming MAR within missing data pattern; and (b) develop and apply novel, appropriate methods of model specification and sensitivity analysis to handle nonmonotone missing data patterns.
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From page 104... ...
Pattern mixture models also can be specified so that the fit to the observed data is identical across all values of the sensitivity parameters; hence, model checking will be straightforward and does not depend on the assumed missing data assumption. Disadvantages of pattern mixture modeling include difficulties in including auxiliary information, which will generally require additional modeling.
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From page 105... ...
The methods can be used to exploit the data recorded throughout the entire follow-up period and, in particular, beyond the end of the reduced analysis interval discussed above. DECISION MAKING Even after model fitting and sensitivity analysis, investigators have to decide about how important the treatment effect is.
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From page 106... ...
We note that there are some often-used models for the analysis of missing data in clinical trials for which the form of a sensitivity analysis has not been fully developed in the literature. Although we have provided principles for the broad development of sensitivity analyses, we have not been prescriptive for many individual models.
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