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476 Targeted learning40.6 Some special topics40.6.1 Sensitivity analysisThe TMLE methodology provides us with statistical inference for the estimandψ 0 . One typically wants to report findings about the actual target quantityof interest ψ0 F ,butitmightnotbereasonabletoassumethatψ 0 = ψ0 F .Onesimple way forward we recently proposed is to define the bias ψ 0 − ψ0 F , andfor each assumed value δ, one can now estimate ψ0F with ψ n − δ and reporta corresponding confidence interval or p-value for the test that H 0 : ψ0 F = 0.Subject matter knowledge combined with data analysis and or simulationsmight now provide a reasonable upper bound for δ and one can then determineif such an upper bound would still provide significant results for the targetquantity of interest. This sensitivity analysis can be made more conservativein exchange for an enhanced interpretation of the sensitivity parameter δ bydefining δ as a particular upper bound of the causal bias ψ 0 − ψ0 F . Such anupper bound might be easier to interpret and thereby improve the sensitivityanalysis. We refer to Diaz and van der Laan (2012) for an introduction ofthis type of sensitivity analysis, a practical demonstration with a few dataexamples, and a preceding literature using alternative approaches; see, e.g.,Rotnitzky et al. (2001), Robins et al. (1999), and Scharfstein et al. (1999).40.6.2 Sample size 1 problemsAbove we demonstrated that the statistical inference relies on establishingasymptotic linearity and thereby asymptotic Normality of the standardizedestimator of ψ 0 . The asymptotic linearity was heavily relying on the centrallimit theorem and uniform probability bounds for sums of independent variables(e.g., Donsker classes). In many applications, the experiment resultingin the observed data cannot be viewed as a series of independent experiments.For example, observing a community of individuals over time might truly be asingle experiment since the individuals might be causally connected through anetwork. In this case, the sample size is one. Nonetheless, one might know foreach individual what other individuals it depends on, or one might know thatthe data at time t only depends on the past through the data collected over thelast x months. Such assumptions imply conditional independence restrictionson the likelihood of the data. As another example, in a group sequential clinicaltrial one might make the randomization probabilities for the next groupof subjects a function of the observed data on all the previously recruitedindividuals. The general field of adaptive designs concerns the constructionof a single experiment that involves data adaptive changes in the design inresponse to previously observed data, and the key challenge of such designs isdevelop methods that provide honest statistical inference; see, e.g., Rosenblumand van der Laan (2011). These examples demonstrate that targeted learning