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The possibility of unmeasured confounding is one of the main limitations for causal inference from observational studies. There are different methods for partially empirically assessing the plausibility of unconfoundedness. However, most currently available methods require (at least partial) assumptions about the confounding structure, which may be difficult to know in practice. In this paper we describe a simple strategy for empirically assessing the plausibility of conditional unconfoundedness (i.e., whether the candidate set of covariates suffices for confounding adjustment) which does not require any assumptions about the confounding structure, requiring instead assumptions related to temporal ordering between covariates, exposure and outcome (which can be guaranteed by design), measurement error and selection into the study. The proposed method essentially relies on testing the association between a subset of covariates (those associated with the exposure given all other covariates) and the outcome conditional on the remaining covariates and the exposure. We describe the assumptions underlying the method, provide proofs, use simulations to corroborate the theory and illustrate the method with an applied example assessing the causal effect of length-for-age measured in childhood and intelligence quotient measured in adulthood using data from the 1982 Pelotas (Brazil) birth cohort. We also discuss the implications of measurement error and some important limitations.

One of the main tasks of causal inference is estimating well-defined causal parameters. One of the main causal parameters is the average causal effect (ACE) - the expected value of the individual level causal effects in the target population. For binary treatments, the individual level causal effect is defined as contrast between potential outcomes. For continuous outcomes, however, there are many such contrasts in finite samples, thus hampering their use as a useful summary of the causal relationship. Here, we proposed a generalized version of the ACE, where individual level causal effects are defined as the derivative (with respect to the treatment) of the individual level causal dose-response function evaluated at treatment value that the individual has. This definition is equivalent to the conventional definition for binary treatments, but also incorporates continuous treatments. We demonstrate that this quantity can be estimated under conventional causal assumptions and illustrate the theoretical ideas with a simulation study., Comment: The reason for withdrawal is that the proposed definition already exists in a literature that the author was unfamiliar with. More specifically, it exists in the econometrics literature under the name "average derivative effect". Therefore, although this work has been conducted independently of such previous work, it does not contribute anything new to the literature

Background: Interpreting instrumental variable results often requires further assumptions in addition to the core assumptions of relevance, independence, and the exclusion restriction. Methods: We assess whether instrument-exposure additive homogeneity renders the Wald estimand equal to the average derivative effect (ADE) in the case of a binary instrument and a continuous exposure. Results: Instrument-exposure additive homogeneity is insufficient for ADE identification when the instrument is binary, the exposure is continuous and the effect of the exposure on the outcome is non-linear on the additive scale. For a binary exposure, the exposure-outcome effect is necessarily additive linear, so the homogeneity condition is sufficient. Conclusions: For binary instruments, instrument-exposure additive homogeneity identifies the ADE if the exposure is also binary. Otherwise, additional assumptions (such as additive linearity of the exposure-outcome effect) are required.