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Europe has been an exception to this trend in recent years, with total fertility increasing from 1. More and more countries now have fertility rates below the level required for the replacement of successive generations roughly 2. The report highlights that a reduction in the fertility level results not only in a slower pace of population growth but also in an older population. Compared to , the number of persons aged 60 or above is expected to more than double by and to more than triple by , rising from million globally in to 2.

Populations in other regions are also projected to age significantly over the next several decades and continuing through Africa, for example, which has the youngest age distribution of any region, is projected to experience a rapid ageing of its population.

Globally, the number of persons aged 80 or over is projected to triple by , from million in to million in By it is expected to increase to million, nearly seven times its value in Population ageing is projected to have a profound effect on societies, underscoring the fiscal and political pressures that the health care, old-age pension and social protection systems of many countries are likely to face in the coming decades.

Substantial improvements in life expectancy have occurred in recent years. Globally, life expectancy at birth has risen from 65 years for men and 69 years for women in to 69 years for men and 73 years for women in We use machine learning to flexibly and data-adaptively model the following relationships: instrument to intermediate confounder, intermediate confounder to mediator, and mediator to outcome.

The data-dependent SDE is interpreted as the direct effect of being randomized to receive a housing voucher on risk of marijuana use that is not mediated through a change in school district. The data-dependent SIE is interpreted as the effect of being randomized to receive a housing voucher on marijuana use that is mediated by changing school districts.

We proposed robust targeted minimum loss-based estimators to estimate fixed and data-dependent stochastic direct and indirect effects that are the first to naturally accommodate instrumental variable scenarios. The SDE and SIE have the appealing properties of 1 relaxing the assumption of no intermediate confounder affected by prior exposure, and 2 utility in studying mediation in the context of instrumental variables that adhere to the exclusion restriction assumption a common assumption of instrumental variables which states that there is no direct effect between A and Y or between A and M Angrist, Imbens, and Rubin due to completely blocking arrows into the mediator by marginalizing over the intermediate confounder, Z.

Given the restrictions that this assumption places on the statistical model, several alternative estimands are not appropriate for understanding mediation in this context as the indirect effect would always equal zero e.

Inference for the fixed SDE and SIE can be obtained from bootstrapping, using parametric models for nuisance parameters. The ability to incorporate machine learning is a significant strength in this case; if using the parametric alternative, multiple models would need to be correctly specified VanderWeele and Tchetgen Tchetgen IC-based variance is possible in estimating the data-dependent SDE and SIE, because the data-dependent EIC has a form that is solvable using existing statistical tools; in contrast, the EIC for the fixed parameters is more complex and is not solvable with current statistical tools.

Our proposed estimator for the fixed and data-dependent parameters is simple to implement in standard statistical software, and we provide R code to lower implementation barriers. Another advantage of our TMLE estimator, which is shared with other estimating equation approaches, is that it is robust to some model misspecification. In estimating the data-dependent SDE and SIE, one could obtain a consistent estimate as long as either the Y model or the A and M models given the past were correctly specified.

In addition, our proposed estimation strategy is less sensitive to positivity violations than weighting-based approaches. First, TMLE is usually less sensitive to these violations than weighting estimators, due in part to it being a substitution estimator, which means that its estimates lie within the global constraints of the statistical model.

This is in contrast to alternative estimating equation approaches, which may result in estimates that lie outside the parameter space. Second, we formulate our TMLE such that the targeting is done as a weighted regression, which may smooth highly variable weights Stitelman, De Gruttola, and van der Laan In addition, moving the targeting into the weights improves computation time Stitelman, De Gruttola, and van der Laan However, there are also limitations to the proposed approach.

We have currently only implemented it for a binary A and M , though extensions to multinomial or continuous versions of those variables are possible Rosenblum and van der Laan ; Diaz and Rosenblum Extending the estimator to allow for a high-dimensional M is less straightforward, though it is of interest and an area for future work as allowing for high-dimensional M is a strength of other mediation approaches Tchetgen Tchetgen ; Zheng and van der Laan Angrist, J.

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A total of 37 RCTs were identified. Results indicate that physical exercise has a positive impact on muscle mass and muscle function in subjects aged 65 years and older.

However, any interactive effect of dietary supplementation appears to be limited. Introduction: In , Denison et al.