Where is my outcome regression balancing confounders?

Update 15/06/2018

Paper based on this work now published.

Update 09/11/2017

Someone mentioned the paper  was a bit equation heavy to read. So I’ll give a simple example. You don’t have to download the data and code to get the idea but you can if you want to. The data comes from this paper. Stata code is here.  There are three binary variables: the outcome, the exposure and the confounder.  The mean of the confounder is 38.5% in the whole population, but it differs across the two levels of the exposure (58.3% for exposure = 0 and 32.5% for exposure = 1) so we need to balance the confounder when looking at the relationship between the exposure and the outcome. One method would be to use inverse probability weighting. This balances the confounder at the population mean in both levels of the exposure i.e. 38.5%. It is easy and standard to compare balance before and after adjustment when using inverse probability weighting, however you usually don’t see this in papers using an outcome regression. An outcome regression is just your standard regression model where the regression includes the outcome as the “dependent” variable and the exposure and confounder as “independent” variables. We illustrate a method to check where the outcome regression is balancing the confounder over the two levels of the exposure. It is at 51.9%. This is not the population mean of the confounder.  The “effect” of the exposure on the outcome is slightly different in the outcome regression compared to the inverse probability weighting as they are different populations (one with a mean of the confounder balanced at 38.5% and the other at 51.9%). In the code I show that it you run the outcome regression with an interaction between the exposure and the confounder (so it is saturated) and then calculate, using standardisation, an average effect of the exposure, if we standardise to a population where the confounder is balanced at 51.9% we get the effect of the exposure on the outcome we obtained from the outcome regression without the interaction. Put another way, the outcome regression isn’t balancing the interaction.

(Yes I am aware that in the code I use a linear regression for a binary outcome, but it doesn’t matter here, it was just a handy dataset!)

Original post

We’ve a new working paper (pre-print) and I would welcome comments either here on the blog or on the OSF site where the pre-print is hosted. There is also R and Stata code.  We’ve not shown anything new statistically but think we have a method of checking confounder balance in  outcome regressions.

The abstract is below.

“An outcome regression controlling for observed confounders remains a popular way to assess the causal effect of an exposure in epidemiology, despite more modern causal techniques for adjusting for observed confounders, such as inverse probability weighting. A feature of inverse probability weighting is that checking balance of confounders in the control and exposure groups after confounder adjustment is simple. However, researchers using outcome regressions commonly do not check confounder balance after controlling for confounders. Although outcome regressions will balance any confounder specified in the model, the confounder value the model balances at is not transparent. We show that a matrix representation of an outcome regression reveals that an outcome regression includes a weight similar to an inverse probability weight. We also show that outcome regressions may not be balancing at the sample mean of the confounders particularly if interactions are not included with the exposure, which is typically the case in outcome regressions. Finally, we show that the coefficient of the exposure in an outcome regression is simply the difference between two weighted counterfactuals. Thus, there is an important connection between traditional outcome regression and modern causal techniques.”


Measures of variance of age of death aren’t age discriminatory.

Age discrimination by a measure of variance?

A recent commentary in AJPH argued that measures like Years of Life Lost (YLL) are age discriminatory. First, because such measures give more weight to deaths at younger ages. Second, this weighting is justified because younger lives have more value to society. I agree with the second criticism, we should value all human life. I strongly disagree with the first.

Why do I disagree?

YLL is similar to measures of variance in demography, which I have highlighted as measures of inequality. Such measures summarise the distribution of deaths by age. One key finding is that there is a close relationship between the mean age of death and the variance. So if you object to measures of variance that give more weight to young deaths  then you object to measures of the mean, like life expectancy, that also reflect years of life lost.

Moreover, even more simple measures like the death rate when used to make comparisons between groups could be regarded as age discriminatory. This is because often the difference is not only due to  higher rates but also due to a different distribution of death. So, essentially the logic of the argument of the commentary leads to all measures of inequality being age discriminatory.

These measures highlight inequality.

Measures of variance in the age of death have highlighted countries like the USA that do poorly in both life expectancy and inequality. This is because of high levels of working age deaths, especially amongst men. This is probably related to high levels of unemployment and deprivation. In fact the USA is an outlier in that it manages to have a slightly higher life expectancy than its level of inequality would suggest. It performs well for older ages but extremely poorly for its young. The argument that measures that highlight early life mortality are somehow age discriminatory has been made elsewhere as well. However, I think the logic is flawed.

Funding and disclaimer

The MRC/CSO Social and Public Health Sciences Unit is funded by the Medical Research Council and the Scottish Government Chief Scientist Office. The views expressed are not those of the Medical Research Council or the Scottish Government.

Relative deprivation: a key theory for health inequality research?

The Black report and relative deprivation

The Black report is the famous 1980 UK report on health inequalities. Its favoured theory for why health inequalities persisted and widened post WWII was structural theory (aka materialist). In some ways this is just Peter Townsend’s relative deprivation theory applied to health inequalities.  Townsend was one of the report’s authors and a leading thinker on why deprivation and poverty persisted in rich countries.  You can read his classic 1979  book “Poverty in the UK” for free.  While the empirical work is dated, the theoretical is still of contemporary importance. I would recommend chapters 27, 1 and 2 for understanding relative deprivation theory. Of course Townsend wrote lots more and this collection is well worth a read. Townsend’s theory has been particularly influential in measuring poverty and measuring area deprivation. Yet it also covers the whole social gradient, individual and household deprivation.

Defining relative deprivation

Townsend defined relative deprivation as “… the absence or inadequacy of those diets, amenities, standards, services and activities which are common or customary in society. People are deprived of the conditions of life which ordinarily define membership of society. If they lack or are denied resources to obtain access to these conditions of life and so fulfil membership of society, they are in poverty.”

Continue reading Relative deprivation: a key theory for health inequality research?

Death expectancy? For studying health inequality?

What’s the opposite of life expectancy? Well I think it might be death expectancy, the area above, rather than below, the survival curve. Say we have a lifetable where the last age is 110+. There are essentially 111 years of life in the lifetable. So death expectancy at birth is 111 minus life expectancy. I am sure you could derive this directly from lifetable elements and demographers have this sorted already. Let me know. Also note I took inspiration from this paper that looked at 100 minus life expectancy.

Continue reading Death expectancy? For studying health inequality?

The link between population health and health inequality

Is life expectancy increasing? Is health inequality decreasing? These are fundamental questions for population health.  It is thus natural to ask if life expectancy and inequality are related. The figure below shows they are. It compares life expectancy – average age at death – to the distribution of the age at death around this average (inequality). If everyone died at the same age there would be no inequality. So average years of life lost per death measures inequality. Higher life expectancy is associated with lower inequality.  Each dot is calculated from 5 years worth of data for a country, with 41 countries observed since 1950 (i.e. one dot is for Scotland in 1950-54).

Continue reading The link between population health and health inequality