What statistical test can I use? If any?

Question

I'm currently investigating mortality rates in my local area compared to England.

Mortality rates in my local area have always been higher than England however recently I've noticed a widening gap between them, with mortality rates in England continuing to decrease over the years but increasing in my local area.

I wanted to investigate potential contributing factors to this widening gap over time, such as deprivation. I'm working with the assumption the amount of deprivation in my local area has not changed over time but I want to see if the more deprived parts of my local community are contributing to this mortality increase more than those less deprived areas and so community work can be focused where necessary.

I thought about creating a line graph for each deprivation level and comparing the slope of these lines. But I was wondering if there were any statistical tests that could be done to help answer this question.

Answer 1

You could consider the number of deaths out of the total number of inhabitants to be a binomial process. You can then use a regression model with deprivation as an explanatory variable, to see whether higher values of deprivation correspond to an increase in the average mortality rate.

Suppose your data is called DF and looks like this:

area	year	deaths	depriv
England	2024	982	0.1
...	...	...

with deaths representing the number of deaths per $100,\!000$.

In R, you could fit a binomial GLM to estimate the relationship between deprivation (depriv) and the probability of death like so:

GLM <- glm(cbind(deaths, 1e5 - deaths) ~ depriv,
           family = "binomial", data = DF)

You can also try to include other effects, like a regression spline for the effect of year:

require("splines")
GLM <- glm(cbind(deaths, 1e5 - deaths) ~ depriv + ns(year, 5),
           family = "binomial", data = DF)

After that, you can use summary for a standard regression table, emmeans for comparisons and a marginal effects plot to see visualize the estimated effect of deprivation on the mortality rate.

In the same manner, you could add other potentially confounding variables.

This is actually a major challenge in what you're trying to do. It is easy to see how two variables are marginally correlated to each other. But why two variables correlate is a much harder question. You'll have to decide on which variables to include in the model.

Finally, it is also possible to correct for the fact that some cities just happen to have higher mortality rates than others. One way is by including all variables that might affect this (like size), and another is by including a random effect for area, by using a mixed model.

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Edit: If you want to know whether the effect of deprivation changes over time, you could add an interaction term (*). This term tells you how the slope of depriv depends on year:

GLM <- glm(cbind(deaths, 1e5 - deaths) ~ depriv * time, 
           family = "binomial", data = DF)