I am looking at post-mortem toxicology results in a specific population across 5 different years. Is there a way to determine whether there is a meaningful change in the mean toxicology measurement in ng/mL each year? There are over 300 measurements each year from different people, but I would like to determine if the mean of these measurements is changing in our population over time. I would also like to adjust for other variables such as age, sex, and race. Is there a way to best approach this situation?
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$\begingroup$ It depends on what you mean by "meaningful" and how those people were selected from the population. Please let us know. $\endgroup$– whuber ♦Commented Dec 22, 2021 at 17:46
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$\begingroup$ The individuals all experienced the same type of death and that's why they were sampled for this toxicology result. I can't share too many details, but let me know if that helps at all. By meaningful, I mean statistically significant change. $\endgroup$– PollyCommented Dec 22, 2021 at 18:00
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$\begingroup$ This might be related to changepoint analysis if your hypothesis is one of a sudden or dramatic shift, and trend in the parameters if the shift is gradual. $\endgroup$– AvrahamCommented Dec 22, 2021 at 18:01
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1$\begingroup$ It appears to be more of a gradual shift $\endgroup$– PollyCommented Dec 22, 2021 at 18:06
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$\begingroup$ @Avraham How do you propose to do a changepoint analysis with just five individual points?? Since we're not being told essential things about the data, about the best we can do is suggest that this might be a classic ANCOVA application to test whether there is any difference at all among the five groups of annual data. In short, just do the regression and read off the results. $\endgroup$– whuber ♦Commented Dec 22, 2021 at 18:31
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Greetings from a fellow forensic toxicologist. The very first thing you should do is to check whether the measurments are normally distributed and have equal variances each year. If they are, you could try one or both of the following, very simple, procedures.
If you are interested in whether there is a statistically significant change from one year to the next, and how large the change is, you could perform t-tests first on the 2011 and 2012 measurements, then 2012 and 2013 etc. But this will not necessarily give a good impression of the general trend during the entire period.
If you are interested the general trend, you could begin by trying a simple linear regression if the mean appears to change relatively linearly. The regression analysis will provide you with significance levels in the form of p-values for the model parameters.
You can split the data according to age, sex, race etc. and then perform the analyses. You could also combine data from all years and perform t-tests to check if there is generally a difference in mean concentrations between males and females etc.
However, although a change may be statistically significant, this doesn't necessarily mean that the change is meaningful i.e. from a a toxicological, epidemiological or societal perspective. For example, you could find that the mean concentration of e.g. morphine increases significantly (in the statistical sense) during a ten year period, but the actual increase is only 5%. In that case, I wouldn't necessarily consider the change meaningful in the sense that it gives us reason to believe that morphine users are taking much higher doses than before or something like that.
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$\begingroup$ The t-testing is incorrect because it is subject to multiple comparisons problems that are difficult to compensate for. Moreover, it doesn't control for the covariates. (Splitting the data is ad hoc, often not feasible, and inferior to commonly available solutions.) That's why ANCOVA is indicated. It's essentially the same as the multiple regression, treating each year as a separate group. Normality of the responses is not necessarily needed, although homoscedasticity does need to be checked carefully. $\endgroup$– whuber ♦Commented Dec 22, 2021 at 18:50
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$\begingroup$ I'm a general insurance actuary, not a toxicologist, so I may not fully understand the domain, but would it be sensible to add an interaction term between year and the independant variables of toxicological interest to capture a measure of trend? $\endgroup$– AvrahamCommented Dec 22, 2021 at 18:53
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$\begingroup$ Thank you! My measurements are not normally distributed and do not have equal variances each year. I was thinking about ANCOVA, but I haven't checked homoscedasticity. I'll do that next. Also, the description of "meaningful in the sense that it gives us reason to believe that morphine users are taking much higher doses than before" is the type of conclusion that I would like to make. $\endgroup$– PollyCommented Dec 22, 2021 at 19:01
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$\begingroup$ @Polly: in that case, the evaluation of "meaningfulness" becomes much more than just a statistical issue. You could for example consider whether the increase in concentration is big enough to substantially increase the risk of serious toxicity or death (check Baselt!), whether the increase coincides with increased availability of the drug in question, or whether there was sharper increase during the pandemic years than before them (this is why I'm suggesting that t-tests may indeed be useful) - or whatever else might be relevant to the aim of your study. $\endgroup$ Commented Dec 22, 2021 at 19:27
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$\begingroup$ @PederHolman Thank you for that explanation! I'm struggling to understand the linear regression approach you recommended. Is is possible to do a linear regression with 5 mean values? Isn't that too small of a sample size? I'm not sure how a regular linear regression with all the measurements across the years would allow me to look at the change in the mean for that year? $\endgroup$– PollyCommented Dec 22, 2021 at 21:31