Timeline for How to create a statistical model to test whether a mean value has significantly changed over time?
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| Dec 23, 2021 at 3:51 | comment | added | Peder Holman | My suggestion is not to do a linear regression of the mean values, but of all the concentration measurements. Rather than comparing years as groups, this would assess if concentration increases by the year, or maybe even date if available. The regression line represents the conditional mean, so if it increases and is significant, this indicates that the mean concentration is increasing with time. Controlling for sex, age etc. requires multiple linear regression. As you seem to have heteroscedasticity and the residuals aren't normally distributed you may need to transform the data first. | |
| Dec 22, 2021 at 21:31 | comment | added | Polly | @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? | |
| Dec 22, 2021 at 19:27 | comment | added | Peder Holman | @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. | |
| Dec 22, 2021 at 19:01 | comment | added | Polly | 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. | |
| Dec 22, 2021 at 18:53 | comment | added | Avraham | 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? | |
| Dec 22, 2021 at 18:51 | history | edited | Avraham | CC BY-SA 4.0 |
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| Dec 22, 2021 at 18:50 | comment | added | whuber♦ | 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. | |
| S Dec 22, 2021 at 18:47 | review | First answers | |||
| Dec 22, 2021 at 18:54 | |||||
| S Dec 22, 2021 at 18:47 | history | answered | Peder Holman | CC BY-SA 4.0 |