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Good morning, i am looking for some help with longitudinal data with time-varying binary exposure in linear mixed model. Outcome is continuous variable. I am going to use R and the lme4 package. I want to identify association between time varying smoking status and hemoglobin A1c with random intercept and random slope.

Here is a sample dataset and R code that i conducted. Is this right analysis for my hypothesis?

id smoking HbA1c visit
1 0 6.5 1
1 0 6.7 2
1 0 6.8 3
1 1 7 4
1 1 7.5 5
2 1 6.8 1
2 1 7.4 2
2 1 7.6 3
2 1 7.5 4
3 0 6.4 1
3 0 6.5 2
3 0 6.6 3
4 0 6.7 1
4 0 6.6 2
4 0 6.7 3
4 0 6.8 4
4 0 6.8 5
5 0 7 1
5 0 7 2
5 1 7 3
6 0 7.1 1
6 0 7 2
6 0 7.1 3
6 0 7.2 4
data1 <- read.xlsx("lmm_test.xlsx")
model1 <- lmer(a1c ~ smk + smk * visit + (visit | id), data = data1)
a <- tidy(model, conf.int = TRUE)
a %>% select(term, estimate, conf.low, conf.high)

# A tibble: 8 x 4
term                   estimate conf.low conf.high
smk                     -0.779   -1.22     -0.336
visit                    0.0373  -0.0218    0.0964
smk:visit                0.268    0.160     0.377 

When the results of the analysis are as above mentioned, can i interpret that glycated hemoglobin increases by 0.268 in the presence of smoking status over time (1 visit unit) than in the absence of smoking?

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1 Answer 1

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The model you have fitted has the following mathematical form: $$\texttt{HbA1c}_i(t) = \beta_0 + \beta_1 \texttt{smoking}_i(t) + \beta_2 t + \beta_3 \{\texttt{smoking}_i(t) \times t\} + b_{i0} + b_{i1} t + \varepsilon_i(t),$$ where $b_i = (b_{i0}, b_{i1})$ are the random effects.

The presence of the interaction terms complicates the interpretation. If, at a particular time point $t$, the smoking status changes from zero to one, then the HbA1c at $t$ is expected to change by $\beta_1 + \beta_3 t$.

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