LMER model with uneven time points Does it matter that my time series are taken at random points? All the examples I've seen have nice time series, like every day or whatever. I have what is otherwise a pretty simple model: one fixed treatment condition and then a random intercept and slope for each subject, but the observations are essentially random, like s1 has observations at 1,3,7, and 14 days, whereas s2 has them at, say day 5, 6, and 15 (not even the same number of observations!) I was thinking of either binning (early/late), or considering the missing days as missing data. Can someone advise, and/or point me to a relevant example? 
P.s., here's the model I'm using: 
lmer(KPS ~ Day + Tx + (Day | Tx) + (Day | SID), data = d)

 A: Short answer: this should be no problem. I'm pretty sure you'll have somewhat lower power than if you had a perfectly balanced design, but there is no fundamental difficulty.
Here's an example where I subsample the (complete/balanced) sleepstudy data set and show that it works fine (and the results don't change very much).
The only specific issue that I can think of is that if you are fitting a model with autoregressive structure (e.g. in lme with the correlation argument), you'll have to switch from an "AR1" specification to a "continuous AR" or "Ornstein-Uhlenbeck" or "exponential correlation" specification (in lme from corAR1 to corCAR: in glmmTMB from ar() to ou()).
This analysis of carbon exchange in tundra ecosystems shows an example of mixed models applied to an unevenly sampled time series.
subsample data set
library(lme4)
set.seed(101)
table(sleepstudy$Subject)
ss <- do.call("rbind",
           lapply(split(sleepstudy,sleepstudy$Subject),
                     function(x) {
                         x[sort(sample(1:10,
                          size=rbinom(1,size=10,prob=0.7),
                                       replace=FALSE)),]
                     }))
lapply(split(ss,ss$Subject), function(x) x$Days)

fit unbalanced/subsampled data set
lmer(Reaction~Days+(Days|Subject), data=ss)
## Linear mixed model fit by REML ['lmerMod']
## Formula: Reaction ~ Days + (Days | Subject)
##    Data: ss
## REML criterion at convergence: 1130.586
## Random effects:
##  Groups   Name        Std.Dev. Corr
##  Subject  (Intercept) 22.634
##           Days         6.303   0.15
##  Residual             21.628
## Number of obs: 119, groups:  Subject, 18
## Fixed Effects:
## (Intercept)         Days
##      250.30        10.44

fit full data set
lmer(Reaction~Days+(Days|Subject), data=sleepstudy)

## Linear mixed model fit by REML ['lmerMod']
## Formula: Reaction ~ Days + (Days | Subject)
##    Data: sleepstudy
## REML criterion at convergence: 1743.628
## Random effects:
##  Groups   Name        Std.Dev. Corr
##  Subject  (Intercept) 24.737       
##           Days         5.923   0.07
##  Residual             25.592       
## Number of obs: 180, groups:  Subject, 18
## Fixed Effects:
## (Intercept)         Days  
##      251.41        10.47  

A: I was intrigued by the comment of @BenBolker that the power will be lower in an unbalanced design compared to a perfectly balanced one. The following simulation study seems to suggest that the power is the same:
simulate_mixed <- function (design = c("balanced", "unbalanced")) {
    design <- match.arg(design)
    n <- 100 # number of subjects
    K <- 8 # number of measurements per subject
    t_max <- 15 # maximum follow-up time

    # we constuct a data frame with the design: 
    DF <- data.frame(id = rep(seq_len(n), each = K),
                     sex = rep(gl(2, n/2, labels = c("male", "female")), each = K))

    DF$time <- if (design == "unbalanced") {
        runif(n * K, 0, t_max)
    } else {
        rep(seq(0, t_max, length.out = K), n)
    }

    X <- model.matrix(~ sex * time, data = DF)
    Z <- model.matrix(~ time, data = DF)
    betas <- c(-2.13, 0.5, 1, -0.5) # fixed effects coefficients
    D11 <- 2 # variance of random intercepts
    D22 <- 1 # variance of random slopes
    D12 <- 0.8 # covariance random intercepts random slopes
    D <- matrix(c(D11, D12, D12, D22), 2, 2)

    # we simulate random effects
    b <- MASS::mvrnorm(n, rep(0, ncol(Z)), D)
    # linear predictor
    eta_y <- drop(X %*% betas + rowSums(Z * b[DF$id, ]))
    # we simulate normal longitudinal data
    DF$y <- rnorm(n * K, mean = eta_y, sd = 1.5)
    DF
}

run_simulation <- function (design, M = 2000L) {
    library("lmerTest")
    opt <- options(warn = (-1))
    on.exit(options(opt))
    p_values <- numeric(M)
    for (i in seq_len(M)) {
        set.seed(i + 2019)
        data_i <- simulate_mixed(design = design)
        fm <- lmer(y ~ sex * time + (time | id), data = data_i)
        p_values[i] <- anova(fm)$`Pr(>F)`[3L]
    }
    mean(p_values < 0.05)
}

#####################################################################
#####################################################################

run_simulation("balanced")
#> [1] 0.691
run_simulation("unbalanced")
#> [1] 0.69

