MBNMAdose: Calculating model predictions

Prediction

For calculating predictions from MBNMAdose we will demonstrate using results from an Emax MBNMA on the triptans dataset:

tripnet <- mbnma.network(triptans)
#> Values for `agent` with dose = 0 have been recoded to `Placebo`
#> agent is being recoded to enforce sequential numbering
trip.emax <- mbnma.run(tripnet, fun = demax(emax = "rel", ed50 = "rel"))
#> `likelihood` not given by user - set to `binomial` based on data provided
#> `link` not given by user - set to `logit` based on assigned value for `likelihood`

After performing an MBNMA, responses can be predicted from the model parameter estimates using predict() on an "mbnma" object. A number of important arguments should be specified for prediction. See ?predict.mbnma for detailed specification of these arguments.

E0 This is the response at dose = 0 (equivalent to the placebo response). Since relative effects are the parameters estimated in MBNMA, the placebo response is not explicitly modelled and therefore must be provided by the user in some way. The simplest approach is to provide either a single numeric value for E0 (deterministic approach), or a string representing a distribution for E0 that can take any Random Number Generator (RNG) distribution for which a function exists in R (stochastic approach). Values should be given on the natural scale. For example for a binomial outcome:

• Deterministic: E0 <- 0.2
• Stochastic: E0 <- "rbeta(n, shape1=2, shape2=10)"

Another approach is to estimate E0 from a set of studies. These would ideally be studies of untreated/placebo-treated patients that closely resemble the population for which predictions are desired, and the studies may be observational. However, synthesising results from the placebo arms of trials in the original network is also possible. For this, E0 is assigned a data frame of studies in the long format (one row per study arm) with the variables studyID, and a selection of y, se, r, n and E (depending on the likelihood used in the MBNMA model). synth can be set to "fixed" or "random" to indicate whether this synthesis should be fixed or random effects.

E0 <- triptans[triptans$dose == 0, ]

Additionally, it’s also necessary to specify the doses at which to predict responses. By default, predict() uses the maximum dose within the dataset for each agent, and predicts doses at a series of cut points. The number of cut points can be specified using n.doses, and the maximum dose to use for prediction for each agent can also be specified using max.doses (a named list of numeric values where element names correspond to agent names).

An alternative approach is to predict responses at specific doses for specific agents using the argument exact.doses. As with max.doses, this is a named list in which element names correspond to agent names, but each element is a numeric vector in which each value within the vector is a dose at which to predict a response for the given agent.

# Predict 20 doses for each agent, with a stochastic distribution for E0
doses <- list(Placebo = 0, eletriptan = 3, sumatriptan = 3, almotriptan = 3, zolmitriptan = 3,
    naratriptan = 3, rizatriptan = 3)

pred <- predict(trip.emax, E0 = "rbeta(n, shape1=2, shape2=10)", max.doses = doses,
    n.dose = 20)


# Predict exact doses for two agents, and estimate E0 from the data
E0.data <- triptans[triptans$dose == 0, ]
doses <- list(eletriptan = c(0, 1, 3), sumatriptan = c(0, 3))

pred <- predict(trip.emax, E0 = E0.data, exact.doses = doses)
#> Values for `agent` with dose = 0 have been recoded to `Placebo`
#> agent is being recoded to enforce sequential numbering

An object of class "mbnma.predict" is returned, which is a list of summary tables and MCMC prediction matrices for each treatment (combination of dose and agent). The summary() method can be used to print mean posterior predictions at each time point for each treatment.

summary(pred)
#>         agent dose      mean          sd      2.5%       25%       50%
#> 1     Placebo    0 0.1238337 0.003242275 0.1175483 0.1216115 0.1238211
#> 2  eletriptan    0 0.1238337 0.003242275 0.1175483 0.1216115 0.1238211
#> 3  eletriptan    1 0.4313033 0.018708273 0.3954567 0.4185240 0.4312956
#> 4  eletriptan    3 0.5529291 0.027212376 0.5001952 0.5342257 0.5531780
#> 5 sumatriptan    0 0.1238337 0.003242275 0.1175483 0.1216115 0.1238211
#> 6 sumatriptan    3 0.3916598 0.018720878 0.3560036 0.3787192 0.3915192
#>         75%     97.5%
#> 1 0.1260122 0.1303499
#> 2 0.1260122 0.1303499
#> 3 0.4441608 0.4672786
#> 4 0.5711588 0.6062237
#> 5 0.1260122 0.1303499
#> 6 0.4039143 0.4301923

# Predict responses using default doses up to the maximum of each agent in the
# dataset
pred <- predict(trip.emax, E0 = 0.2, n.dose = 20)

plot(pred)

plot(pred, disp.obs = TRUE)
#> 66 placebo arms in the dataset are not shown within the plots

alognet <- mbnma.network(alog_pcfb)
alog.emax <- mbnma.run(alognet, fun = demax(), method = "random")
pred <- predict(alog.emax, E0 = 0, n.dose = 20)
plot(pred, overlay.split = TRUE, method = "random")

pred <- predict(trip.emax, E0 = 0.2, n.doses = 4, max.doses = list(eletriptan = 5,
    sumatriptan = 5, frovatriptan = 5, zolmitriptan = 5))

ranks <- rank(pred)
plot(ranks)

References