| predict.stan_nma {multinma} | R Documentation |
Predictions of absolute effects from NMA models
Description
Obtain predictions of absolute effects from NMA models fitted with nma().
For example, if a model is fitted to binary data with a logit link, predicted
outcome probabilities or log odds can be produced. For survival models,
predictions can be made for survival probabilities, (cumulative) hazards,
(restricted) mean survival times, and quantiles including median survival
times.
When an IPD NMA or ML-NMR model has been fitted, predictions can be
produced either at an individual level or at an aggregate level.
Aggregate-level predictions are population-average absolute effects; these
are marginalised or standardised over a population. For example, average
event probabilities from a logistic regression, or marginal (standardised)
survival probabilities from a survival model.
Usage
## S3 method for class 'stan_nma'
predict(
object,
...,
baseline = NULL,
newdata = NULL,
study = NULL,
type = c("link", "response"),
level = c("aggregate", "individual"),
baseline_trt = NULL,
baseline_type = c("link", "response"),
baseline_level = c("individual", "aggregate"),
probs = c(0.025, 0.25, 0.5, 0.75, 0.975),
predictive_distribution = FALSE,
summary = TRUE,
progress = FALSE,
trt_ref = NULL
)
## S3 method for class 'stan_nma_surv'
predict(
object,
times = NULL,
...,
baseline_trt = NULL,
baseline = NULL,
aux = NULL,
newdata = NULL,
study = NULL,
type = c("survival", "hazard", "cumhaz", "mean", "median", "quantile", "rmst", "link"),
quantiles = c(0.25, 0.5, 0.75),
level = c("aggregate", "individual"),
times_seq = NULL,
probs = c(0.025, 0.25, 0.5, 0.75, 0.975),
predictive_distribution = FALSE,
summary = TRUE,
progress = interactive(),
trt_ref = NULL
)
Arguments
object |
A |
... |
Additional arguments, passed to |
baseline |
An optional For regression models, this may be a list of Use the Use the |
newdata |
Only required if a regression model is fitted and If If If |
study |
Column of |
type |
Whether to produce predictions on the For survival models, the options are |
level |
The level at which predictions are produced, either
|
baseline_trt |
Treatment to which the |
baseline_type |
When a |
baseline_level |
When a |
probs |
Numeric vector of quantiles of interest to present in computed
summary, default |
predictive_distribution |
Logical, when a random effects model has been
fitted, should the predictive distribution for absolute effects in a new
study be returned? Default |
summary |
Logical, calculate posterior summaries? Default |
progress |
Logical, display progress for potentially long-running calculations? Population-average predictions from ML-NMR models are computationally intensive, especially for survival outcomes. Currently the default is to display progress only when running interactively and producing predictions for a survival ML-NMR model. |
trt_ref |
Deprecated, renamed to |
times |
A numeric vector of times to evaluate predictions at.
Alternatively, if |
aux |
An optional For regression models, this may be a list of |
quantiles |
A numeric vector of quantiles of the survival time
distribution to produce estimates for when |
times_seq |
A positive integer, when specified evaluate predictions at
this many evenly-spaced event times between 0 and the latest follow-up time
in each study, instead of every observed event/censoring time. Only used if
|
Value
A nma_summary object if summary = TRUE, otherwise a list
containing a 3D MCMC array of samples and (for regression models) a data
frame of study information.
Aggregate-level predictions from IPD NMA and ML-NMR models
Population-average absolute effects can be produced from IPD NMA and ML-NMR
models with level = "aggregate". Predictions are averaged over the target
population (i.e. standardised/marginalised), either by (numerical)
integration over the joint covariate distribution (for AgD studies in the
network for ML-NMR, or AgD newdata with integration points created by
add_integration()), or by averaging predictions for a sample of individuals
(for IPD studies in the network for IPD NMA/ML-NMR, or IPD newdata).
For example, with a binary outcome, the population-average event
probabilities on treatment k in study/population j are
\bar{p}_{jk} = \int_\mathfrak{X} p_{jk}(\mathbf{x}) f_{jk}(\mathbf{x})
d\mathbf{x}
for a joint covariate distribution f_{jk}(\mathbf{x}) with
support \mathfrak{X} or
\bar{p}_{jk} = \sum_i p_{jk}(\mathbf{x}_i)
for a sample of individuals with covariates \mathbf{x}_i.
Population-average absolute predictions follow similarly for other types of outcomes, however for survival outcomes there are specific considerations.
Standardised survival predictions
Different types of population-average survival predictions, often called
standardised survival predictions, follow from the standardised survival
function created by integrating (or equivalently averaging) the
individual-level survival functions at each time t:
\bar{S}_{jk}(t) = \int_\mathfrak{X} S_{jk}(t | \mathbf{x}) f_{jk}(\mathbf{x})
d\mathbf{x}
which is itself produced using type = "survival".
The standardised hazard function corresponding to this standardised survival function is a weighted average of the individual-level hazard functions
\bar{h}_{jk}(t) = \frac{\int_\mathfrak{X} S_{jk}(t | \mathbf{x}) h_{jk}(t | \mathbf{x}) f_{jk}(\mathbf{x})
d\mathbf{x} }{\bar{S}_{jk}(t)}
weighted by the probability of surviving to time t. This is produced
using type = "hazard".
The corresponding standardised cumulative hazard function is
\bar{H}_{jk}(t) = -\log(\bar{S}_{jk}(t))
and is produced using type = "cumhaz".
Quantiles and medians of the standardised survival times are found by solving
\bar{S}_{jk}(t) = 1-\alpha
for the \alpha\% quantile, using numerical root finding. These are
produced using type = "quantile" or "median".
(Restricted) means of the standardised survival times are found by integrating
\mathrm{RMST}_{jk}(t^*) = \int_0^{t^*} \bar{S}_{jk}(t) dt
up to the restricted time horizon t^*, with t^*=\infty for mean
standardised survival time. These are produced using type = "rmst" or
"mean".
See Also
plot.nma_summary() for plotting the predictions.
Examples
## Smoking cessation
# Run smoking RE NMA example if not already available
if (!exists("smk_fit_RE")) example("example_smk_re", run.donttest = TRUE)
# Predicted log odds of success in each study in the network
predict(smk_fit_RE)
# Predicted probabilities of success in each study in the network
predict(smk_fit_RE, type = "response")
# Predicted probabilities in a population with 67 observed events out of 566
# individuals on No Intervention, corresponding to a Beta(67, 566 - 67)
# distribution on the baseline probability of response, using
# `baseline_type = "response"`
(smk_pred_RE <- predict(smk_fit_RE,
baseline = distr(qbeta, 67, 566 - 67),
baseline_type = "response",
type = "response"))
plot(smk_pred_RE, ref_line = c(0, 1))
# Predicted probabilities in a population with a baseline log odds of
# response on No Intervention given a Normal distribution with mean -2
# and SD 0.13, using `baseline_type = "link"` (the default)
# Note: this is approximately equivalent to the above Beta distribution on
# the baseline probability
(smk_pred_RE2 <- predict(smk_fit_RE,
baseline = distr(qnorm, mean = -2, sd = 0.13),
type = "response"))
plot(smk_pred_RE2, ref_line = c(0, 1))
## Plaque psoriasis ML-NMR
# Run plaque psoriasis ML-NMR example if not already available
if (!exists("pso_fit")) example("example_pso_mlnmr", run.donttest = TRUE)
# Predicted probabilities of response in each study in the network
(pso_pred <- predict(pso_fit, type = "response"))
plot(pso_pred, ref_line = c(0, 1))
# Predicted probabilites of response in a new target population, with means
# and SDs or proportions given by
new_agd_int <- data.frame(
bsa_mean = 0.6,
bsa_sd = 0.3,
prevsys = 0.1,
psa = 0.2,
weight_mean = 10,
weight_sd = 1,
durnpso_mean = 3,
durnpso_sd = 1
)
# We need to add integration points to this data frame of new data
# We use the weighted mean correlation matrix computed from the IPD studies
new_agd_int <- add_integration(new_agd_int,
durnpso = distr(qgamma, mean = durnpso_mean, sd = durnpso_sd),
prevsys = distr(qbern, prob = prevsys),
bsa = distr(qlogitnorm, mean = bsa_mean, sd = bsa_sd),
weight = distr(qgamma, mean = weight_mean, sd = weight_sd),
psa = distr(qbern, prob = psa),
cor = pso_net$int_cor,
n_int = 64)
# Predicted probabilities of achieving PASI 75 in this target population, given
# a Normal(-1.75, 0.08^2) distribution on the baseline probit-probability of
# response on Placebo (at the reference levels of the covariates), are given by
(pso_pred_new <- predict(pso_fit,
type = "response",
newdata = new_agd_int,
baseline = distr(qnorm, -1.75, 0.08)))
plot(pso_pred_new, ref_line = c(0, 1))
## Progression free survival with newly-diagnosed multiple myeloma
# Run newly-diagnosed multiple myeloma example if not already available
if (!exists("ndmm_fit")) example("example_ndmm", run.donttest = TRUE)
# We can produce a range of predictions from models with survival outcomes,
# chosen with the type argument to predict
# Predicted survival probabilities at 5 years
predict(ndmm_fit, type = "survival", times = 5)
# Survival curves
plot(predict(ndmm_fit, type = "survival"))
# Hazard curves
# Here we specify a vector of times to avoid attempting to plot infinite
# hazards for some studies at t=0
plot(predict(ndmm_fit, type = "hazard", times = seq(0.001, 6, length.out = 50)))
# Cumulative hazard curves
plot(predict(ndmm_fit, type = "cumhaz"))
# Survival time quantiles and median survival
predict(ndmm_fit, type = "quantile", quantiles = c(0.2, 0.5, 0.8))
plot(predict(ndmm_fit, type = "median"))
# Mean survival time
predict(ndmm_fit, type = "mean")
# Restricted mean survival time
# By default, the time horizon is the shortest follow-up time in the network
predict(ndmm_fit, type = "rmst")
# An alternative restriction time can be set using the times argument
predict(ndmm_fit, type = "rmst", times = 5) # 5-year RMST