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
stan_nmaobject created bynma().- ...
Additional arguments, passed to
uniroot()for regression models ifbaseline_level = "aggregate".- baseline
An optional
distr()distribution for the baseline response (i.e. intercept), about which to produce absolute effects. Can also be a character string naming a study in the network to take the estimated baseline response distribution from. IfNULL, predictions are produced using the baseline response for each study in the network with IPD or arm-based AgD.For regression models, this may be a list of
distr()distributions (or study names in the network to use the baseline distributions from) of the same length as the number of studies innewdata, possibly named by the studies innewdataor otherwise in order of appearance innewdata.Use the
baseline_typeandbaseline_levelarguments to specify whether this distribution is on the response or linear predictor scale, and (for ML-NMR or models including IPD) whether this applies to an individual at the reference level of the covariates or over the entirenewdatapopulation, respectively. For example, in a model with a logit link withbaseline_type = "link", this would be a distribution for the baseline log odds of an event. For survival models,baselinealways corresponds to the intercept parameters in the linear predictor (i.e.baseline_typeis always"link", andbaseline_levelis"individual"for IPD NMA or ML-NMR, and"aggregate"for AgD NMA).Use the
baseline_trtargument to specify which treatment this distribution applies to.- newdata
Only required if a regression model is fitted and
baselineis specified. A data frame of covariate details, for which to produce predictions. Column names must match variables in the regression model.If
level = "aggregate"this should either be a data frame with integration points as produced byadd_integration()(one row per study), or a data frame with individual covariate values (one row per individual) which are summarised over.If
level = "individual"this should be a data frame of individual covariate values, one row per individual.If
NULL, predictions are produced for all studies with IPD and/or arm-based AgD in the network, depending on the value oflevel.- study
Column of
newdatawhich specifies study names or IDs. When not specified: ifnewdatacontains integration points produced byadd_integration(), studies will be labelled sequentially by row; otherwise data will be assumed to come from a single study.- type
Whether to produce predictions on the
"link"scale (the default, e.g. log odds) or"response"scale (e.g. probabilities).For survival models, the options are
"survival"for survival probabilities (the default),"hazard"for hazards,"cumhaz"for cumulative hazards,"mean"for mean survival times,"quantile"for quantiles of the survival time distribution,"median"for median survival times (equivalent totype = "quantile"withquantiles = 0.5),"rmst"for restricted mean survival times, or"link"for the linear predictor. Fortype = "survival","hazard"or"cumhaz", predictions are given at the times specified bytimesor at the event/censoring times in the network iftimes = NULL. Fortype = "rmst", the restricted time horizon is specified bytimes, or iftimes = NULLthe earliest last follow-up time amongst the studies in the network is used. Whenlevel = "aggregate", these all correspond to the standardised survival function (see details).- level
The level at which predictions are produced, either
"aggregate"(the default), or"individual". Ifbaselineis not specified, predictions are produced for all IPD studies in the network iflevelis"individual"or"aggregate", and for all arm-based AgD studies in the network iflevelis"aggregate".- baseline_trt
Treatment to which the
baselineresponse distribution refers, ifbaselineis specified. By default, the baseline response distribution will refer to the network reference treatment. Coerced to character string.- baseline_type
When a
baselinedistribution is given, specifies whether this corresponds to the"link"scale (the default, e.g. log odds) or"response"scale (e.g. probabilities). For survival models,baselinealways corresponds to the intercept parameters in the linear predictor (i.e.baseline_typeis always"link").- baseline_level
When a
baselinedistribution is given, specifies whether this corresponds to an individual at the reference level of the covariates ("individual", the default), or from an (unadjusted) average outcome on the reference treatment in thenewdatapopulation ("aggregate"). Ignored for AgD NMA, since the only option is"aggregate"in this instance. For survival models,baselinealways corresponds to the intercept parameters in the linear predictor (i.e.baseline_levelis"individual"for IPD NMA or ML-NMR, and"aggregate"for AgD NMA).- probs
Numeric vector of quantiles of interest to present in computed summary, default
c(0.025, 0.25, 0.5, 0.75, 0.975)- 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
FALSE.- summary
Logical, calculate posterior summaries? Default
TRUE.- 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
baseline_trt.- times
A numeric vector of times to evaluate predictions at. Alternatively, if
newdatais specified,timescan be the name of a column innewdatawhich contains the times. IfNULL(the default) then predictions are made at the event/censoring times from the studies included in the network (or according totimes_seq). Only used iftypeis"survival","hazard","cumhaz"or"rmst".- aux
An optional
distr()distribution for the auxiliary parameter(s) in the baseline hazard (e.g. shapes). Can also be a character string naming a study in the network to take the estimated auxiliary parameter distribution from. IfNULL, predictions are produced using the parameter estimates for each study in the network with IPD or arm-based AgD.For regression models, this may be a list of
distr()distributions (or study names in the network to use the auxiliary parameters from) of the same length as the number of studies innewdata, possibly named by the study names or otherwise in order of appearance innewdata.- quantiles
A numeric vector of quantiles of the survival time distribution to produce estimates for when
type = "quantile".- 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
newdata = NULLandtypeis"survival","hazard"or"cumhaz". This can be useful for plotting survival or (cumulative) hazard curves, where prediction at every observed even/censoring time is unnecessary and can be slow. When a call from withinplot()is detected, e.g. likeplot(predict(fit, type = "survival")),times_seqwill default to 50.
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
# \donttest{
# Run smoking RE NMA example if not already available
if (!exists("smk_fit_RE")) example("example_smk_re", run.donttest = TRUE)
# }
# \donttest{
# Predicted log odds of success in each study in the network
predict(smk_fit_RE)
#> ---------------------------------------------------------------------- Study: 1 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[1: No intervention] -2.78 0.33 -3.46 -3.00 -2.77 -2.56 -2.17
#> pred[1: Group counselling] -1.70 0.51 -2.72 -2.04 -1.71 -1.37 -0.70
#> pred[1: Individual counselling] -1.95 0.39 -2.73 -2.19 -1.95 -1.70 -1.20
#> pred[1: Self-help] -2.28 0.49 -3.24 -2.61 -2.28 -1.96 -1.33
#> Bulk_ESS Tail_ESS Rhat
#> pred[1: No intervention] 4702 3002 1
#> pred[1: Group counselling] 2238 2777 1
#> pred[1: Individual counselling] 2467 2714 1
#> pred[1: Self-help] 2663 2915 1
#>
#> ---------------------------------------------------------------------- Study: 2 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[2: No intervention] -2.58 0.78 -4.17 -3.07 -2.56 -2.07 -1.08
#> pred[2: Group counselling] -1.50 0.76 -3.02 -1.98 -1.49 -1.01 -0.01
#> pred[2: Individual counselling] -1.74 0.76 -3.23 -2.23 -1.74 -1.26 -0.26
#> pred[2: Self-help] -2.08 0.77 -3.67 -2.58 -2.07 -1.58 -0.59
#> Bulk_ESS Tail_ESS Rhat
#> pred[2: No intervention] 2551 2147 1
#> pred[2: Group counselling] 2816 2393 1
#> pred[2: Individual counselling] 2942 2735 1
#> pred[2: Self-help] 3156 2100 1
#>
#> ---------------------------------------------------------------------- Study: 3 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[3: No intervention] -2.14 0.12 -2.38 -2.22 -2.14 -2.06 -1.91
#> pred[3: Group counselling] -1.06 0.43 -1.92 -1.34 -1.06 -0.78 -0.19
#> pred[3: Individual counselling] -1.31 0.26 -1.80 -1.48 -1.31 -1.13 -0.78
#> pred[3: Self-help] -1.64 0.41 -2.44 -1.92 -1.65 -1.36 -0.81
#> Bulk_ESS Tail_ESS Rhat
#> pred[3: No intervention] 6854 2907 1
#> pred[3: Group counselling] 2055 2160 1
#> pred[3: Individual counselling] 1365 1995 1
#> pred[3: Self-help] 2101 2602 1
#>
#> ---------------------------------------------------------------------- Study: 4 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[4: No intervention] -4.05 0.57 -5.29 -4.41 -4.03 -3.66 -3.02
#> pred[4: Group counselling] -2.98 0.68 -4.40 -3.40 -2.96 -2.53 -1.68
#> pred[4: Individual counselling] -3.22 0.58 -4.43 -3.60 -3.20 -2.83 -2.10
#> pred[4: Self-help] -3.55 0.67 -4.90 -4.00 -3.53 -3.11 -2.31
#> Bulk_ESS Tail_ESS Rhat
#> pred[4: No intervention] 4139 2720 1
#> pred[4: Group counselling] 3332 2450 1
#> pred[4: Individual counselling] 3683 3051 1
#> pred[4: Self-help] 3308 2967 1
#>
#> ---------------------------------------------------------------------- Study: 5 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[5: No intervention] -2.16 0.14 -2.45 -2.25 -2.15 -2.06 -1.89
#> pred[5: Group counselling] -1.08 0.44 -1.94 -1.38 -1.08 -0.78 -0.21
#> pred[5: Individual counselling] -1.33 0.28 -1.86 -1.51 -1.32 -1.15 -0.76
#> pred[5: Self-help] -1.66 0.42 -2.50 -1.94 -1.67 -1.38 -0.82
#> Bulk_ESS Tail_ESS Rhat
#> pred[5: No intervention] 6945 3037 1
#> pred[5: Group counselling] 2070 2182 1
#> pred[5: Individual counselling] 1443 2111 1
#> pred[5: Self-help] 2201 2545 1
#>
#> ---------------------------------------------------------------------- Study: 6 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[6: No intervention] -3.42 0.75 -5.08 -3.83 -3.33 -2.91 -2.17
#> pred[6: Group counselling] -2.34 0.83 -4.15 -2.82 -2.27 -1.78 -0.87
#> pred[6: Individual counselling] -2.58 0.73 -4.21 -3.02 -2.51 -2.08 -1.32
#> pred[6: Self-help] -2.92 0.81 -4.70 -3.37 -2.87 -2.37 -1.49
#> Bulk_ESS Tail_ESS Rhat
#> pred[6: No intervention] 3245 2270 1
#> pred[6: Group counselling] 3360 2266 1
#> pred[6: Individual counselling] 3417 2215 1
#> pred[6: Self-help] 3234 2043 1
#>
#> ---------------------------------------------------------------------- Study: 7 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[7: No intervention] -3.01 0.44 -3.94 -3.29 -2.98 -2.71 -2.24
#> pred[7: Group counselling] -1.93 0.57 -3.12 -2.30 -1.92 -1.53 -0.86
#> pred[7: Individual counselling] -2.18 0.46 -3.14 -2.47 -2.16 -1.87 -1.33
#> pred[7: Self-help] -2.51 0.57 -3.67 -2.88 -2.49 -2.12 -1.43
#> Bulk_ESS Tail_ESS Rhat
#> pred[7: No intervention] 4406 2276 1
#> pred[7: Group counselling] 2902 2446 1
#> pred[7: Individual counselling] 3154 2415 1
#> pred[7: Self-help] 3036 2352 1
#>
#> ---------------------------------------------------------------------- Study: 8 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[8: No intervention] -2.69 0.59 -3.97 -3.06 -2.65 -2.28 -1.65
#> pred[8: Group counselling] -1.62 0.70 -3.12 -2.06 -1.59 -1.15 -0.30
#> pred[8: Individual counselling] -1.86 0.59 -3.13 -2.23 -1.82 -1.46 -0.80
#> pred[8: Self-help] -2.20 0.69 -3.62 -2.63 -2.17 -1.72 -0.94
#> Bulk_ESS Tail_ESS Rhat
#> pred[8: No intervention] 3176 2768 1
#> pred[8: Group counselling] 2915 2319 1
#> pred[8: Individual counselling] 3376 2434 1
#> pred[8: Self-help] 2996 2163 1
#>
#> ---------------------------------------------------------------------- Study: 9 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[9: No intervention] -1.84 0.42 -2.72 -2.11 -1.82 -1.55 -1.07
#> pred[9: Group counselling] -0.76 0.58 -1.93 -1.13 -0.76 -0.37 0.35
#> pred[9: Individual counselling] -1.00 0.46 -1.94 -1.30 -1.00 -0.69 -0.10
#> pred[9: Self-help] -1.34 0.57 -2.45 -1.71 -1.33 -0.94 -0.26
#> Bulk_ESS Tail_ESS Rhat
#> pred[9: No intervention] 4671 2776 1
#> pred[9: Group counselling] 2615 2371 1
#> pred[9: Individual counselling] 2725 2573 1
#> pred[9: Self-help] 2622 2836 1
#>
#> --------------------------------------------------------------------- Study: 10 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[10: No intervention] -2.08 0.12 -2.32 -2.16 -2.08 -2.00 -1.86
#> pred[10: Group counselling] -1.01 0.44 -1.87 -1.29 -1.01 -0.73 -0.12
#> pred[10: Individual counselling] -1.25 0.27 -1.75 -1.43 -1.26 -1.08 -0.70
#> pred[10: Self-help] -1.58 0.41 -2.38 -1.86 -1.59 -1.33 -0.74
#> Bulk_ESS Tail_ESS Rhat
#> pred[10: No intervention] 7850 2512 1
#> pred[10: Group counselling] 2112 2197 1
#> pred[10: Individual counselling] 1372 2117 1
#> pred[10: Self-help] 2123 2416 1
#>
#> --------------------------------------------------------------------- Study: 11 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[11: No intervention] -3.62 0.23 -4.10 -3.77 -3.61 -3.46 -3.20
#> pred[11: Group counselling] -2.55 0.47 -3.47 -2.85 -2.56 -2.24 -1.63
#> pred[11: Individual counselling] -2.79 0.33 -3.44 -3.01 -2.78 -2.57 -2.15
#> pred[11: Self-help] -3.12 0.43 -3.97 -3.40 -3.12 -2.84 -2.27
#> Bulk_ESS Tail_ESS Rhat
#> pred[11: No intervention] 6283 2985 1
#> pred[11: Group counselling] 2427 2560 1
#> pred[11: Individual counselling] 2096 2432 1
#> pred[11: Self-help] 2247 2565 1
#>
#> --------------------------------------------------------------------- Study: 12 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[12: No intervention] -2.22 0.13 -2.47 -2.31 -2.22 -2.13 -1.97
#> pred[12: Group counselling] -1.14 0.44 -2.01 -1.43 -1.14 -0.85 -0.27
#> pred[12: Individual counselling] -1.39 0.27 -1.91 -1.57 -1.39 -1.21 -0.82
#> pred[12: Self-help] -1.72 0.41 -2.53 -2.00 -1.74 -1.45 -0.86
#> Bulk_ESS Tail_ESS Rhat
#> pred[12: No intervention] 6818 3243 1
#> pred[12: Group counselling] 2034 2184 1
#> pred[12: Individual counselling] 1399 2057 1
#> pred[12: Self-help] 2096 2440 1
#>
#> --------------------------------------------------------------------- Study: 13 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[13: No intervention] -2.68 0.44 -3.59 -2.96 -2.66 -2.38 -1.88
#> pred[13: Group counselling] -1.60 0.58 -2.75 -1.99 -1.59 -1.20 -0.50
#> pred[13: Individual counselling] -1.84 0.47 -2.83 -2.15 -1.83 -1.53 -0.98
#> pred[13: Self-help] -2.18 0.57 -3.32 -2.56 -2.18 -1.80 -1.05
#> Bulk_ESS Tail_ESS Rhat
#> pred[13: No intervention] 4644 3373 1
#> pred[13: Group counselling] 3193 3544 1
#> pred[13: Individual counselling] 3387 3379 1
#> pred[13: Self-help] 3294 3361 1
#>
#> --------------------------------------------------------------------- Study: 14 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[14: No intervention] -2.41 0.23 -2.88 -2.56 -2.40 -2.26 -1.98
#> pred[14: Group counselling] -1.33 0.48 -2.24 -1.64 -1.34 -1.02 -0.37
#> pred[14: Individual counselling] -1.58 0.32 -2.21 -1.79 -1.58 -1.37 -0.93
#> pred[14: Self-help] -1.91 0.45 -2.82 -2.21 -1.92 -1.62 -0.99
#> Bulk_ESS Tail_ESS Rhat
#> pred[14: No intervention] 4980 3103 1
#> pred[14: Group counselling] 2296 2302 1
#> pred[14: Individual counselling] 1780 2511 1
#> pred[14: Self-help] 2370 2910 1
#>
#> --------------------------------------------------------------------- Study: 15 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[15: No intervention] -2.65 0.71 -4.22 -3.08 -2.58 -2.15 -1.41
#> pred[15: Group counselling] -1.57 0.69 -3.07 -2.00 -1.52 -1.09 -0.35
#> pred[15: Individual counselling] -1.82 0.71 -3.39 -2.24 -1.75 -1.33 -0.57
#> pred[15: Self-help] -2.15 0.76 -3.75 -2.63 -2.11 -1.63 -0.80
#> Bulk_ESS Tail_ESS Rhat
#> pred[15: No intervention] 3742 2832 1
#> pred[15: Group counselling] 3669 2931 1
#> pred[15: Individual counselling] 3988 2941 1
#> pred[15: Self-help] 3711 3017 1
#>
#> --------------------------------------------------------------------- Study: 16 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[16: No intervention] -2.62 0.34 -3.34 -2.84 -2.60 -2.39 -1.99
#> pred[16: Group counselling] -1.54 0.53 -2.61 -1.89 -1.54 -1.20 -0.51
#> pred[16: Individual counselling] -1.79 0.41 -2.60 -2.05 -1.79 -1.52 -0.98
#> pred[16: Self-help] -2.12 0.48 -3.09 -2.42 -2.12 -1.81 -1.17
#> Bulk_ESS Tail_ESS Rhat
#> pred[16: No intervention] 6163 2816 1
#> pred[16: Group counselling] 2694 2766 1
#> pred[16: Individual counselling] 2767 2886 1
#> pred[16: Self-help] 2898 2809 1
#>
#> --------------------------------------------------------------------- Study: 17 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[17: No intervention] -2.38 0.11 -2.59 -2.45 -2.38 -2.30 -2.17
#> pred[17: Group counselling] -1.30 0.44 -2.17 -1.59 -1.30 -1.02 -0.44
#> pred[17: Individual counselling] -1.54 0.26 -2.04 -1.72 -1.55 -1.38 -1.01
#> pred[17: Self-help] -1.88 0.41 -2.69 -2.15 -1.88 -1.61 -1.06
#> Bulk_ESS Tail_ESS Rhat
#> pred[17: No intervention] 7542 2893 1
#> pred[17: Group counselling] 2010 2308 1
#> pred[17: Individual counselling] 1314 2029 1
#> pred[17: Self-help] 2068 2602 1
#>
#> --------------------------------------------------------------------- Study: 18 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[18: No intervention] -2.57 0.27 -3.13 -2.75 -2.56 -2.39 -2.07
#> pred[18: Group counselling] -1.49 0.50 -2.43 -1.83 -1.50 -1.17 -0.47
#> pred[18: Individual counselling] -1.74 0.36 -2.42 -1.98 -1.74 -1.49 -1.04
#> pred[18: Self-help] -2.07 0.48 -3.00 -2.39 -2.07 -1.76 -1.10
#> Bulk_ESS Tail_ESS Rhat
#> pred[18: No intervention] 4771 2967 1
#> pred[18: Group counselling] 2287 2646 1
#> pred[18: Individual counselling] 1945 2670 1
#> pred[18: Self-help] 2501 2793 1
#>
#> --------------------------------------------------------------------- Study: 19 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[19: No intervention] -1.90 0.12 -2.13 -1.98 -1.90 -1.82 -1.68
#> pred[19: Group counselling] -0.82 0.44 -1.69 -1.11 -0.82 -0.54 0.04
#> pred[19: Individual counselling] -1.07 0.27 -1.58 -1.24 -1.07 -0.90 -0.53
#> pred[19: Self-help] -1.40 0.41 -2.23 -1.67 -1.40 -1.13 -0.55
#> Bulk_ESS Tail_ESS Rhat
#> pred[19: No intervention] 7289 3104 1
#> pred[19: Group counselling] 2024 2129 1
#> pred[19: Individual counselling] 1371 2013 1
#> pred[19: Self-help] 2112 2576 1
#>
#> --------------------------------------------------------------------- Study: 20 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[20: No intervention] -2.80 0.13 -3.05 -2.89 -2.80 -2.72 -2.56
#> pred[20: Group counselling] -1.73 0.44 -2.61 -2.02 -1.72 -1.45 -0.86
#> pred[20: Individual counselling] -1.97 0.27 -2.50 -2.14 -1.98 -1.80 -1.41
#> pred[20: Self-help] -2.30 0.41 -3.10 -2.58 -2.31 -2.03 -1.45
#> Bulk_ESS Tail_ESS Rhat
#> pred[20: No intervention] 7743 3112 1
#> pred[20: Group counselling] 2034 2354 1
#> pred[20: Individual counselling] 1370 2062 1
#> pred[20: Self-help] 2126 2517 1
#>
#> --------------------------------------------------------------------- Study: 21 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[21: No intervention] -1.13 0.81 -2.71 -1.63 -1.12 -0.61 0.46
#> pred[21: Group counselling] -0.05 0.86 -1.75 -0.61 -0.06 0.48 1.69
#> pred[21: Individual counselling] -0.30 0.79 -1.84 -0.79 -0.29 0.20 1.27
#> pred[21: Self-help] -0.63 0.79 -2.21 -1.12 -0.64 -0.13 0.94
#> Bulk_ESS Tail_ESS Rhat
#> pred[21: No intervention] 3014 2654 1
#> pred[21: Group counselling] 3252 2822 1
#> pred[21: Individual counselling] 3269 2826 1
#> pred[21: Self-help] 3678 2552 1
#>
#> --------------------------------------------------------------------- Study: 22 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[22: No intervention] -2.40 0.84 -4.12 -2.91 -2.39 -1.86 -0.76
#> pred[22: Group counselling] -1.32 0.78 -2.88 -1.81 -1.31 -0.82 0.22
#> pred[22: Individual counselling] -1.57 0.84 -3.25 -2.09 -1.56 -1.02 0.10
#> pred[22: Self-help] -1.90 0.82 -3.53 -2.41 -1.90 -1.37 -0.34
#> Bulk_ESS Tail_ESS Rhat
#> pred[22: No intervention] 2692 2450 1
#> pred[22: Group counselling] 3652 2867 1
#> pred[22: Individual counselling] 3024 2591 1
#> pred[22: Self-help] 3665 2677 1
#>
#> --------------------------------------------------------------------- Study: 23 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[23: No intervention] -2.30 0.82 -3.93 -2.84 -2.29 -1.77 -0.72
#> pred[23: Group counselling] -1.23 0.79 -2.80 -1.75 -1.21 -0.70 0.30
#> pred[23: Individual counselling] -1.47 0.79 -3.05 -1.98 -1.46 -0.96 0.08
#> pred[23: Self-help] -1.80 0.85 -3.46 -2.38 -1.80 -1.24 -0.11
#> Bulk_ESS Tail_ESS Rhat
#> pred[23: No intervention] 2619 2203 1
#> pred[23: Group counselling] 3721 2841 1
#> pred[23: Individual counselling] 3590 2493 1
#> pred[23: Self-help] 3469 2589 1
#>
#> --------------------------------------------------------------------- Study: 24 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[24: No intervention] -2.78 0.85 -4.55 -3.32 -2.75 -2.22 -1.10
#> pred[24: Group counselling] -1.70 0.83 -3.37 -2.24 -1.69 -1.15 -0.08
#> pred[24: Individual counselling] -1.95 0.83 -3.64 -2.49 -1.94 -1.41 -0.27
#> pred[24: Self-help] -2.28 0.90 -4.06 -2.85 -2.26 -1.71 -0.45
#> Bulk_ESS Tail_ESS Rhat
#> pred[24: No intervention] 3443 2796 1
#> pred[24: Group counselling] 3870 2783 1
#> pred[24: Individual counselling] 4041 2710 1
#> pred[24: Self-help] 3725 3025 1
#>
# Predicted probabilities of success in each study in the network
predict(smk_fit_RE, type = "response")
#> ---------------------------------------------------------------------- Study: 1 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[1: No intervention] 0.06 0.02 0.03 0.05 0.06 0.07 0.10 4702
#> pred[1: Group counselling] 0.16 0.07 0.06 0.12 0.15 0.20 0.33 2238
#> pred[1: Individual counselling] 0.13 0.04 0.06 0.10 0.12 0.15 0.23 2467
#> pred[1: Self-help] 0.10 0.05 0.04 0.07 0.09 0.12 0.21 2663
#> Tail_ESS Rhat
#> pred[1: No intervention] 3002 1
#> pred[1: Group counselling] 2777 1
#> pred[1: Individual counselling] 2714 1
#> pred[1: Self-help] 2915 1
#>
#> ---------------------------------------------------------------------- Study: 2 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[2: No intervention] 0.09 0.06 0.02 0.04 0.07 0.11 0.25 2551
#> pred[2: Group counselling] 0.21 0.12 0.05 0.12 0.18 0.27 0.50 2816
#> pred[2: Individual counselling] 0.17 0.10 0.04 0.10 0.15 0.22 0.44 2942
#> pred[2: Self-help] 0.13 0.09 0.02 0.07 0.11 0.17 0.36 3156
#> Tail_ESS Rhat
#> pred[2: No intervention] 2147 1
#> pred[2: Group counselling] 2393 1
#> pred[2: Individual counselling] 2735 1
#> pred[2: Self-help] 2100 1
#>
#> ---------------------------------------------------------------------- Study: 3 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[3: No intervention] 0.11 0.01 0.08 0.10 0.11 0.11 0.13 6854
#> pred[3: Group counselling] 0.26 0.08 0.13 0.21 0.26 0.31 0.45 2055
#> pred[3: Individual counselling] 0.22 0.04 0.14 0.19 0.21 0.24 0.31 1365
#> pred[3: Self-help] 0.17 0.06 0.08 0.13 0.16 0.20 0.31 2101
#> Tail_ESS Rhat
#> pred[3: No intervention] 2907 1
#> pred[3: Group counselling] 2160 1
#> pred[3: Individual counselling] 1995 1
#> pred[3: Self-help] 2602 1
#>
#> ---------------------------------------------------------------------- Study: 4 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[4: No intervention] 0.02 0.01 0.01 0.01 0.02 0.03 0.05 4139
#> pred[4: Group counselling] 0.06 0.04 0.01 0.03 0.05 0.07 0.16 3332
#> pred[4: Individual counselling] 0.04 0.02 0.01 0.03 0.04 0.06 0.11 3683
#> pred[4: Self-help] 0.03 0.02 0.01 0.02 0.03 0.04 0.09 3308
#> Tail_ESS Rhat
#> pred[4: No intervention] 2720 1
#> pred[4: Group counselling] 2450 1
#> pred[4: Individual counselling] 3051 1
#> pred[4: Self-help] 2967 1
#>
#> ---------------------------------------------------------------------- Study: 5 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[5: No intervention] 0.10 0.01 0.08 0.10 0.10 0.11 0.13 6945
#> pred[5: Group counselling] 0.26 0.08 0.13 0.20 0.25 0.31 0.45 2070
#> pred[5: Individual counselling] 0.21 0.05 0.13 0.18 0.21 0.24 0.32 1443
#> pred[5: Self-help] 0.17 0.06 0.08 0.13 0.16 0.20 0.31 2201
#> Tail_ESS Rhat
#> pred[5: No intervention] 3037 1
#> pred[5: Group counselling] 2182 1
#> pred[5: Individual counselling] 2111 1
#> pred[5: Self-help] 2545 1
#>
#> ---------------------------------------------------------------------- Study: 6 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[6: No intervention] 0.04 0.03 0.01 0.02 0.03 0.05 0.10 3245
#> pred[6: Group counselling] 0.11 0.07 0.02 0.06 0.09 0.14 0.30 3360
#> pred[6: Individual counselling] 0.08 0.05 0.01 0.05 0.08 0.11 0.21 3417
#> pred[6: Self-help] 0.06 0.05 0.01 0.03 0.05 0.09 0.18 3234
#> Tail_ESS Rhat
#> pred[6: No intervention] 2270 1
#> pred[6: Group counselling] 2266 1
#> pred[6: Individual counselling] 2215 1
#> pred[6: Self-help] 2043 1
#>
#> ---------------------------------------------------------------------- Study: 7 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[7: No intervention] 0.05 0.02 0.02 0.04 0.05 0.06 0.10 4406
#> pred[7: Group counselling] 0.14 0.07 0.04 0.09 0.13 0.18 0.30 2902
#> pred[7: Individual counselling] 0.11 0.04 0.04 0.08 0.10 0.13 0.21 3154
#> pred[7: Self-help] 0.08 0.04 0.02 0.05 0.08 0.11 0.19 3036
#> Tail_ESS Rhat
#> pred[7: No intervention] 2276 1
#> pred[7: Group counselling] 2446 1
#> pred[7: Individual counselling] 2415 1
#> pred[7: Self-help] 2352 1
#>
#> ---------------------------------------------------------------------- Study: 8 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[8: No intervention] 0.07 0.04 0.02 0.04 0.07 0.09 0.16 3176
#> pred[8: Group counselling] 0.19 0.10 0.04 0.11 0.17 0.24 0.43 2915
#> pred[8: Individual counselling] 0.15 0.07 0.04 0.10 0.14 0.19 0.31 3376
#> pred[8: Self-help] 0.12 0.07 0.03 0.07 0.10 0.15 0.28 2996
#> Tail_ESS Rhat
#> pred[8: No intervention] 2768 1
#> pred[8: Group counselling] 2319 1
#> pred[8: Individual counselling] 2434 1
#> pred[8: Self-help] 2163 1
#>
#> ---------------------------------------------------------------------- Study: 9 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[9: No intervention] 0.14 0.05 0.06 0.11 0.14 0.17 0.26 4671
#> pred[9: Group counselling] 0.33 0.12 0.13 0.24 0.32 0.41 0.59 2615
#> pred[9: Individual counselling] 0.28 0.09 0.13 0.21 0.27 0.33 0.48 2725
#> pred[9: Self-help] 0.22 0.09 0.08 0.15 0.21 0.28 0.43 2622
#> Tail_ESS Rhat
#> pred[9: No intervention] 2776 1
#> pred[9: Group counselling] 2371 1
#> pred[9: Individual counselling] 2573 1
#> pred[9: Self-help] 2836 1
#>
#> --------------------------------------------------------------------- Study: 10 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[10: No intervention] 0.11 0.01 0.09 0.10 0.11 0.12 0.13 7850
#> pred[10: Group counselling] 0.28 0.09 0.13 0.22 0.27 0.33 0.47 2112
#> pred[10: Individual counselling] 0.23 0.05 0.15 0.19 0.22 0.25 0.33 1372
#> pred[10: Self-help] 0.18 0.06 0.08 0.14 0.17 0.21 0.32 2123
#> Tail_ESS Rhat
#> pred[10: No intervention] 2512 1
#> pred[10: Group counselling] 2197 1
#> pred[10: Individual counselling] 2117 1
#> pred[10: Self-help] 2416 1
#>
#> --------------------------------------------------------------------- Study: 11 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[11: No intervention] 0.03 0.01 0.02 0.02 0.03 0.03 0.04 6283
#> pred[11: Group counselling] 0.08 0.04 0.03 0.05 0.07 0.10 0.16 2427
#> pred[11: Individual counselling] 0.06 0.02 0.03 0.05 0.06 0.07 0.10 2096
#> pred[11: Self-help] 0.05 0.02 0.02 0.03 0.04 0.05 0.09 2247
#> Tail_ESS Rhat
#> pred[11: No intervention] 2985 1
#> pred[11: Group counselling] 2560 1
#> pred[11: Individual counselling] 2432 1
#> pred[11: Self-help] 2565 1
#>
#> --------------------------------------------------------------------- Study: 12 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[12: No intervention] 0.10 0.01 0.08 0.09 0.10 0.11 0.12 6818
#> pred[12: Group counselling] 0.25 0.08 0.12 0.19 0.24 0.30 0.43 2034
#> pred[12: Individual counselling] 0.20 0.04 0.13 0.17 0.20 0.23 0.31 1399
#> pred[12: Self-help] 0.16 0.06 0.07 0.12 0.15 0.19 0.30 2096
#> Tail_ESS Rhat
#> pred[12: No intervention] 3243 1
#> pred[12: Group counselling] 2184 1
#> pred[12: Individual counselling] 2057 1
#> pred[12: Self-help] 2440 1
#>
#> --------------------------------------------------------------------- Study: 13 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[13: No intervention] 0.07 0.03 0.03 0.05 0.07 0.08 0.13 4644
#> pred[13: Group counselling] 0.18 0.08 0.06 0.12 0.17 0.23 0.38 3193
#> pred[13: Individual counselling] 0.15 0.06 0.06 0.10 0.14 0.18 0.27 3387
#> pred[13: Self-help] 0.11 0.06 0.03 0.07 0.10 0.14 0.26 3294
#> Tail_ESS Rhat
#> pred[13: No intervention] 3373 1
#> pred[13: Group counselling] 3544 1
#> pred[13: Individual counselling] 3379 1
#> pred[13: Self-help] 3361 1
#>
#> --------------------------------------------------------------------- Study: 14 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[14: No intervention] 0.08 0.02 0.05 0.07 0.08 0.09 0.12 4980
#> pred[14: Group counselling] 0.22 0.08 0.10 0.16 0.21 0.26 0.41 2296
#> pred[14: Individual counselling] 0.18 0.05 0.10 0.14 0.17 0.20 0.28 1780
#> pred[14: Self-help] 0.14 0.05 0.06 0.10 0.13 0.17 0.27 2370
#> Tail_ESS Rhat
#> pred[14: No intervention] 3103 1
#> pred[14: Group counselling] 2302 1
#> pred[14: Individual counselling] 2511 1
#> pred[14: Self-help] 2910 1
#>
#> --------------------------------------------------------------------- Study: 15 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[15: No intervention] 0.08 0.05 0.01 0.04 0.07 0.10 0.20 3742
#> pred[15: Group counselling] 0.19 0.10 0.04 0.12 0.18 0.25 0.41 3669
#> pred[15: Individual counselling] 0.16 0.09 0.03 0.10 0.15 0.21 0.36 3988
#> pred[15: Self-help] 0.12 0.08 0.02 0.07 0.11 0.16 0.31 3711
#> Tail_ESS Rhat
#> pred[15: No intervention] 2832 1
#> pred[15: Group counselling] 2931 1
#> pred[15: Individual counselling] 2941 1
#> pred[15: Self-help] 3017 1
#>
#> --------------------------------------------------------------------- Study: 16 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[16: No intervention] 0.07 0.02 0.03 0.06 0.07 0.08 0.12 6163
#> pred[16: Group counselling] 0.19 0.08 0.07 0.13 0.18 0.23 0.38 2694
#> pred[16: Individual counselling] 0.15 0.05 0.07 0.11 0.14 0.18 0.27 2767
#> pred[16: Self-help] 0.12 0.05 0.04 0.08 0.11 0.14 0.24 2898
#> Tail_ESS Rhat
#> pred[16: No intervention] 2816 1
#> pred[16: Group counselling] 2766 1
#> pred[16: Individual counselling] 2886 1
#> pred[16: Self-help] 2809 1
#>
#> --------------------------------------------------------------------- Study: 17 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[17: No intervention] 0.09 0.01 0.07 0.08 0.09 0.09 0.10 7542
#> pred[17: Group counselling] 0.22 0.07 0.10 0.17 0.21 0.27 0.39 2010
#> pred[17: Individual counselling] 0.18 0.04 0.12 0.15 0.17 0.20 0.27 1314
#> pred[17: Self-help] 0.14 0.05 0.06 0.10 0.13 0.17 0.26 2068
#> Tail_ESS Rhat
#> pred[17: No intervention] 2893 1
#> pred[17: Group counselling] 2308 1
#> pred[17: Individual counselling] 2029 1
#> pred[17: Self-help] 2602 1
#>
#> --------------------------------------------------------------------- Study: 18 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[18: No intervention] 0.07 0.02 0.04 0.06 0.07 0.08 0.11 4771
#> pred[18: Group counselling] 0.19 0.08 0.08 0.14 0.18 0.24 0.38 2287
#> pred[18: Individual counselling] 0.16 0.05 0.08 0.12 0.15 0.18 0.26 1945
#> pred[18: Self-help] 0.12 0.05 0.05 0.08 0.11 0.15 0.25 2501
#> Tail_ESS Rhat
#> pred[18: No intervention] 2967 1
#> pred[18: Group counselling] 2646 1
#> pred[18: Individual counselling] 2670 1
#> pred[18: Self-help] 2793 1
#>
#> --------------------------------------------------------------------- Study: 19 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[19: No intervention] 0.13 0.01 0.11 0.12 0.13 0.14 0.16 7289
#> pred[19: Group counselling] 0.31 0.09 0.16 0.25 0.31 0.37 0.51 2024
#> pred[19: Individual counselling] 0.26 0.05 0.17 0.22 0.26 0.29 0.37 1371
#> pred[19: Self-help] 0.21 0.07 0.10 0.16 0.20 0.24 0.37 2112
#> Tail_ESS Rhat
#> pred[19: No intervention] 3104 1
#> pred[19: Group counselling] 2129 1
#> pred[19: Individual counselling] 2013 1
#> pred[19: Self-help] 2576 1
#>
#> --------------------------------------------------------------------- Study: 20 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[20: No intervention] 0.06 0.01 0.05 0.05 0.06 0.06 0.07 7743
#> pred[20: Group counselling] 0.16 0.06 0.07 0.12 0.15 0.19 0.30 2034
#> pred[20: Individual counselling] 0.13 0.03 0.08 0.10 0.12 0.14 0.20 1370
#> pred[20: Self-help] 0.10 0.04 0.04 0.07 0.09 0.12 0.19 2126
#> Tail_ESS Rhat
#> pred[20: No intervention] 3112 1
#> pred[20: Group counselling] 2354 1
#> pred[20: Individual counselling] 2062 1
#> pred[20: Self-help] 2517 1
#>
#> --------------------------------------------------------------------- Study: 21 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[21: No intervention] 0.27 0.14 0.06 0.16 0.25 0.35 0.61 3014
#> pred[21: Group counselling] 0.49 0.18 0.15 0.35 0.49 0.62 0.84 3252
#> pred[21: Individual counselling] 0.43 0.17 0.14 0.31 0.43 0.55 0.78 3269
#> pred[21: Self-help] 0.36 0.16 0.10 0.25 0.34 0.47 0.72 3678
#> Tail_ESS Rhat
#> pred[21: No intervention] 2654 1
#> pred[21: Group counselling] 2822 1
#> pred[21: Individual counselling] 2826 1
#> pred[21: Self-help] 2552 1
#>
#> --------------------------------------------------------------------- Study: 22 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[22: No intervention] 0.11 0.08 0.02 0.05 0.08 0.14 0.32 2692
#> pred[22: Group counselling] 0.24 0.13 0.05 0.14 0.21 0.31 0.55 3652
#> pred[22: Individual counselling] 0.20 0.13 0.04 0.11 0.17 0.26 0.53 3024
#> pred[22: Self-help] 0.16 0.10 0.03 0.08 0.13 0.20 0.42 3665
#> Tail_ESS Rhat
#> pred[22: No intervention] 2450 1
#> pred[22: Group counselling] 2867 1
#> pred[22: Individual counselling] 2591 1
#> pred[22: Self-help] 2677 1
#>
#> --------------------------------------------------------------------- Study: 23 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[23: No intervention] 0.11 0.08 0.02 0.06 0.09 0.15 0.33 2619
#> pred[23: Group counselling] 0.25 0.14 0.06 0.15 0.23 0.33 0.58 3721
#> pred[23: Individual counselling] 0.21 0.12 0.05 0.12 0.19 0.28 0.52 3590
#> pred[23: Self-help] 0.17 0.12 0.03 0.08 0.14 0.22 0.47 3469
#> Tail_ESS Rhat
#> pred[23: No intervention] 2203 1
#> pred[23: Group counselling] 2841 1
#> pred[23: Individual counselling] 2493 1
#> pred[23: Self-help] 2589 1
#>
#> --------------------------------------------------------------------- Study: 24 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[24: No intervention] 0.08 0.06 0.01 0.03 0.06 0.10 0.25 3443
#> pred[24: Group counselling] 0.18 0.12 0.03 0.10 0.16 0.24 0.48 3870
#> pred[24: Individual counselling] 0.15 0.10 0.03 0.08 0.13 0.20 0.43 4041
#> pred[24: Self-help] 0.12 0.10 0.02 0.05 0.09 0.15 0.39 3725
#> Tail_ESS Rhat
#> pred[24: No intervention] 2796 1
#> pred[24: Group counselling] 2783 1
#> pred[24: Individual counselling] 2710 1
#> pred[24: Self-help] 3025 1
#>
# 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"))
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[No intervention] 0.12 0.01 0.09 0.11 0.12 0.13 0.15 4260
#> pred[Group counselling] 0.29 0.09 0.14 0.23 0.28 0.34 0.48 1982
#> pred[Individual counselling] 0.24 0.05 0.15 0.20 0.23 0.27 0.35 1446
#> pred[Self-help] 0.19 0.06 0.09 0.14 0.18 0.23 0.34 2165
#> Tail_ESS Rhat
#> pred[No intervention] 4099 1
#> pred[Group counselling] 2350 1
#> pred[Individual counselling] 2128 1
#> pred[Self-help] 2657 1
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"))
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[No intervention] 0.12 0.01 0.10 0.11 0.12 0.13 0.15 3990
#> pred[Group counselling] 0.29 0.09 0.15 0.23 0.28 0.35 0.49 2088
#> pred[Individual counselling] 0.24 0.05 0.16 0.21 0.24 0.27 0.35 1349
#> pred[Self-help] 0.19 0.06 0.09 0.14 0.18 0.23 0.34 2098
#> Tail_ESS Rhat
#> pred[No intervention] 3834 1
#> pred[Group counselling] 2173 1
#> pred[Individual counselling] 2111 1
#> pred[Self-help] 2591 1
plot(smk_pred_RE2, ref_line = c(0, 1))
# }
## Plaque psoriasis ML-NMR
# \donttest{
# Run plaque psoriasis ML-NMR example if not already available
if (!exists("pso_fit")) example("example_pso_mlnmr", run.donttest = TRUE)
# }
# \donttest{
# Predicted probabilities of response in each study in the network
(pso_pred <- predict(pso_fit, type = "response"))
#> ---------------------------------------------------------------- Study: FIXTURE ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> pred[FIXTURE: PBO] 0.04 0.01 0.03 0.04 0.04 0.05 0.06 4105 3407
#> pred[FIXTURE: ETN] 0.46 0.02 0.41 0.44 0.46 0.47 0.50 8858 3237
#> pred[FIXTURE: IXE_Q2W] 0.89 0.02 0.85 0.88 0.89 0.90 0.92 6318 2400
#> pred[FIXTURE: IXE_Q4W] 0.80 0.03 0.74 0.78 0.80 0.81 0.84 6689 3001
#> pred[FIXTURE: SEC_150] 0.67 0.03 0.62 0.65 0.67 0.69 0.72 10610 2728
#> pred[FIXTURE: SEC_300] 0.77 0.02 0.72 0.75 0.77 0.79 0.81 10121 3045
#> Rhat
#> pred[FIXTURE: PBO] 1
#> pred[FIXTURE: ETN] 1
#> pred[FIXTURE: IXE_Q2W] 1
#> pred[FIXTURE: IXE_Q4W] 1
#> pred[FIXTURE: SEC_150] 1
#> pred[FIXTURE: SEC_300] 1
#>
#> -------------------------------------------------------------- Study: UNCOVER-1 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> pred[UNCOVER-1: PBO] 0.06 0.01 0.04 0.05 0.06 0.06 0.07 4931 3319
#> pred[UNCOVER-1: ETN] 0.46 0.03 0.41 0.44 0.46 0.48 0.52 6377 2941
#> pred[UNCOVER-1: IXE_Q2W] 0.90 0.01 0.88 0.89 0.90 0.91 0.92 8100 3024
#> pred[UNCOVER-1: IXE_Q4W] 0.81 0.02 0.78 0.80 0.81 0.82 0.84 10661 3361
#> pred[UNCOVER-1: SEC_150] 0.69 0.04 0.60 0.66 0.69 0.72 0.77 6520 3125
#> pred[UNCOVER-1: SEC_300] 0.78 0.04 0.71 0.76 0.79 0.81 0.85 7400 3162
#> Rhat
#> pred[UNCOVER-1: PBO] 1
#> pred[UNCOVER-1: ETN] 1
#> pred[UNCOVER-1: IXE_Q2W] 1
#> pred[UNCOVER-1: IXE_Q4W] 1
#> pred[UNCOVER-1: SEC_150] 1
#> pred[UNCOVER-1: SEC_300] 1
#>
#> -------------------------------------------------------------- Study: UNCOVER-2 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> pred[UNCOVER-2: PBO] 0.05 0.01 0.03 0.04 0.05 0.05 0.06 5473 2890
#> pred[UNCOVER-2: ETN] 0.42 0.02 0.38 0.40 0.42 0.43 0.46 8304 3314
#> pred[UNCOVER-2: IXE_Q2W] 0.88 0.01 0.86 0.87 0.88 0.89 0.91 6866 2941
#> pred[UNCOVER-2: IXE_Q4W] 0.78 0.02 0.75 0.77 0.78 0.79 0.81 8852 3156
#> pred[UNCOVER-2: SEC_150] 0.65 0.04 0.57 0.62 0.65 0.68 0.73 7611 2912
#> pred[UNCOVER-2: SEC_300] 0.75 0.04 0.68 0.73 0.75 0.78 0.82 9053 3143
#> Rhat
#> pred[UNCOVER-2: PBO] 1
#> pred[UNCOVER-2: ETN] 1
#> pred[UNCOVER-2: IXE_Q2W] 1
#> pred[UNCOVER-2: IXE_Q4W] 1
#> pred[UNCOVER-2: SEC_150] 1
#> pred[UNCOVER-2: SEC_300] 1
#>
#> -------------------------------------------------------------- Study: UNCOVER-3 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> pred[UNCOVER-3: PBO] 0.08 0.01 0.06 0.07 0.08 0.08 0.10 5428 3133
#> pred[UNCOVER-3: ETN] 0.53 0.02 0.49 0.52 0.53 0.54 0.57 7523 3150
#> pred[UNCOVER-3: IXE_Q2W] 0.93 0.01 0.91 0.92 0.93 0.93 0.94 6352 3314
#> pred[UNCOVER-3: IXE_Q4W] 0.85 0.01 0.83 0.85 0.85 0.86 0.88 7670 3373
#> pred[UNCOVER-3: SEC_150] 0.75 0.04 0.67 0.72 0.75 0.77 0.81 8074 2961
#> pred[UNCOVER-3: SEC_300] 0.83 0.03 0.77 0.81 0.83 0.85 0.88 9014 3430
#> Rhat
#> pred[UNCOVER-3: PBO] 1
#> pred[UNCOVER-3: ETN] 1
#> pred[UNCOVER-3: IXE_Q2W] 1
#> pred[UNCOVER-3: IXE_Q4W] 1
#> pred[UNCOVER-3: SEC_150] 1
#> pred[UNCOVER-3: SEC_300] 1
#>
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)))
#> ------------------------------------------------------------------ Study: New 1 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS Rhat
#> pred[New 1: PBO] 0.06 0.03 0.03 0.04 0.06 0.08 0.12 5809 3317 1
#> pred[New 1: ETN] 0.37 0.06 0.26 0.33 0.37 0.41 0.49 6233 3348 1
#> pred[New 1: IXE_Q2W] 0.90 0.03 0.84 0.88 0.90 0.91 0.94 5595 3207 1
#> pred[New 1: IXE_Q4W] 0.80 0.04 0.73 0.78 0.81 0.83 0.87 5720 3714 1
#> pred[New 1: SEC_150] 0.68 0.06 0.56 0.64 0.68 0.72 0.78 5254 3416 1
#> pred[New 1: SEC_300] 0.78 0.05 0.68 0.75 0.78 0.81 0.86 5696 3245 1
#>
plot(pso_pred_new, ref_line = c(0, 1))
# }
## Progression free survival with newly-diagnosed multiple myeloma
# \donttest{
# Run newly-diagnosed multiple myeloma example if not already available
if (!exists("ndmm_fit")) example("example_ndmm", run.donttest = TRUE)
# }
# \donttest{
# 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)
#> -------------------------------------------------------------- Study: Attal2012 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Attal2012: Pbo, 1] 5 0.19 0.02 0.15 0.18 0.19 0.20 0.23 4945
#> pred[Attal2012: Len, 1] 5 0.38 0.02 0.33 0.36 0.38 0.40 0.43 5230
#> pred[Attal2012: Thal, 1] 5 0.23 0.04 0.16 0.20 0.23 0.25 0.30 5171
#> Tail_ESS Rhat
#> pred[Attal2012: Pbo, 1] 3325 1
#> pred[Attal2012: Len, 1] 2936 1
#> pred[Attal2012: Thal, 1] 3367 1
#>
#> ------------------------------------------------------------ Study: Jackson2019 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Jackson2019: Pbo, 1] 5 0.25 0.01 0.22 0.24 0.25 0.26 0.28 5020
#> pred[Jackson2019: Len, 1] 5 0.45 0.01 0.42 0.44 0.45 0.45 0.47 5434
#> pred[Jackson2019: Thal, 1] 5 0.29 0.03 0.23 0.27 0.29 0.31 0.36 4982
#> Tail_ESS Rhat
#> pred[Jackson2019: Pbo, 1] 3299 1
#> pred[Jackson2019: Len, 1] 3468 1
#> pred[Jackson2019: Thal, 1] 3218 1
#>
#> ----------------------------------------------------------- Study: McCarthy2012 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[McCarthy2012: Pbo, 1] 5 0.27 0.02 0.22 0.25 0.27 0.28 0.31 4828
#> pred[McCarthy2012: Len, 1] 5 0.46 0.02 0.41 0.45 0.46 0.48 0.51 4819
#> pred[McCarthy2012: Thal, 1] 5 0.31 0.04 0.23 0.28 0.31 0.33 0.38 4772
#> Tail_ESS Rhat
#> pred[McCarthy2012: Pbo, 1] 3369 1
#> pred[McCarthy2012: Len, 1] 3160 1
#> pred[McCarthy2012: Thal, 1] 3572 1
#>
#> ------------------------------------------------------------- Study: Morgan2012 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Morgan2012: Pbo, 1] 5 0.24 0.02 0.20 0.22 0.24 0.25 0.28 5229
#> pred[Morgan2012: Len, 1] 5 0.43 0.03 0.38 0.41 0.43 0.45 0.49 5046
#> pred[Morgan2012: Thal, 1] 5 0.28 0.02 0.23 0.26 0.28 0.29 0.33 5154
#> Tail_ESS Rhat
#> pred[Morgan2012: Pbo, 1] 3606 1
#> pred[Morgan2012: Len, 1] 3638 1
#> pred[Morgan2012: Thal, 1] 3230 1
#>
#> ------------------------------------------------------------ Study: Palumbo2014 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Palumbo2014: Pbo, 1] 5 0.20 0.03 0.14 0.18 0.19 0.22 0.26 5684
#> pred[Palumbo2014: Len, 1] 5 0.38 0.04 0.32 0.36 0.38 0.41 0.45 5738
#> pred[Palumbo2014: Thal, 1] 5 0.23 0.04 0.15 0.20 0.23 0.26 0.32 5239
#> Tail_ESS Rhat
#> pred[Palumbo2014: Pbo, 1] 2666 1
#> pred[Palumbo2014: Len, 1] 3088 1
#> pred[Palumbo2014: Thal, 1] 3644 1
#>
# 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))
#> -------------------------------------------------------------- Study: Attal2012 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Attal2012: Pbo, 0.2] 1.07 0.07 0.92 1.02 1.07 1.12 1.21 4443
#> pred[Attal2012: Pbo, 0.5] 2.56 0.12 2.34 2.47 2.55 2.63 2.79 4840
#> pred[Attal2012: Pbo, 0.8] 4.90 0.25 4.45 4.73 4.88 5.06 5.43 4918
#> pred[Attal2012: Len, 0.2] 1.61 0.09 1.43 1.55 1.61 1.68 1.80 4566
#> pred[Attal2012: Len, 0.5] 3.87 0.18 3.53 3.75 3.87 3.99 4.25 5350
#> pred[Attal2012: Len, 0.8] 7.42 0.46 6.59 7.10 7.39 7.72 8.40 4942
#> pred[Attal2012: Thal, 0.2] 1.17 0.11 0.96 1.09 1.16 1.24 1.39 4512
#> pred[Attal2012: Thal, 0.5] 2.79 0.23 2.38 2.63 2.78 2.94 3.27 4962
#> pred[Attal2012: Thal, 0.8] 5.35 0.45 4.55 5.04 5.33 5.65 6.31 5168
#> Tail_ESS Rhat
#> pred[Attal2012: Pbo, 0.2] 2964 1
#> pred[Attal2012: Pbo, 0.5] 3453 1
#> pred[Attal2012: Pbo, 0.8] 3414 1
#> pred[Attal2012: Len, 0.2] 3101 1
#> pred[Attal2012: Len, 0.5] 2958 1
#> pred[Attal2012: Len, 0.8] 3068 1
#> pred[Attal2012: Thal, 0.2] 2326 1
#> pred[Attal2012: Thal, 0.5] 3230 1
#> pred[Attal2012: Thal, 0.8] 3255 1
#>
#> ------------------------------------------------------------ Study: Jackson2019 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Jackson2019: Pbo, 0.2] 0.71 0.04 0.63 0.68 0.71 0.73 0.79 4094
#> pred[Jackson2019: Pbo, 0.5] 2.39 0.10 2.20 2.32 2.38 2.45 2.57 4334
#> pred[Jackson2019: Pbo, 0.8] 5.88 0.25 5.41 5.71 5.88 6.05 6.37 5202
#> pred[Jackson2019: Len, 0.2] 1.26 0.06 1.14 1.22 1.26 1.30 1.39 5714
#> pred[Jackson2019: Len, 0.5] 4.25 0.16 3.94 4.13 4.24 4.35 4.57 5497
#> pred[Jackson2019: Len, 0.8] 10.47 0.46 9.61 10.15 10.45 10.77 11.41 5081
#> pred[Jackson2019: Thal, 0.2] 0.80 0.09 0.64 0.74 0.80 0.86 0.98 4867
#> pred[Jackson2019: Thal, 0.5] 2.70 0.27 2.21 2.51 2.69 2.88 3.26 4938
#> pred[Jackson2019: Thal, 0.8] 6.66 0.67 5.44 6.19 6.63 7.10 8.05 5010
#> Tail_ESS Rhat
#> pred[Jackson2019: Pbo, 0.2] 2941 1
#> pred[Jackson2019: Pbo, 0.5] 3259 1
#> pred[Jackson2019: Pbo, 0.8] 3284 1
#> pred[Jackson2019: Len, 0.2] 3632 1
#> pred[Jackson2019: Len, 0.5] 3421 1
#> pred[Jackson2019: Len, 0.8] 3419 1
#> pred[Jackson2019: Thal, 0.2] 2989 1
#> pred[Jackson2019: Thal, 0.5] 3179 1
#> pred[Jackson2019: Thal, 0.8] 3333 1
#>
#> ----------------------------------------------------------- Study: McCarthy2012 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[McCarthy2012: Pbo, 0.2] 1.26 0.10 1.07 1.20 1.26 1.33 1.45 4289
#> pred[McCarthy2012: Pbo, 0.5] 3.03 0.16 2.73 2.93 3.03 3.13 3.35 4251
#> pred[McCarthy2012: Pbo, 0.8] 5.83 0.32 5.26 5.60 5.80 6.04 6.51 4918
#> pred[McCarthy2012: Len, 0.2] 1.91 0.12 1.67 1.83 1.91 1.99 2.15 4463
#> pred[McCarthy2012: Len, 0.5] 4.60 0.24 4.15 4.44 4.59 4.76 5.08 4767
#> pred[McCarthy2012: Len, 0.8] 8.85 0.58 7.80 8.44 8.81 9.23 10.11 4930
#> pred[McCarthy2012: Thal, 0.2] 1.38 0.13 1.12 1.29 1.38 1.46 1.66 4524
#> pred[McCarthy2012: Thal, 0.5] 3.31 0.28 2.80 3.13 3.30 3.49 3.89 4597
#> pred[McCarthy2012: Thal, 0.8] 6.37 0.56 5.36 5.99 6.34 6.75 7.55 4819
#> Tail_ESS Rhat
#> pred[McCarthy2012: Pbo, 0.2] 3120 1
#> pred[McCarthy2012: Pbo, 0.5] 3588 1
#> pred[McCarthy2012: Pbo, 0.8] 3286 1
#> pred[McCarthy2012: Len, 0.2] 2917 1
#> pred[McCarthy2012: Len, 0.5] 3160 1
#> pred[McCarthy2012: Len, 0.8] 3680 1
#> pred[McCarthy2012: Thal, 0.2] 2965 1
#> pred[McCarthy2012: Thal, 0.5] 3412 1
#> pred[McCarthy2012: Thal, 0.8] 3678 1
#>
#> ------------------------------------------------------------- Study: Morgan2012 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Morgan2012: Pbo, 0.2] 0.61 0.05 0.51 0.57 0.60 0.64 0.72 4455
#> pred[Morgan2012: Pbo, 0.5] 2.20 0.16 1.91 2.09 2.19 2.30 2.52 4787
#> pred[Morgan2012: Pbo, 0.8] 5.73 0.43 4.98 5.42 5.71 6.01 6.65 5283
#> pred[Morgan2012: Len, 0.2] 1.12 0.10 0.93 1.05 1.11 1.18 1.34 4635
#> pred[Morgan2012: Len, 0.5] 4.06 0.36 3.42 3.80 4.04 4.29 4.82 5063
#> pred[Morgan2012: Len, 0.8] 10.59 1.06 8.74 9.84 10.51 11.26 12.85 5246
#> pred[Morgan2012: Thal, 0.2] 0.69 0.06 0.57 0.65 0.69 0.73 0.81 5366
#> pred[Morgan2012: Thal, 0.5] 2.50 0.18 2.16 2.37 2.49 2.61 2.87 5328
#> pred[Morgan2012: Thal, 0.8] 6.51 0.50 5.60 6.16 6.47 6.82 7.62 5076
#> Tail_ESS Rhat
#> pred[Morgan2012: Pbo, 0.2] 2969 1
#> pred[Morgan2012: Pbo, 0.5] 3436 1
#> pred[Morgan2012: Pbo, 0.8] 3567 1
#> pred[Morgan2012: Len, 0.2] 3468 1
#> pred[Morgan2012: Len, 0.5] 3563 1
#> pred[Morgan2012: Len, 0.8] 3034 1
#> pred[Morgan2012: Thal, 0.2] 3403 1
#> pred[Morgan2012: Thal, 0.5] 3357 1
#> pred[Morgan2012: Thal, 0.8] 3087 1
#>
#> ------------------------------------------------------------ Study: Palumbo2014 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Palumbo2014: Pbo, 0.2] 0.71 0.09 0.53 0.64 0.70 0.77 0.90 4408
#> pred[Palumbo2014: Pbo, 0.5] 2.15 0.19 1.80 2.02 2.15 2.28 2.55 5059
#> pred[Palumbo2014: Pbo, 0.8] 4.96 0.48 4.13 4.63 4.92 5.25 5.99 5612
#> pred[Palumbo2014: Len, 0.2] 1.20 0.13 0.96 1.11 1.19 1.28 1.45 4759
#> pred[Palumbo2014: Len, 0.5] 3.67 0.33 3.08 3.44 3.65 3.87 4.36 5615
#> pred[Palumbo2014: Len, 0.8] 8.46 0.99 6.77 7.77 8.35 9.04 10.71 5550
#> pred[Palumbo2014: Thal, 0.2] 0.79 0.12 0.57 0.71 0.79 0.87 1.04 4699
#> pred[Palumbo2014: Thal, 0.5] 2.42 0.29 1.89 2.21 2.41 2.61 3.02 4975
#> pred[Palumbo2014: Thal, 0.8] 5.56 0.73 4.29 5.05 5.50 6.02 7.12 5209
#> Tail_ESS Rhat
#> pred[Palumbo2014: Pbo, 0.2] 2553 1
#> pred[Palumbo2014: Pbo, 0.5] 3359 1
#> pred[Palumbo2014: Pbo, 0.8] 2709 1
#> pred[Palumbo2014: Len, 0.2] 3139 1
#> pred[Palumbo2014: Len, 0.5] 3322 1
#> pred[Palumbo2014: Len, 0.8] 3108 1
#> pred[Palumbo2014: Thal, 0.2] 3099 1
#> pred[Palumbo2014: Thal, 0.5] 3508 1
#> pred[Palumbo2014: Thal, 0.8] 3385 1
#>
plot(predict(ndmm_fit, type = "median"))
# Mean survival time
predict(ndmm_fit, type = "mean")
#> -------------------------------------------------------------- Study: Attal2012 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> pred[Attal2012: Pbo] 3.14 0.15 2.87 3.03 3.13 3.23 3.45 4953 3301
#> pred[Attal2012: Len] 4.75 0.27 4.26 4.56 4.74 4.93 5.33 5082 3052
#> pred[Attal2012: Thal] 3.43 0.28 2.92 3.22 3.41 3.61 4.03 5160 3175
#> Rhat
#> pred[Attal2012: Pbo] 1
#> pred[Attal2012: Len] 1
#> pred[Attal2012: Thal] 1
#>
#> ------------------------------------------------------------ Study: Jackson2019 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> pred[Jackson2019: Pbo] 3.65 0.15 3.36 3.54 3.65 3.75 3.95 5199 3346
#> pred[Jackson2019: Len] 6.49 0.29 5.96 6.29 6.48 6.68 7.08 5092 3450
#> pred[Jackson2019: Thal] 4.13 0.42 3.37 3.84 4.11 4.40 4.99 5014 3332
#> Rhat
#> pred[Jackson2019: Pbo] 1
#> pred[Jackson2019: Len] 1
#> pred[Jackson2019: Thal] 1
#>
#> ----------------------------------------------------------- Study: McCarthy2012 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> pred[McCarthy2012: Pbo] 3.73 0.19 3.38 3.60 3.72 3.85 4.15 4779 3454
#> pred[McCarthy2012: Len] 5.66 0.35 5.05 5.43 5.64 5.88 6.40 4892 3298
#> pred[McCarthy2012: Thal] 4.08 0.35 3.44 3.84 4.05 4.31 4.80 4750 3534
#> Rhat
#> pred[McCarthy2012: Pbo] 1
#> pred[McCarthy2012: Len] 1
#> pred[McCarthy2012: Thal] 1
#>
#> ------------------------------------------------------------- Study: Morgan2012 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> pred[Morgan2012: Pbo] 3.56 0.27 3.09 3.37 3.54 3.73 4.14 5282 3567
#> pred[Morgan2012: Len] 6.57 0.66 5.42 6.10 6.53 6.99 8.00 5248 2986
#> pred[Morgan2012: Thal] 4.04 0.31 3.47 3.82 4.02 4.24 4.73 5067 3165
#> Rhat
#> pred[Morgan2012: Pbo] 1
#> pred[Morgan2012: Len] 1
#> pred[Morgan2012: Thal] 1
#>
#> ------------------------------------------------------------ Study: Palumbo2014 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS Tail_ESS
#> pred[Palumbo2014: Pbo] 3.09 0.29 2.58 2.89 3.06 3.27 3.72 5571 2765
#> pred[Palumbo2014: Len] 5.27 0.60 4.25 4.84 5.20 5.62 6.64 5551 3102
#> pred[Palumbo2014: Thal] 3.46 0.45 2.68 3.15 3.43 3.74 4.42 5191 3588
#> Rhat
#> pred[Palumbo2014: Pbo] 1
#> pred[Palumbo2014: Len] 1
#> pred[Palumbo2014: Thal] 1
#>
# Restricted mean survival time
# By default, the time horizon is the shortest follow-up time in the network
predict(ndmm_fit, type = "rmst")
#> -------------------------------------------------------------- Study: Attal2012 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Attal2012: Pbo] 4.01 2.49 0.06 2.37 2.45 2.49 2.54 2.61 4798
#> pred[Attal2012: Len] 4.01 2.99 0.05 2.89 2.96 2.99 3.03 3.09 5015
#> pred[Attal2012: Thal] 4.01 2.60 0.11 2.40 2.53 2.61 2.68 2.81 4865
#> Tail_ESS Rhat
#> pred[Attal2012: Pbo] 3348 1
#> pred[Attal2012: Len] 3659 1
#> pred[Attal2012: Thal] 3243 1
#>
#> ------------------------------------------------------------ Study: Jackson2019 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Jackson2019: Pbo] 4.01 2.36 0.04 2.27 2.33 2.36 2.39 2.44 4216
#> pred[Jackson2019: Len] 4.01 2.91 0.03 2.84 2.88 2.91 2.93 2.97 5743
#> pred[Jackson2019: Thal] 4.01 2.48 0.10 2.28 2.41 2.48 2.55 2.67 4919
#> Tail_ESS Rhat
#> pred[Jackson2019: Pbo] 3100 1
#> pred[Jackson2019: Len] 3998 1
#> pred[Jackson2019: Thal] 3170 1
#>
#> ----------------------------------------------------------- Study: McCarthy2012 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[McCarthy2012: Pbo] 4.01 2.71 0.07 2.57 2.66 2.71 2.76 2.84 4147
#> pred[McCarthy2012: Len] 4.01 3.16 0.05 3.05 3.12 3.16 3.19 3.26 4400
#> pred[McCarthy2012: Thal] 4.01 2.81 0.10 2.61 2.75 2.82 2.88 3.01 4543
#> Tail_ESS Rhat
#> pred[McCarthy2012: Pbo] 3665 1
#> pred[McCarthy2012: Len] 3216 1
#> pred[McCarthy2012: Thal] 3321 1
#>
#> ------------------------------------------------------------- Study: Morgan2012 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Morgan2012: Pbo] 4.01 2.26 0.07 2.12 2.21 2.26 2.31 2.41 4728
#> pred[Morgan2012: Len] 4.01 2.83 0.07 2.69 2.79 2.83 2.88 2.97 4816
#> pred[Morgan2012: Thal] 4.01 2.39 0.07 2.25 2.35 2.39 2.44 2.53 5355
#> Tail_ESS Rhat
#> pred[Morgan2012: Pbo] 3404 1
#> pred[Morgan2012: Len] 3750 1
#> pred[Morgan2012: Thal] 3588 1
#>
#> ------------------------------------------------------------ Study: Palumbo2014 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Palumbo2014: Pbo] 4.01 2.25 0.10 2.04 2.18 2.25 2.32 2.45 4890
#> pred[Palumbo2014: Len] 4.01 2.81 0.08 2.65 2.76 2.82 2.87 2.97 5211
#> pred[Palumbo2014: Thal] 4.01 2.38 0.14 2.10 2.28 2.38 2.47 2.63 4942
#> Tail_ESS Rhat
#> pred[Palumbo2014: Pbo] 3358 1
#> pred[Palumbo2014: Len] 3665 1
#> pred[Palumbo2014: Thal] 3296 1
#>
# An alternative restriction time can be set using the times argument
predict(ndmm_fit, type = "rmst", times = 5) # 5-year RMST
#> -------------------------------------------------------------- Study: Attal2012 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Attal2012: Pbo] 5 2.73 0.08 2.57 2.67 2.72 2.78 2.88 4860
#> pred[Attal2012: Len] 5 3.41 0.07 3.27 3.37 3.41 3.46 3.55 5222
#> pred[Attal2012: Thal] 5 2.88 0.14 2.60 2.78 2.88 2.97 3.15 4961
#> Tail_ESS Rhat
#> pred[Attal2012: Pbo] 3463 1
#> pred[Attal2012: Len] 3449 1
#> pred[Attal2012: Thal] 3150 1
#>
#> ------------------------------------------------------------ Study: Jackson2019 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Jackson2019: Pbo] 5 2.64 0.06 2.53 2.60 2.64 2.68 2.75 4355
#> pred[Jackson2019: Len] 5 3.38 0.05 3.29 3.35 3.38 3.41 3.47 5685
#> pred[Jackson2019: Thal] 5 2.80 0.14 2.53 2.71 2.81 2.90 3.06 4932
#> Tail_ESS Rhat
#> pred[Jackson2019: Pbo] 3287 1
#> pred[Jackson2019: Len] 3671 1
#> pred[Jackson2019: Thal] 3261 1
#>
#> ----------------------------------------------------------- Study: McCarthy2012 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[McCarthy2012: Pbo] 5 3.02 0.09 2.85 2.96 3.02 3.08 3.19 4182
#> pred[McCarthy2012: Len] 5 3.66 0.07 3.51 3.61 3.66 3.71 3.80 4395
#> pred[McCarthy2012: Thal] 5 3.16 0.14 2.89 3.07 3.17 3.26 3.43 4586
#> Tail_ESS Rhat
#> pred[McCarthy2012: Pbo] 3657 1
#> pred[McCarthy2012: Len] 3362 1
#> pred[McCarthy2012: Thal] 3345 1
#>
#> ------------------------------------------------------------- Study: Morgan2012 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Morgan2012: Pbo] 5 2.53 0.09 2.35 2.47 2.53 2.59 2.72 4830
#> pred[Morgan2012: Len] 5 3.29 0.10 3.10 3.23 3.29 3.36 3.48 4909
#> pred[Morgan2012: Thal] 5 2.70 0.09 2.51 2.64 2.70 2.76 2.89 5334
#> Tail_ESS Rhat
#> pred[Morgan2012: Pbo] 3436 1
#> pred[Morgan2012: Len] 3715 1
#> pred[Morgan2012: Thal] 3545 1
#>
#> ------------------------------------------------------------ Study: Palumbo2014 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Palumbo2014: Pbo] 5 2.48 0.13 2.23 2.39 2.48 2.56 2.73 5051
#> pred[Palumbo2014: Len] 5 3.23 0.11 3.01 3.16 3.23 3.31 3.45 5533
#> pred[Palumbo2014: Thal] 5 2.64 0.18 2.28 2.52 2.65 2.77 2.97 5022
#> Tail_ESS Rhat
#> pred[Palumbo2014: Pbo] 3578 1
#> pred[Palumbo2014: Len] 3421 1
#> pred[Palumbo2014: Thal] 3378 1
#>
# }