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 stan_nma
predict(
object,
...,
baseline = NULL,
newdata = NULL,
study = NULL,
trt_ref = NULL,
type = c("link", "response"),
level = c("aggregate", "individual"),
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
)
# S3 method for stan_nma_surv
predict(
object,
times = NULL,
...,
baseline = NULL,
aux = NULL,
newdata = NULL,
study = NULL,
trt_ref = 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
)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
trt_refargument 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.- trt_ref
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.- 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_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.- 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] -2.79 0.33 -3.46 -3.00 -2.78 -2.56 -2.16
#> pred[1: Group counselling] -1.68 0.50 -2.67 -2.01 -1.70 -1.34 -0.68
#> pred[1: Individual counselling] -1.94 0.39 -2.71 -2.20 -1.94 -1.68 -1.17
#> pred[1: Self-help] -2.29 0.51 -3.29 -2.62 -2.29 -1.95 -1.30
#> Bulk_ESS Tail_ESS Rhat
#> pred[1: No intervention] 5721 3121 1
#> pred[1: Group counselling] 2749 2677 1
#> pred[1: Individual counselling] 2577 2884 1
#> pred[1: Self-help] 2743 2773 1
#>
#> ---------------------------------------------------------------------- Study: 2 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[2: No intervention] -2.58 0.77 -4.19 -3.06 -2.57 -2.08 -1.12
#> pred[2: Group counselling] -1.47 0.77 -3.03 -1.97 -1.47 -0.98 0.02
#> pred[2: Individual counselling] -1.73 0.76 -3.26 -2.21 -1.74 -1.25 -0.23
#> pred[2: Self-help] -2.08 0.76 -3.60 -2.56 -2.07 -1.60 -0.57
#> Bulk_ESS Tail_ESS Rhat
#> pred[2: No intervention] 2739 2354 1
#> pred[2: Group counselling] 3287 2592 1
#> pred[2: Individual counselling] 3076 2524 1
#> pred[2: Self-help] 3811 2812 1
#>
#> ---------------------------------------------------------------------- Study: 3 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[3: No intervention] -2.14 0.12 -2.39 -2.22 -2.14 -2.06 -1.92
#> pred[3: Group counselling] -1.04 0.45 -1.91 -1.32 -1.05 -0.75 -0.14
#> pred[3: Individual counselling] -1.29 0.26 -1.81 -1.47 -1.29 -1.13 -0.77
#> pred[3: Self-help] -1.64 0.41 -2.51 -1.91 -1.64 -1.38 -0.85
#> Bulk_ESS Tail_ESS Rhat
#> pred[3: No intervention] 7281 3087 1
#> pred[3: Group counselling] 2442 2702 1
#> pred[3: Individual counselling] 1490 2630 1
#> pred[3: Self-help] 2045 2636 1
#>
#> ---------------------------------------------------------------------- Study: 4 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[4: No intervention] -4.05 0.56 -5.22 -4.41 -4.03 -3.66 -3.03
#> pred[4: Group counselling] -2.94 0.69 -4.36 -3.39 -2.94 -2.49 -1.63
#> pred[4: Individual counselling] -3.20 0.57 -4.39 -3.56 -3.18 -2.81 -2.13
#> pred[4: Self-help] -3.55 0.68 -4.91 -3.99 -3.52 -3.08 -2.25
#> Bulk_ESS Tail_ESS Rhat
#> pred[4: No intervention] 4649 2750 1
#> pred[4: Group counselling] 4284 3136 1
#> pred[4: Individual counselling] 4909 3179 1
#> pred[4: Self-help] 3718 3062 1
#>
#> ---------------------------------------------------------------------- Study: 5 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[5: No intervention] -2.15 0.14 -2.43 -2.25 -2.15 -2.06 -1.89
#> pred[5: Group counselling] -1.05 0.45 -1.94 -1.34 -1.06 -0.75 -0.15
#> pred[5: Individual counselling] -1.30 0.28 -1.83 -1.48 -1.32 -1.12 -0.75
#> pred[5: Self-help] -1.66 0.42 -2.49 -1.92 -1.65 -1.38 -0.84
#> Bulk_ESS Tail_ESS Rhat
#> pred[5: No intervention] 6408 2986 1
#> pred[5: Group counselling] 2379 2672 1
#> pred[5: Individual counselling] 1431 2558 1
#> pred[5: Self-help] 2006 2566 1
#>
#> ---------------------------------------------------------------------- Study: 6 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[6: No intervention] -3.42 0.73 -5.07 -3.85 -3.36 -2.92 -2.16
#> pred[6: Group counselling] -2.31 0.80 -4.06 -2.81 -2.26 -1.77 -0.95
#> pred[6: Individual counselling] -2.57 0.71 -4.13 -3.00 -2.53 -2.08 -1.33
#> pred[6: Self-help] -2.92 0.80 -4.69 -3.41 -2.86 -2.37 -1.53
#> Bulk_ESS Tail_ESS Rhat
#> pred[6: No intervention] 3052 2287 1
#> pred[6: Group counselling] 3643 2614 1
#> pred[6: Individual counselling] 3270 2354 1
#> pred[6: Self-help] 3136 2632 1
#>
#> ---------------------------------------------------------------------- Study: 7 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[7: No intervention] -3.02 0.44 -3.96 -3.29 -2.99 -2.71 -2.25
#> pred[7: Group counselling] -1.91 0.58 -3.14 -2.28 -1.88 -1.51 -0.81
#> pred[7: Individual counselling] -2.17 0.46 -3.16 -2.46 -2.14 -1.85 -1.34
#> pred[7: Self-help] -2.52 0.57 -3.68 -2.88 -2.50 -2.12 -1.45
#> Bulk_ESS Tail_ESS Rhat
#> pred[7: No intervention] 4486 2888 1
#> pred[7: Group counselling] 3504 2610 1
#> pred[7: Individual counselling] 3496 2560 1
#> pred[7: Self-help] 3301 2516 1
#>
#> ---------------------------------------------------------------------- Study: 8 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[8: No intervention] -2.72 0.62 -4.06 -3.11 -2.68 -2.29 -1.63
#> pred[8: Group counselling] -1.61 0.71 -3.11 -2.05 -1.57 -1.14 -0.32
#> pred[8: Individual counselling] -1.87 0.61 -3.17 -2.26 -1.83 -1.45 -0.77
#> pred[8: Self-help] -2.22 0.71 -3.79 -2.67 -2.16 -1.74 -0.92
#> Bulk_ESS Tail_ESS Rhat
#> pred[8: No intervention] 4104 2933 1
#> pred[8: Group counselling] 4601 2860 1
#> pred[8: Individual counselling] 4107 2633 1
#> pred[8: Self-help] 3857 2827 1
#>
#> ---------------------------------------------------------------------- Study: 9 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[9: No intervention] -1.85 0.43 -2.72 -2.11 -1.84 -1.55 -1.06
#> pred[9: Group counselling] -0.74 0.60 -1.95 -1.13 -0.74 -0.35 0.46
#> pred[9: Individual counselling] -1.00 0.47 -1.93 -1.30 -0.99 -0.68 -0.09
#> pred[9: Self-help] -1.35 0.58 -2.49 -1.73 -1.34 -0.97 -0.23
#> Bulk_ESS Tail_ESS Rhat
#> pred[9: No intervention] 5637 2874 1
#> pred[9: Group counselling] 3310 2857 1
#> pred[9: Individual counselling] 3531 2899 1
#> pred[9: Self-help] 3260 2722 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 -1.85
#> pred[10: Group counselling] -0.97 0.44 -1.81 -1.27 -0.98 -0.69 -0.09
#> pred[10: Individual counselling] -1.23 0.27 -1.75 -1.41 -1.24 -1.07 -0.69
#> pred[10: Self-help] -1.58 0.41 -2.38 -1.83 -1.58 -1.31 -0.79
#> Bulk_ESS Tail_ESS Rhat
#> pred[10: No intervention] 7633 3017 1
#> pred[10: Group counselling] 2401 2716 1
#> pred[10: Individual counselling] 1523 2494 1
#> pred[10: Self-help] 2049 2573 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] -2.52 0.48 -3.46 -2.84 -2.52 -2.20 -1.56
#> pred[11: Individual counselling] -2.77 0.33 -3.43 -2.98 -2.77 -2.56 -2.13
#> pred[11: Self-help] -3.12 0.44 -4.00 -3.41 -3.13 -2.83 -2.26
#> Bulk_ESS Tail_ESS Rhat
#> pred[11: No intervention] 6723 2840 1
#> pred[11: Group counselling] 2569 3080 1
#> pred[11: Individual counselling] 2086 2936 1
#> pred[11: Self-help] 2082 2650 1
#>
#> --------------------------------------------------------------------- Study: 12 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[12: No intervention] -2.22 0.13 -2.48 -2.30 -2.22 -2.13 -1.97
#> pred[12: Group counselling] -1.11 0.45 -1.96 -1.40 -1.13 -0.82 -0.22
#> pred[12: Individual counselling] -1.37 0.27 -1.90 -1.55 -1.38 -1.19 -0.84
#> pred[12: Self-help] -1.72 0.41 -2.55 -1.99 -1.72 -1.44 -0.88
#> Bulk_ESS Tail_ESS Rhat
#> pred[12: No intervention] 7081 3186 1
#> pred[12: Group counselling] 2369 2614 1
#> pred[12: Individual counselling] 1398 2413 1
#> pred[12: Self-help] 2040 2510 1
#>
#> --------------------------------------------------------------------- Study: 13 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[13: No intervention] -2.69 0.44 -3.58 -2.98 -2.67 -2.39 -1.87
#> pred[13: Group counselling] -1.58 0.61 -2.78 -1.99 -1.59 -1.18 -0.39
#> pred[13: Individual counselling] -1.84 0.48 -2.80 -2.15 -1.82 -1.52 -0.92
#> pred[13: Self-help] -2.19 0.58 -3.34 -2.57 -2.19 -1.80 -1.05
#> Bulk_ESS Tail_ESS Rhat
#> pred[13: No intervention] 4599 2805 1
#> pred[13: Group counselling] 3220 3058 1
#> pred[13: Individual counselling] 3122 2644 1
#> pred[13: Self-help] 2870 3021 1
#>
#> --------------------------------------------------------------------- Study: 14 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[14: No intervention] -2.41 0.23 -2.88 -2.57 -2.40 -2.26 -1.97
#> pred[14: Group counselling] -1.30 0.48 -2.23 -1.63 -1.32 -0.99 -0.34
#> pred[14: Individual counselling] -1.56 0.32 -2.17 -1.78 -1.56 -1.36 -0.92
#> pred[14: Self-help] -1.91 0.46 -2.80 -2.21 -1.92 -1.61 -1.01
#> Bulk_ESS Tail_ESS Rhat
#> pred[14: No intervention] 4830 2956 1
#> pred[14: Group counselling] 2729 2728 1
#> pred[14: Individual counselling] 2042 2834 1
#> pred[14: Self-help] 2349 2967 1
#>
#> --------------------------------------------------------------------- Study: 15 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[15: No intervention] -2.69 0.73 -4.30 -3.12 -2.63 -2.18 -1.43
#> pred[15: Group counselling] -1.58 0.72 -3.13 -2.02 -1.54 -1.10 -0.28
#> pred[15: Individual counselling] -1.84 0.73 -3.46 -2.27 -1.78 -1.34 -0.56
#> pred[15: Self-help] -2.19 0.79 -3.92 -2.67 -2.15 -1.65 -0.78
#> Bulk_ESS Tail_ESS Rhat
#> pred[15: No intervention] 3275 2521 1
#> pred[15: Group counselling] 4021 2667 1
#> pred[15: Individual counselling] 3536 2343 1
#> pred[15: Self-help] 3217 2426 1
#>
#> --------------------------------------------------------------------- Study: 16 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[16: No intervention] -2.61 0.34 -3.33 -2.84 -2.60 -2.38 -1.99
#> pred[16: Group counselling] -1.51 0.54 -2.56 -1.87 -1.50 -1.16 -0.46
#> pred[16: Individual counselling] -1.77 0.41 -2.60 -2.04 -1.77 -1.48 -0.98
#> pred[16: Self-help] -2.12 0.48 -3.07 -2.43 -2.11 -1.80 -1.20
#> Bulk_ESS Tail_ESS Rhat
#> pred[16: No intervention] 5542 2995 1
#> pred[16: Group counselling] 3204 3154 1
#> pred[16: Individual counselling] 2537 2777 1
#> pred[16: Self-help] 2637 3039 1
#>
#> --------------------------------------------------------------------- Study: 17 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[17: No intervention] -2.38 0.11 -2.60 -2.45 -2.37 -2.30 -2.17
#> pred[17: Group counselling] -1.27 0.44 -2.11 -1.56 -1.28 -0.98 -0.39
#> pred[17: Individual counselling] -1.53 0.26 -2.02 -1.70 -1.53 -1.36 -1.00
#> pred[17: Self-help] -1.88 0.41 -2.70 -2.14 -1.87 -1.61 -1.08
#> Bulk_ESS Tail_ESS Rhat
#> pred[17: No intervention] 7637 2637 1
#> pred[17: Group counselling] 2289 2719 1
#> pred[17: Individual counselling] 1272 2140 1
#> pred[17: Self-help] 1964 2331 1
#>
#> --------------------------------------------------------------------- Study: 18 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[18: No intervention] -2.57 0.28 -3.14 -2.74 -2.56 -2.38 -2.06
#> pred[18: Group counselling] -1.46 0.51 -2.45 -1.80 -1.48 -1.13 -0.44
#> pred[18: Individual counselling] -1.72 0.36 -2.40 -1.96 -1.72 -1.48 -1.03
#> pred[18: Self-help] -2.07 0.48 -3.04 -2.37 -2.07 -1.75 -1.14
#> Bulk_ESS Tail_ESS Rhat
#> pred[18: No intervention] 5825 2592 1
#> pred[18: Group counselling] 2591 2595 1
#> pred[18: Individual counselling] 2069 2669 1
#> pred[18: Self-help] 2356 3009 1
#>
#> --------------------------------------------------------------------- Study: 19 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[19: No intervention] -1.90 0.12 -2.14 -1.99 -1.90 -1.82 -1.68
#> pred[19: Group counselling] -0.80 0.45 -1.64 -1.09 -0.81 -0.51 0.11
#> pred[19: Individual counselling] -1.05 0.27 -1.57 -1.23 -1.06 -0.87 -0.51
#> pred[19: Self-help] -1.40 0.42 -2.23 -1.67 -1.41 -1.13 -0.58
#> Bulk_ESS Tail_ESS Rhat
#> pred[19: No intervention] 8801 2983 1
#> pred[19: Group counselling] 2301 2514 1
#> pred[19: Individual counselling] 1406 2127 1
#> pred[19: Self-help] 2012 2554 1
#>
#> --------------------------------------------------------------------- Study: 20 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[20: No intervention] -2.80 0.12 -3.05 -2.88 -2.80 -2.72 -2.57
#> pred[20: Group counselling] -1.69 0.45 -2.54 -1.99 -1.71 -1.40 -0.78
#> pred[20: Individual counselling] -1.95 0.26 -2.46 -2.13 -1.96 -1.78 -1.40
#> pred[20: Self-help] -2.30 0.42 -3.14 -2.58 -2.30 -2.02 -1.50
#> Bulk_ESS Tail_ESS Rhat
#> pred[20: No intervention] 7216 3235 1
#> pred[20: Group counselling] 2271 2444 1
#> pred[20: Individual counselling] 1417 2249 1
#> pred[20: Self-help] 1961 2522 1
#>
#> --------------------------------------------------------------------- Study: 21 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[21: No intervention] -1.11 0.80 -2.69 -1.62 -1.10 -0.60 0.47
#> pred[21: Group counselling] 0.00 0.86 -1.67 -0.55 0.00 0.54 1.68
#> pred[21: Individual counselling] -0.26 0.79 -1.81 -0.78 -0.27 0.23 1.30
#> pred[21: Self-help] -0.61 0.80 -2.15 -1.13 -0.61 -0.10 0.97
#> Bulk_ESS Tail_ESS Rhat
#> pred[21: No intervention] 3000 2832 1
#> pred[21: Group counselling] 3273 2809 1
#> pred[21: Individual counselling] 3348 3010 1
#> pred[21: Self-help] 3816 3013 1
#>
#> --------------------------------------------------------------------- Study: 22 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[22: No intervention] -2.41 0.85 -4.09 -2.96 -2.39 -1.86 -0.80
#> pred[22: Group counselling] -1.30 0.80 -2.87 -1.82 -1.29 -0.78 0.26
#> pred[22: Individual counselling] -1.56 0.84 -3.22 -2.09 -1.55 -1.02 0.07
#> pred[22: Self-help] -1.91 0.83 -3.55 -2.47 -1.89 -1.36 -0.33
#> Bulk_ESS Tail_ESS Rhat
#> pred[22: No intervention] 2838 2694 1
#> pred[22: Group counselling] 3471 3018 1
#> pred[22: Individual counselling] 3073 2748 1
#> pred[22: Self-help] 3569 2597 1
#>
#> --------------------------------------------------------------------- Study: 23 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[23: No intervention] -2.32 0.80 -3.87 -2.85 -2.31 -1.79 -0.74
#> pred[23: Group counselling] -1.21 0.78 -2.71 -1.72 -1.21 -0.72 0.38
#> pred[23: Individual counselling] -1.47 0.77 -2.97 -1.97 -1.47 -0.96 0.04
#> pred[23: Self-help] -1.82 0.84 -3.47 -2.38 -1.82 -1.27 -0.14
#> Bulk_ESS Tail_ESS Rhat
#> pred[23: No intervention] 3095 2901 1
#> pred[23: Group counselling] 3906 2858 1
#> pred[23: Individual counselling] 3850 2854 1
#> pred[23: Self-help] 3508 2639 1
#>
#> --------------------------------------------------------------------- Study: 24 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5%
#> pred[24: No intervention] -2.82 0.84 -4.55 -3.36 -2.81 -2.29 -1.14
#> pred[24: Group counselling] -1.72 0.83 -3.36 -2.26 -1.72 -1.16 -0.09
#> pred[24: Individual counselling] -1.97 0.81 -3.57 -2.49 -1.97 -1.44 -0.36
#> pred[24: Self-help] -2.32 0.88 -4.08 -2.90 -2.33 -1.74 -0.59
#> Bulk_ESS Tail_ESS Rhat
#> pred[24: No intervention] 3352 2569 1
#> pred[24: Group counselling] 4027 2956 1
#> pred[24: Individual counselling] 3922 3219 1
#> pred[24: Self-help] 3522 2926 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 5721
#> pred[1: Group counselling] 0.17 0.07 0.06 0.12 0.16 0.21 0.34 2749
#> pred[1: Individual counselling] 0.13 0.04 0.06 0.10 0.13 0.16 0.24 2577
#> pred[1: Self-help] 0.10 0.05 0.04 0.07 0.09 0.12 0.21 2743
#> Tail_ESS Rhat
#> pred[1: No intervention] 3121 1
#> pred[1: Group counselling] 2677 1
#> pred[1: Individual counselling] 2884 1
#> pred[1: Self-help] 2773 1
#>
#> ---------------------------------------------------------------------- Study: 2 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[2: No intervention] 0.09 0.06 0.01 0.04 0.07 0.11 0.25 2739
#> pred[2: Group counselling] 0.21 0.12 0.05 0.12 0.19 0.27 0.51 3287
#> pred[2: Individual counselling] 0.17 0.10 0.04 0.10 0.15 0.22 0.44 3076
#> pred[2: Self-help] 0.13 0.09 0.03 0.07 0.11 0.17 0.36 3811
#> Tail_ESS Rhat
#> pred[2: No intervention] 2354 1
#> pred[2: Group counselling] 2592 1
#> pred[2: Individual counselling] 2524 1
#> pred[2: Self-help] 2812 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 7281
#> pred[3: Group counselling] 0.27 0.09 0.13 0.21 0.26 0.32 0.47 2442
#> pred[3: Individual counselling] 0.22 0.04 0.14 0.19 0.22 0.24 0.32 1490
#> pred[3: Self-help] 0.17 0.06 0.08 0.13 0.16 0.20 0.30 2045
#> Tail_ESS Rhat
#> pred[3: No intervention] 3087 1
#> pred[3: Group counselling] 2702 1
#> pred[3: Individual counselling] 2630 1
#> pred[3: Self-help] 2636 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 4649
#> pred[4: Group counselling] 0.06 0.04 0.01 0.03 0.05 0.08 0.16 4284
#> pred[4: Individual counselling] 0.04 0.02 0.01 0.03 0.04 0.06 0.11 4909
#> pred[4: Self-help] 0.03 0.02 0.01 0.02 0.03 0.04 0.09 3718
#> Tail_ESS Rhat
#> pred[4: No intervention] 2750 1
#> pred[4: Group counselling] 3136 1
#> pred[4: Individual counselling] 3179 1
#> pred[4: Self-help] 3062 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 6408
#> pred[5: Group counselling] 0.27 0.09 0.13 0.21 0.26 0.32 0.46 2379
#> pred[5: Individual counselling] 0.22 0.05 0.14 0.18 0.21 0.25 0.32 1431
#> pred[5: Self-help] 0.17 0.06 0.08 0.13 0.16 0.20 0.30 2006
#> Tail_ESS Rhat
#> pred[5: No intervention] 2986 1
#> pred[5: Group counselling] 2672 1
#> pred[5: Individual counselling] 2558 1
#> pred[5: Self-help] 2566 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 3052
#> pred[6: Group counselling] 0.11 0.07 0.02 0.06 0.09 0.15 0.28 3643
#> pred[6: Individual counselling] 0.08 0.05 0.02 0.05 0.07 0.11 0.21 3270
#> pred[6: Self-help] 0.06 0.04 0.01 0.03 0.05 0.09 0.18 3136
#> Tail_ESS Rhat
#> pred[6: No intervention] 2287 1
#> pred[6: Group counselling] 2614 1
#> pred[6: Individual counselling] 2354 1
#> pred[6: Self-help] 2632 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 4486
#> pred[7: Group counselling] 0.14 0.07 0.04 0.09 0.13 0.18 0.31 3504
#> pred[7: Individual counselling] 0.11 0.04 0.04 0.08 0.11 0.14 0.21 3496
#> pred[7: Self-help] 0.08 0.04 0.02 0.05 0.08 0.11 0.19 3301
#> Tail_ESS Rhat
#> pred[7: No intervention] 2888 1
#> pred[7: Group counselling] 2610 1
#> pred[7: Individual counselling] 2560 1
#> pred[7: Self-help] 2516 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 0.06 0.09 0.16 4104
#> pred[8: Group counselling] 0.19 0.10 0.04 0.11 0.17 0.24 0.42 4601
#> pred[8: Individual counselling] 0.15 0.07 0.04 0.09 0.14 0.19 0.32 4107
#> pred[8: Self-help] 0.11 0.07 0.02 0.06 0.10 0.15 0.28 3857
#> Tail_ESS Rhat
#> pred[8: No intervention] 2933 1
#> pred[8: Group counselling] 2860 1
#> pred[8: Individual counselling] 2633 1
#> pred[8: Self-help] 2827 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 5637
#> pred[9: Group counselling] 0.34 0.13 0.12 0.24 0.32 0.41 0.61 3310
#> pred[9: Individual counselling] 0.28 0.09 0.13 0.21 0.27 0.34 0.48 3531
#> pred[9: Self-help] 0.22 0.10 0.08 0.15 0.21 0.28 0.44 3260
#> Tail_ESS Rhat
#> pred[9: No intervention] 2874 1
#> pred[9: Group counselling] 2857 1
#> pred[9: Individual counselling] 2899 1
#> pred[9: Self-help] 2722 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 0.14 7633
#> pred[10: Group counselling] 0.28 0.09 0.14 0.22 0.27 0.33 0.48 2401
#> pred[10: Individual counselling] 0.23 0.05 0.15 0.20 0.23 0.26 0.33 1523
#> pred[10: Self-help] 0.18 0.06 0.08 0.14 0.17 0.21 0.31 2049
#> Tail_ESS Rhat
#> pred[10: No intervention] 3017 1
#> pred[10: Group counselling] 2716 1
#> pred[10: Individual counselling] 2494 1
#> pred[10: Self-help] 2573 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 6723
#> pred[11: Group counselling] 0.08 0.04 0.03 0.06 0.07 0.10 0.17 2569
#> pred[11: Individual counselling] 0.06 0.02 0.03 0.05 0.06 0.07 0.11 2086
#> pred[11: Self-help] 0.05 0.02 0.02 0.03 0.04 0.06 0.09 2082
#> Tail_ESS Rhat
#> pred[11: No intervention] 2840 1
#> pred[11: Group counselling] 3080 1
#> pred[11: Individual counselling] 2936 1
#> pred[11: Self-help] 2650 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 7081
#> pred[12: Group counselling] 0.26 0.08 0.12 0.20 0.24 0.31 0.45 2369
#> pred[12: Individual counselling] 0.21 0.04 0.13 0.18 0.20 0.23 0.30 1398
#> pred[12: Self-help] 0.16 0.06 0.07 0.12 0.15 0.19 0.29 2040
#> Tail_ESS Rhat
#> pred[12: No intervention] 3186 1
#> pred[12: Group counselling] 2614 1
#> pred[12: Individual counselling] 2413 1
#> pred[12: Self-help] 2510 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 0.06 0.08 0.13 4599
#> pred[13: Group counselling] 0.19 0.09 0.06 0.12 0.17 0.24 0.40 3220
#> pred[13: Individual counselling] 0.15 0.06 0.06 0.10 0.14 0.18 0.29 3122
#> pred[13: Self-help] 0.11 0.06 0.03 0.07 0.10 0.14 0.26 2870
#> Tail_ESS Rhat
#> pred[13: No intervention] 2805 1
#> pred[13: Group counselling] 3058 1
#> pred[13: Individual counselling] 2644 1
#> pred[13: Self-help] 3021 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 4830
#> pred[14: Group counselling] 0.22 0.08 0.10 0.16 0.21 0.27 0.42 2729
#> pred[14: Individual counselling] 0.18 0.05 0.10 0.14 0.17 0.20 0.29 2042
#> pred[14: Self-help] 0.14 0.05 0.06 0.10 0.13 0.17 0.27 2349
#> Tail_ESS Rhat
#> pred[14: No intervention] 2956 1
#> pred[14: Group counselling] 2728 1
#> pred[14: Individual counselling] 2834 1
#> pred[14: Self-help] 2967 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 0.19 3275
#> pred[15: Group counselling] 0.19 0.10 0.04 0.12 0.18 0.25 0.43 4021
#> pred[15: Individual counselling] 0.16 0.09 0.03 0.09 0.14 0.21 0.36 3536
#> pred[15: Self-help] 0.12 0.08 0.02 0.06 0.10 0.16 0.31 3217
#> Tail_ESS Rhat
#> pred[15: No intervention] 2521 1
#> pred[15: Group counselling] 2667 1
#> pred[15: Individual counselling] 2343 1
#> pred[15: Self-help] 2426 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 5542
#> pred[16: Group counselling] 0.19 0.08 0.07 0.13 0.18 0.24 0.39 3204
#> pred[16: Individual counselling] 0.15 0.05 0.07 0.12 0.15 0.19 0.27 2537
#> pred[16: Self-help] 0.12 0.05 0.04 0.08 0.11 0.14 0.23 2637
#> Tail_ESS Rhat
#> pred[16: No intervention] 2995 1
#> pred[16: Group counselling] 3154 1
#> pred[16: Individual counselling] 2777 1
#> pred[16: Self-help] 3039 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 7637
#> pred[17: Group counselling] 0.23 0.08 0.11 0.17 0.22 0.27 0.40 2289
#> pred[17: Individual counselling] 0.18 0.04 0.12 0.16 0.18 0.20 0.27 1272
#> pred[17: Self-help] 0.14 0.05 0.06 0.11 0.13 0.17 0.25 1964
#> Tail_ESS Rhat
#> pred[17: No intervention] 2637 1
#> pred[17: Group counselling] 2719 1
#> pred[17: Individual counselling] 2140 1
#> pred[17: Self-help] 2331 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 5825
#> pred[18: Group counselling] 0.20 0.08 0.08 0.14 0.19 0.24 0.39 2591
#> pred[18: Individual counselling] 0.16 0.05 0.08 0.12 0.15 0.19 0.26 2069
#> pred[18: Self-help] 0.12 0.05 0.05 0.09 0.11 0.15 0.24 2356
#> Tail_ESS Rhat
#> pred[18: No intervention] 2592 1
#> pred[18: Group counselling] 2595 1
#> pred[18: Individual counselling] 2669 1
#> pred[18: Self-help] 3009 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 8801
#> pred[19: Group counselling] 0.32 0.09 0.16 0.25 0.31 0.38 0.53 2301
#> pred[19: Individual counselling] 0.26 0.05 0.17 0.23 0.26 0.29 0.37 1406
#> pred[19: Self-help] 0.21 0.07 0.10 0.16 0.20 0.24 0.36 2012
#> Tail_ESS Rhat
#> pred[19: No intervention] 2983 1
#> pred[19: Group counselling] 2514 1
#> pred[19: Individual counselling] 2127 1
#> pred[19: Self-help] 2554 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 7216
#> pred[20: Group counselling] 0.16 0.06 0.07 0.12 0.15 0.20 0.31 2271
#> pred[20: Individual counselling] 0.13 0.03 0.08 0.11 0.12 0.14 0.20 1417
#> pred[20: Self-help] 0.10 0.04 0.04 0.07 0.09 0.12 0.18 1961
#> Tail_ESS Rhat
#> pred[20: No intervention] 3235 1
#> pred[20: Group counselling] 2444 1
#> pred[20: Individual counselling] 2249 1
#> pred[20: Self-help] 2522 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 0.62 3000
#> pred[21: Group counselling] 0.50 0.18 0.16 0.37 0.50 0.63 0.84 3273
#> pred[21: Individual counselling] 0.44 0.17 0.14 0.31 0.43 0.56 0.79 3348
#> pred[21: Self-help] 0.37 0.16 0.10 0.24 0.35 0.48 0.73 3816
#> Tail_ESS Rhat
#> pred[21: No intervention] 2832 1
#> pred[21: Group counselling] 2809 1
#> pred[21: Individual counselling] 3010 1
#> pred[21: Self-help] 3013 1
#>
#> --------------------------------------------------------------------- Study: 22 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[22: No intervention] 0.10 0.08 0.02 0.05 0.08 0.13 0.31 2838
#> pred[22: Group counselling] 0.24 0.13 0.05 0.14 0.22 0.31 0.56 3471
#> pred[22: Individual counselling] 0.20 0.13 0.04 0.11 0.18 0.27 0.52 3073
#> pred[22: Self-help] 0.16 0.11 0.03 0.08 0.13 0.20 0.42 3569
#> Tail_ESS Rhat
#> pred[22: No intervention] 2694 1
#> pred[22: Group counselling] 3018 1
#> pred[22: Individual counselling] 2748 1
#> pred[22: Self-help] 2597 1
#>
#> --------------------------------------------------------------------- Study: 23 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[23: No intervention] 0.11 0.08 0.02 0.05 0.09 0.14 0.32 3095
#> pred[23: Group counselling] 0.25 0.14 0.06 0.15 0.23 0.33 0.59 3906
#> pred[23: Individual counselling] 0.21 0.12 0.05 0.12 0.19 0.28 0.51 3850
#> pred[23: Self-help] 0.17 0.11 0.03 0.08 0.14 0.22 0.47 3508
#> Tail_ESS Rhat
#> pred[23: No intervention] 2901 1
#> pred[23: Group counselling] 2858 1
#> pred[23: Individual counselling] 2854 1
#> pred[23: Self-help] 2639 1
#>
#> --------------------------------------------------------------------- Study: 24 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[24: No intervention] 0.07 0.06 0.01 0.03 0.06 0.09 0.24 3352
#> pred[24: Group counselling] 0.18 0.12 0.03 0.09 0.15 0.24 0.48 4027
#> pred[24: Individual counselling] 0.15 0.10 0.03 0.08 0.12 0.19 0.41 3922
#> pred[24: Self-help] 0.11 0.09 0.02 0.05 0.09 0.15 0.36 3522
#> Tail_ESS Rhat
#> pred[24: No intervention] 2569 1
#> pred[24: Group counselling] 2956 1
#> pred[24: Individual counselling] 3219 1
#> pred[24: Self-help] 2926 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 4317
#> pred[Group counselling] 0.30 0.09 0.15 0.23 0.29 0.35 0.50 2359
#> pred[Individual counselling] 0.24 0.05 0.16 0.21 0.24 0.27 0.35 1480
#> pred[Self-help] 0.19 0.06 0.09 0.14 0.18 0.22 0.34 1976
#> Tail_ESS Rhat
#> pred[No intervention] 3618 1
#> pred[Group counselling] 2649 1
#> pred[Individual counselling] 2547 1
#> pred[Self-help] 2673 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 0.09 0.11 0.12 0.13 0.15 3656
#> pred[Group counselling] 0.30 0.09 0.15 0.23 0.29 0.35 0.50 2453
#> pred[Individual counselling] 0.24 0.05 0.16 0.21 0.24 0.27 0.36 1486
#> pred[Self-help] 0.19 0.06 0.09 0.15 0.18 0.23 0.33 2118
#> Tail_ESS Rhat
#> pred[No intervention] 3884 1
#> pred[Group counselling] 2696 1
#> pred[Individual counselling] 2774 1
#> pred[Self-help] 2849 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 4067 3180
#> pred[FIXTURE: ETN] 0.46 0.03 0.41 0.44 0.46 0.47 0.51 8302 3512
#> pred[FIXTURE: IXE_Q2W] 0.89 0.02 0.85 0.88 0.89 0.90 0.92 6488 2927
#> pred[FIXTURE: IXE_Q4W] 0.80 0.03 0.74 0.78 0.80 0.81 0.84 7785 3251
#> pred[FIXTURE: SEC_150] 0.67 0.02 0.62 0.65 0.67 0.69 0.72 10529 3146
#> pred[FIXTURE: SEC_300] 0.77 0.02 0.72 0.75 0.77 0.79 0.81 9368 3032
#> 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 0.08 6635 3388
#> pred[UNCOVER-1: ETN] 0.46 0.03 0.41 0.44 0.46 0.48 0.52 8773 3460
#> pred[UNCOVER-1: IXE_Q2W] 0.90 0.01 0.88 0.89 0.90 0.91 0.92 8810 2988
#> pred[UNCOVER-1: IXE_Q4W] 0.81 0.02 0.78 0.80 0.81 0.82 0.84 10746 2905
#> pred[UNCOVER-1: SEC_150] 0.69 0.04 0.60 0.66 0.69 0.72 0.77 7423 3019
#> pred[UNCOVER-1: SEC_300] 0.78 0.04 0.71 0.76 0.79 0.81 0.85 7994 3321
#> 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 6361 3619
#> pred[UNCOVER-2: ETN] 0.42 0.02 0.38 0.41 0.42 0.43 0.46 10733 2751
#> pred[UNCOVER-2: IXE_Q2W] 0.88 0.01 0.86 0.87 0.88 0.89 0.91 7787 3283
#> pred[UNCOVER-2: IXE_Q4W] 0.78 0.02 0.75 0.77 0.78 0.79 0.81 10686 3031
#> pred[UNCOVER-2: SEC_150] 0.65 0.04 0.57 0.62 0.65 0.68 0.73 8799 3405
#> pred[UNCOVER-2: SEC_300] 0.75 0.04 0.68 0.73 0.75 0.78 0.82 9426 3210
#> 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 5773 3231
#> pred[UNCOVER-3: ETN] 0.53 0.02 0.49 0.51 0.53 0.54 0.57 10008 3343
#> pred[UNCOVER-3: IXE_Q2W] 0.93 0.01 0.91 0.92 0.93 0.93 0.94 7523 3471
#> pred[UNCOVER-3: IXE_Q4W] 0.85 0.01 0.83 0.85 0.85 0.86 0.88 9695 2538
#> pred[UNCOVER-3: SEC_150] 0.75 0.04 0.67 0.72 0.75 0.77 0.81 8261 3356
#> pred[UNCOVER-3: SEC_300] 0.83 0.03 0.77 0.81 0.83 0.85 0.88 8633 3200
#> Rhat
#> pred[UNCOVER-3: PBO] 1.00
#> pred[UNCOVER-3: ETN] 1.00
#> pred[UNCOVER-3: IXE_Q2W] 1.00
#> pred[UNCOVER-3: IXE_Q4W] 1.00
#> pred[UNCOVER-3: SEC_150] 1.00
#> pred[UNCOVER-3: SEC_300] 1.01
#>
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 0.07 0.12 7201 3599 1
#> pred[New 1: ETN] 0.37 0.06 0.26 0.33 0.37 0.41 0.49 6249 3799 1
#> pred[New 1: IXE_Q2W] 0.90 0.02 0.84 0.88 0.90 0.92 0.94 5801 3724 1
#> pred[New 1: IXE_Q4W] 0.81 0.04 0.73 0.78 0.81 0.83 0.87 5712 3396 1
#> pred[New 1: SEC_150] 0.68 0.05 0.57 0.64 0.68 0.72 0.78 5153 3656 1
#> pred[New 1: SEC_300] 0.78 0.05 0.68 0.75 0.78 0.81 0.86 5390 3590 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 0.21 0.23 5320
#> pred[Attal2012: Len, 1] 5 0.38 0.02 0.33 0.36 0.38 0.40 0.43 4522
#> pred[Attal2012: Thal, 1] 5 0.23 0.04 0.16 0.20 0.23 0.25 0.30 5621
#> Tail_ESS Rhat
#> pred[Attal2012: Pbo, 1] 3308 1
#> pred[Attal2012: Len, 1] 2989 1
#> pred[Attal2012: Thal, 1] 3517 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 4767
#> pred[Jackson2019: Len, 1] 5 0.45 0.01 0.42 0.44 0.45 0.45 0.47 5015
#> pred[Jackson2019: Thal, 1] 5 0.29 0.03 0.22 0.27 0.29 0.31 0.36 5896
#> Tail_ESS Rhat
#> pred[Jackson2019: Pbo, 1] 3559 1
#> pred[Jackson2019: Len, 1] 3552 1
#> pred[Jackson2019: Thal, 1] 3491 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 5109
#> pred[McCarthy2012: Len, 1] 5 0.46 0.02 0.41 0.45 0.46 0.48 0.50 5060
#> pred[McCarthy2012: Thal, 1] 5 0.31 0.04 0.23 0.28 0.31 0.33 0.38 5912
#> Tail_ESS Rhat
#> pred[McCarthy2012: Pbo, 1] 3589 1
#> pred[McCarthy2012: Len, 1] 3226 1
#> pred[McCarthy2012: Thal, 1] 3614 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 5683
#> pred[Morgan2012: Len, 1] 5 0.43 0.03 0.38 0.41 0.43 0.45 0.49 6100
#> pred[Morgan2012: Thal, 1] 5 0.28 0.02 0.24 0.26 0.28 0.29 0.32 4862
#> Tail_ESS Rhat
#> pred[Morgan2012: Pbo, 1] 3419 1
#> pred[Morgan2012: Len, 1] 3585 1
#> pred[Morgan2012: Thal, 1] 3105 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 0.17 0.20 0.22 0.26 5105
#> pred[Palumbo2014: Len, 1] 5 0.38 0.04 0.32 0.36 0.38 0.41 0.46 5240
#> pred[Palumbo2014: Thal, 1] 5 0.23 0.04 0.15 0.20 0.23 0.26 0.32 5521
#> Tail_ESS Rhat
#> pred[Palumbo2014: Pbo, 1] 3071 1
#> pred[Palumbo2014: Len, 1] 2971 1
#> pred[Palumbo2014: Thal, 1] 3649 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 0.93 1.02 1.07 1.11 1.21 5138
#> pred[Attal2012: Pbo, 0.5] 2.56 0.12 2.34 2.48 2.55 2.64 2.79 5225
#> pred[Attal2012: Pbo, 0.8] 4.90 0.25 4.46 4.73 4.89 5.06 5.42 5251
#> pred[Attal2012: Len, 0.2] 1.61 0.09 1.44 1.55 1.61 1.67 1.79 4869
#> pred[Attal2012: Len, 0.5] 3.87 0.19 3.54 3.74 3.86 3.99 4.27 4403
#> pred[Attal2012: Len, 0.8] 7.42 0.47 6.60 7.08 7.39 7.73 8.46 4663
#> pred[Attal2012: Thal, 0.2] 1.17 0.11 0.97 1.10 1.16 1.24 1.38 5513
#> pred[Attal2012: Thal, 0.5] 2.80 0.22 2.39 2.64 2.79 2.94 3.25 5761
#> pred[Attal2012: Thal, 0.8] 5.36 0.45 4.54 5.05 5.35 5.64 6.29 5616
#> Tail_ESS Rhat
#> pred[Attal2012: Pbo, 0.2] 3208 1
#> pred[Attal2012: Pbo, 0.5] 3045 1
#> pred[Attal2012: Pbo, 0.8] 3265 1
#> pred[Attal2012: Len, 0.2] 3683 1
#> pred[Attal2012: Len, 0.5] 2876 1
#> pred[Attal2012: Len, 0.8] 3386 1
#> pred[Attal2012: Thal, 0.2] 2858 1
#> pred[Attal2012: Thal, 0.5] 3573 1
#> pred[Attal2012: Thal, 0.8] 3511 1
#>
#> ------------------------------------------------------------ Study: Jackson2019 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Jackson2019: Pbo, 0.2] 0.71 0.04 0.64 0.68 0.71 0.74 0.79 5405
#> pred[Jackson2019: Pbo, 0.5] 2.39 0.10 2.20 2.32 2.39 2.45 2.59 5137
#> pred[Jackson2019: Pbo, 0.8] 5.89 0.25 5.42 5.72 5.89 6.06 6.40 4738
#> pred[Jackson2019: Len, 0.2] 1.26 0.06 1.15 1.22 1.26 1.30 1.38 5761
#> pred[Jackson2019: Len, 0.5] 4.24 0.16 3.94 4.13 4.24 4.35 4.57 5098
#> pred[Jackson2019: Len, 0.8] 10.47 0.46 9.62 10.15 10.45 10.76 11.42 4524
#> pred[Jackson2019: Thal, 0.2] 0.80 0.09 0.64 0.75 0.80 0.86 0.98 5915
#> pred[Jackson2019: Thal, 0.5] 2.71 0.27 2.19 2.53 2.70 2.88 3.27 5845
#> pred[Jackson2019: Thal, 0.8] 6.68 0.68 5.41 6.21 6.65 7.10 8.11 5908
#> Tail_ESS Rhat
#> pred[Jackson2019: Pbo, 0.2] 3221 1
#> pred[Jackson2019: Pbo, 0.5] 3292 1
#> pred[Jackson2019: Pbo, 0.8] 3583 1
#> pred[Jackson2019: Len, 0.2] 3482 1
#> pred[Jackson2019: Len, 0.5] 3381 1
#> pred[Jackson2019: Len, 0.8] 3651 1
#> pred[Jackson2019: Thal, 0.2] 3425 1
#> pred[Jackson2019: Thal, 0.5] 3613 1
#> pred[Jackson2019: Thal, 0.8] 3428 1
#>
#> ----------------------------------------------------------- Study: McCarthy2012 ----
#>
#> mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[McCarthy2012: Pbo, 0.2] 1.26 0.10 1.08 1.19 1.26 1.33 1.46 4687
#> pred[McCarthy2012: Pbo, 0.5] 3.03 0.15 2.75 2.93 3.03 3.13 3.34 4960
#> pred[McCarthy2012: Pbo, 0.8] 5.82 0.30 5.28 5.62 5.81 6.02 6.46 5096
#> pred[McCarthy2012: Len, 0.2] 1.91 0.12 1.68 1.83 1.91 1.99 2.15 4963
#> pred[McCarthy2012: Len, 0.5] 4.59 0.23 4.17 4.44 4.59 4.74 5.05 5055
#> pred[McCarthy2012: Len, 0.8] 8.83 0.56 7.84 8.44 8.80 9.19 10.00 4903
#> pred[McCarthy2012: Thal, 0.2] 1.38 0.14 1.12 1.29 1.38 1.47 1.66 5118
#> pred[McCarthy2012: Thal, 0.5] 3.32 0.28 2.79 3.13 3.31 3.50 3.87 5709
#> pred[McCarthy2012: Thal, 0.8] 6.37 0.55 5.36 5.99 6.35 6.71 7.53 5921
#> Tail_ESS Rhat
#> pred[McCarthy2012: Pbo, 0.2] 3097 1
#> pred[McCarthy2012: Pbo, 0.5] 3351 1
#> pred[McCarthy2012: Pbo, 0.8] 3719 1
#> pred[McCarthy2012: Len, 0.2] 3470 1
#> pred[McCarthy2012: Len, 0.5] 3253 1
#> pred[McCarthy2012: Len, 0.8] 3153 1
#> pred[McCarthy2012: Thal, 0.2] 2550 1
#> pred[McCarthy2012: Thal, 0.5] 3124 1
#> pred[McCarthy2012: Thal, 0.8] 3667 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 4711
#> pred[Morgan2012: Pbo, 0.5] 2.20 0.16 1.91 2.09 2.19 2.30 2.52 5149
#> pred[Morgan2012: Pbo, 0.8] 5.72 0.43 4.94 5.43 5.70 5.99 6.62 5771
#> pred[Morgan2012: Len, 0.2] 1.12 0.10 0.93 1.05 1.11 1.18 1.34 5213
#> pred[Morgan2012: Len, 0.5] 4.05 0.36 3.41 3.80 4.03 4.27 4.79 5968
#> pred[Morgan2012: Len, 0.8] 10.56 1.04 8.72 9.82 10.48 11.20 12.82 6369
#> pred[Morgan2012: Thal, 0.2] 0.69 0.06 0.58 0.65 0.69 0.73 0.82 5602
#> pred[Morgan2012: Thal, 0.5] 2.50 0.18 2.17 2.37 2.49 2.61 2.86 5126
#> pred[Morgan2012: Thal, 0.8] 6.51 0.49 5.63 6.16 6.47 6.82 7.55 4763
#> Tail_ESS Rhat
#> pred[Morgan2012: Pbo, 0.2] 2815 1
#> pred[Morgan2012: Pbo, 0.5] 3094 1
#> pred[Morgan2012: Pbo, 0.8] 3405 1
#> pred[Morgan2012: Len, 0.2] 3146 1
#> pred[Morgan2012: Len, 0.5] 3650 1
#> pred[Morgan2012: Len, 0.8] 3681 1
#> pred[Morgan2012: Thal, 0.2] 3458 1
#> pred[Morgan2012: Thal, 0.5] 3216 1
#> pred[Morgan2012: Thal, 0.8] 2732 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 0.76 0.89 5406
#> pred[Palumbo2014: Pbo, 0.5] 2.16 0.19 1.81 2.02 2.15 2.28 2.54 5433
#> pred[Palumbo2014: Pbo, 0.8] 4.97 0.48 4.15 4.63 4.93 5.27 6.02 5008
#> pred[Palumbo2014: Len, 0.2] 1.20 0.13 0.95 1.11 1.19 1.28 1.46 5244
#> pred[Palumbo2014: Len, 0.5] 3.67 0.33 3.09 3.43 3.65 3.87 4.39 5309
#> pred[Palumbo2014: Len, 0.8] 8.47 1.01 6.79 7.77 8.36 9.07 10.72 5027
#> pred[Palumbo2014: Thal, 0.2] 0.79 0.12 0.58 0.71 0.79 0.87 1.04 5420
#> pred[Palumbo2014: Thal, 0.5] 2.42 0.30 1.89 2.21 2.41 2.60 3.08 5258
#> pred[Palumbo2014: Thal, 0.8] 5.58 0.75 4.33 5.05 5.51 6.02 7.22 5384
#> Tail_ESS Rhat
#> pred[Palumbo2014: Pbo, 0.2] 3186 1
#> pred[Palumbo2014: Pbo, 0.5] 3569 1
#> pred[Palumbo2014: Pbo, 0.8] 2983 1
#> pred[Palumbo2014: Len, 0.2] 3189 1
#> pred[Palumbo2014: Len, 0.5] 2939 1
#> pred[Palumbo2014: Len, 0.8] 3048 1
#> pred[Palumbo2014: Thal, 0.2] 2730 1
#> pred[Palumbo2014: Thal, 0.5] 3117 1
#> pred[Palumbo2014: Thal, 0.8] 3758 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 3.04 3.13 3.24 3.45 5227 3449
#> pred[Attal2012: Len] 4.75 0.28 4.27 4.55 4.73 4.93 5.36 4586 3126
#> pred[Attal2012: Thal] 3.43 0.28 2.92 3.24 3.42 3.61 4.01 5809 3681
#> 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 3.55 3.65 3.76 3.97 4740 3625
#> pred[Jackson2019: Len] 6.49 0.29 5.97 6.29 6.48 6.67 7.08 4520 3686
#> pred[Jackson2019: Thal] 4.14 0.42 3.35 3.85 4.12 4.40 5.03 5909 3428
#> 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 0.18 3.40 3.60 3.72 3.85 4.11 5097 3220
#> pred[McCarthy2012: Len] 5.65 0.33 5.06 5.42 5.63 5.87 6.34 4969 3141
#> pred[McCarthy2012: Thal] 4.08 0.34 3.44 3.84 4.06 4.29 4.80 5917 3550
#> 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] 3.55 0.27 3.06 3.37 3.54 3.72 4.12 5782 3532
#> pred[Morgan2012: Len] 6.55 0.65 5.41 6.09 6.50 6.95 7.97 6371 3644
#> pred[Morgan2012: Thal] 4.04 0.31 3.49 3.82 4.02 4.24 4.69 4736 2733
#> 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 2.59 2.89 3.07 3.27 3.74 4922 2984
#> pred[Palumbo2014: Len] 5.27 0.62 4.27 4.84 5.20 5.64 6.65 4996 2977
#> pred[Palumbo2014: Thal] 3.47 0.46 2.70 3.15 3.43 3.74 4.48 5355 3685
#> 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 5184
#> pred[Attal2012: Len] 4.01 2.99 0.05 2.89 2.96 2.99 3.03 3.09 4614
#> pred[Attal2012: Thal] 4.01 2.61 0.10 2.40 2.54 2.61 2.67 2.80 5710
#> Tail_ESS Rhat
#> pred[Attal2012: Pbo] 3096 1
#> pred[Attal2012: Len] 3665 1
#> pred[Attal2012: Thal] 3182 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 2.45 5189
#> pred[Jackson2019: Len] 4.01 2.91 0.03 2.84 2.88 2.91 2.93 2.97 5538
#> pred[Jackson2019: Thal] 4.01 2.48 0.10 2.27 2.42 2.49 2.55 2.68 5824
#> Tail_ESS Rhat
#> pred[Jackson2019: Pbo] 3264 1
#> pred[Jackson2019: Len] 3579 1
#> pred[Jackson2019: Thal] 3579 1
#>
#> ----------------------------------------------------------- Study: McCarthy2012 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[McCarthy2012: Pbo] 4.01 2.71 0.07 2.58 2.66 2.71 2.76 2.84 4801
#> pred[McCarthy2012: Len] 4.01 3.16 0.05 3.05 3.12 3.16 3.19 3.26 5050
#> pred[McCarthy2012: Thal] 4.01 2.81 0.10 2.60 2.75 2.82 2.88 3.01 5482
#> Tail_ESS Rhat
#> pred[McCarthy2012: Pbo] 3329 1
#> pred[McCarthy2012: Len] 3680 1
#> pred[McCarthy2012: Thal] 3204 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 5090
#> pred[Morgan2012: Len] 4.01 2.83 0.07 2.69 2.79 2.83 2.88 2.97 5576
#> pred[Morgan2012: Thal] 4.01 2.39 0.07 2.25 2.34 2.39 2.44 2.53 5281
#> Tail_ESS Rhat
#> pred[Morgan2012: Pbo] 3049 1
#> pred[Morgan2012: Len] 3276 1
#> pred[Morgan2012: Thal] 3412 1
#>
#> ------------------------------------------------------------ Study: Palumbo2014 ----
#>
#> .time mean sd 2.5% 25% 50% 75% 97.5% Bulk_ESS
#> pred[Palumbo2014: Pbo] 4.01 2.25 0.10 2.05 2.18 2.25 2.32 2.45 5489
#> pred[Palumbo2014: Len] 4.01 2.81 0.08 2.64 2.76 2.81 2.87 2.97 5728
#> pred[Palumbo2014: Thal] 4.01 2.38 0.14 2.10 2.28 2.38 2.47 2.65 5480
#> Tail_ESS Rhat
#> pred[Palumbo2014: Pbo] 3523 1
#> pred[Palumbo2014: Len] 3319 1
#> pred[Palumbo2014: Thal] 3142 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 2.73 2.78 2.88 5220
#> pred[Attal2012: Len] 5 3.41 0.07 3.28 3.37 3.41 3.46 3.55 4492
#> pred[Attal2012: Thal] 5 2.88 0.14 2.61 2.79 2.88 2.97 3.14 5718
#> Tail_ESS Rhat
#> pred[Attal2012: Pbo] 3228 1
#> pred[Attal2012: Len] 3002 1
#> pred[Attal2012: Thal] 3506 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 5103
#> pred[Jackson2019: Len] 5 3.38 0.05 3.29 3.35 3.38 3.41 3.47 5430
#> pred[Jackson2019: Thal] 5 2.81 0.14 2.52 2.72 2.81 2.90 3.07 5842
#> Tail_ESS Rhat
#> pred[Jackson2019: Pbo] 3306 1
#> pred[Jackson2019: Len] 3560 1
#> pred[Jackson2019: Thal] 3540 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 4902
#> pred[McCarthy2012: Len] 5 3.66 0.07 3.52 3.61 3.66 3.70 3.80 5122
#> pred[McCarthy2012: Thal] 5 3.16 0.14 2.88 3.07 3.17 3.26 3.43 5622
#> Tail_ESS Rhat
#> pred[McCarthy2012: Pbo] 3440 1
#> pred[McCarthy2012: Len] 3581 1
#> pred[McCarthy2012: Thal] 3080 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 5197
#> pred[Morgan2012: Len] 5 3.29 0.10 3.10 3.23 3.29 3.36 3.48 5712
#> pred[Morgan2012: Thal] 5 2.70 0.09 2.52 2.64 2.70 2.76 2.88 5138
#> Tail_ESS Rhat
#> pred[Morgan2012: Pbo] 3094 1
#> pred[Morgan2012: Len] 3455 1
#> pred[Morgan2012: Thal] 3320 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 5513
#> pred[Palumbo2014: Len] 5 3.23 0.11 3.00 3.15 3.23 3.31 3.45 5674
#> pred[Palumbo2014: Thal] 5 2.64 0.18 2.29 2.52 2.65 2.76 3.00 5292
#> Tail_ESS Rhat
#> pred[Palumbo2014: Pbo] 3566 1
#> pred[Palumbo2014: Len] 3202 1
#> pred[Palumbo2014: Thal] 3181 1
#>
# }