STEM compatibility

Introduction

This vignette describes the use of the convSTEM function which enables backwards compatibility with STEM economic models which use an alternative formulation of parametric survival models. For most users this vignette can be safely ignored. The following packages are required to run this example:

library(flexsurvPlus)
library(tibble)
library(dplyr)
library(boot)

Read in the data

To perform survival analyses, patient level data is required for the survival endpoints.

This example uses a standard simulated data set (adtte). There is no standard naming that is needed for this package however, there are some set variables that are needed:

Time - a numeric variable
Event - a binary variable (event=1, censor=0)

In this example, we use only progression-free survival (PFS).



# simulate data with a medium correlation between PFS & OS on the patient level
adtte <- sim_adtte(seed = 2020, # for reproducibility
                   rho = 0.6 # defines a correlation on underlying survival times
                   ) 

# subset PFS data and rename
PFS_data <- adtte %>%
  filter(PARAMCD=="PFS") %>%
  transmute(USUBJID, ARMCD,
            AVAL,
            event = 1 - CNSR #needs to be coded as 1 for event
  )

Fitting models

This section uses runPSM as described in other vignettes to estimate survival models. As described in other vignettes flexsurvPlus primarily uses bootstrapping to handle uncertainty with the bootPSM function in conjunction with boot.


# For speed only 4 models are considered for this example but 
# all models could be considered

psm_PFS_expweib <- runPSM(data = PFS_data,
                          time_var = "AVAL",
                          event_var ="event",
                          model.type = c("Common shape", 
                                         "Separate"),
                     distr = c('exp',
                               'weibull'),
                     strata_var = "ARMCD",
                     int_name = "A",
                     ref_name = "B")


# Apply bootstrapping for illustration 100 samples are taken
# In practice a larger number maybe preferable.

psm_boot_PFS_expweib  <- do.call(boot, args = c(psm_PFS_expweib$config, statistic = bootPSM, R = 100))

Converting to a STEM format

This is done using convSTEM. Depending on if a runPSM object or a bootPSM object or both are provided different quantities will be estimated.


# only supplying x
PFS_conv_x <- convSTEM(x = psm_PFS_expweib)

# only supplying samples
PFS_conv_samples <-  convSTEM(samples = psm_boot_PFS_expweib)

# supplying both x and samples from the same set of models
PFS_conv_both <-  convSTEM(x = psm_PFS_expweib, samples = psm_boot_PFS_expweib)

The output of convSTEM

convSTEM returns a list of four data frames containing parameters converted to match those reported by an existing SAS macro.

stem_param The parameter estimates
stem_cov Estimates for a covariance matrix for the parameters derived from the bootstrap samples.
stem_modsum A summary of the model fit statistics.
stem_boot A data frame of converted boot strap estimates.

stem_param

stem_param contains the parameter estimates and is calculated if either x or samples is provided.


names(PFS_conv_x$stem_param)
#> [1] "Model"    "ModelF"   "Dist"     "DistF"    "Param"    "ParamF"   "Estimate"

PFS_conv_x$stem_param %>%
  transmute(Model, Dist, Param, Estimate) 
#>                      Model        Dist            Param   Estimate
#> 1             Common shape Exponential        INTERCEPT  6.1145985
#> 2             Common shape Exponential TX(Intervention) -0.7675910
#> 3             Common shape     Weibull        INTERCEPT  6.0800704
#> 4             Common shape     Weibull TX(Intervention) -0.6623183
#> 5             Common shape     Weibull            SCALE  0.7204249
#> 6     Separate - Reference Exponential        INTERCEPT  6.1145985
#> 7     Separate - Reference     Weibull        INTERCEPT  6.0798340
#> 8     Separate - Reference     Weibull            SCALE  0.7171585
#> 9  Separate - Intervention Exponential        INTERCEPT  5.3470075
#> 10 Separate - Intervention     Weibull        INTERCEPT  5.4170457
#> 11 Separate - Intervention     Weibull            SCALE  0.7224962

PFS_conv_samples$stem_param %>%
  transmute(Model, Dist, Param, Estimate) 
#>                      Model        Dist            Param   Estimate
#> 1             Common shape Exponential        INTERCEPT  6.1145985
#> 2             Common shape Exponential TX(Intervention) -0.7675910
#> 3             Common shape     Weibull        INTERCEPT  6.0800704
#> 4             Common shape     Weibull TX(Intervention) -0.6623183
#> 5             Common shape     Weibull            SCALE  0.7204249
#> 6     Separate - Reference Exponential        INTERCEPT  6.1145985
#> 7     Separate - Reference     Weibull        INTERCEPT  6.0798340
#> 8     Separate - Reference     Weibull            SCALE  0.7171585
#> 9  Separate - Intervention Exponential        INTERCEPT  5.3470075
#> 10 Separate - Intervention     Weibull        INTERCEPT  5.4170457
#> 11 Separate - Intervention     Weibull            SCALE  0.7224962

stem_cov

stem_cov contains estimates for a covariance matrix for the parameters and is only derived if samples is provided.


names(PFS_conv_x$stem_cov)
#>  [1] "Model"     "ModelF"    "Dist"      "DistF"     "rowParam"  "colParam" 
#>  [7] "rowParamF" "colParamF" "rowNum"    "colNum"    "CovEst"

# note is empty here as samples were not provided
nrow(PFS_conv_x$stem_cov)
#> [1] 0

PFS_conv_samples$stem_cov %>%
  transmute(Model, Dist, rowParam, colParam, rowNum, colNum, CovEst) 
#> # A tibble: 23 × 7
#>    Model        Dist        rowParam         colParam     rowNum colNum   CovEst
#>    <chr>        <chr>       <chr>            <chr>         <dbl>  <dbl>    <dbl>
#>  1 Common shape Exponential INTERCEPT        INTERCEPT         1      1  4.54e-3
#>  2 Common shape Exponential INTERCEPT        TX(Interven…      1      2 -4.86e-3
#>  3 Common shape Exponential TX(Intervention) INTERCEPT         2      1 -4.86e-3
#>  4 Common shape Exponential TX(Intervention) TX(Interven…      2      2  7.93e-3
#>  5 Common shape Weibull     INTERCEPT        INTERCEPT         1      1  2.98e-3
#>  6 Common shape Weibull     INTERCEPT        TX(Interven…      1      2 -3.18e-3
#>  7 Common shape Weibull     INTERCEPT        SCALE             1      3  8.86e-5
#>  8 Common shape Weibull     TX(Intervention) INTERCEPT         2      1 -3.18e-3
#>  9 Common shape Weibull     TX(Intervention) TX(Interven…      2      2  5.80e-3
#> 10 Common shape Weibull     TX(Intervention) SCALE             2      3 -7.51e-5
#> # ℹ 13 more rows

The matrix is described by row and column numbers so can be back converted to a matrix if desired.


# select a single model from the data frame
weibull_common_data <- PFS_conv_samples$stem_cov %>%
  filter(Model == "Common shape", Dist == "Weibull") %>%
  transmute(rowParam, colParam, rowNum, colNum, CovEst)

weibull_common_data
#> # A tibble: 9 × 5
#>   rowParam         colParam         rowNum colNum     CovEst
#>   <chr>            <chr>             <dbl>  <dbl>      <dbl>
#> 1 INTERCEPT        INTERCEPT             1      1  0.00298  
#> 2 INTERCEPT        TX(Intervention)      1      2 -0.00318  
#> 3 INTERCEPT        SCALE                 1      3  0.0000886
#> 4 TX(Intervention) INTERCEPT             2      1 -0.00318  
#> 5 TX(Intervention) TX(Intervention)      2      2  0.00580  
#> 6 TX(Intervention) SCALE                 2      3 -0.0000751
#> 7 SCALE            INTERCEPT             3      1  0.0000886
#> 8 SCALE            TX(Intervention)      3      2 -0.0000751
#> 9 SCALE            SCALE                 3      3  0.000750

# can see is ordered by row so can convert to a matrix

weibull_common_matrix <- matrix(data = weibull_common_data$CovEst,
                                nrow = 3, ncol = 3, byrow = TRUE)

# applying names
rownames(weibull_common_matrix) <- colnames(weibull_common_matrix) <- weibull_common_data$colParam[1:3]

weibull_common_matrix
#>                      INTERCEPT TX(Intervention)         SCALE
#> INTERCEPT         2.976351e-03    -3.184138e-03  8.859245e-05
#> TX(Intervention) -3.184138e-03     5.803708e-03 -7.510364e-05
#> SCALE             8.859245e-05    -7.510364e-05  7.501754e-04

stem_modsum

stem_modsum contains a summary of the model fit statistics and is only produced if x is provided.


names(PFS_conv_x$stem_modsum)
#> [1] "Model"   "ModelF"  "Dist"    "DistF"   "Status"  "AIC"     "AIC_SAS"
#> [8] "BIC"     "BIC_SAS"

# note is empty here as x was not provided
nrow(PFS_conv_samples$stem_modsum)
#> [1] 0

PFS_conv_x$stem_modsum %>%
  transmute(Model, Dist, Status, AIC, AIC_SAS, BIC, BIC_SAS) 
#>                     Model        Dist    Status      AIC   AIC_SAS      BIC
#> 1            Common shape Exponential Converged 5600.660 1326.3479 5609.089
#> 2            Common shape     Weibull Converged 5545.222 1270.9094 5557.866
#> 3 Separate - Intervention Exponential Converged 3023.176  671.5601 3026.697
#> 4 Separate - Intervention     Weibull Converged 2990.943  639.3272 2997.986
#> 5    Separate - Reference Exponential Converged 2577.485  654.7878 2581.006
#> 6    Separate - Reference     Weibull Converged 2556.271  633.5741 2563.314
#>     BIC_SAS
#> 1 1334.7771
#> 2 1283.5533
#> 3  675.0816
#> 4  646.3702
#> 5  658.3092
#> 6  640.6170

stem_boot

stem_boot contains a data frame of converted boot strap estimates and is only derived if samples is provided.


names(PFS_conv_samples$stem_boot)
#> [1] "Model"      "ModelF"     "Dist"       "DistF"      "BootSample"
#> [6] "Param"      "ParamF"     "Estimate"

# note is empty here as samples were not provided
nrow(PFS_conv_x$stem_boot)
#> [1] 0

PFS_conv_samples$stem_boot %>%
  transmute(Model, Dist, BootSample, Param, Estimate) %>%
  head()
#>          Model        Dist BootSample            Param   Estimate
#> 1 Common shape Exponential          1        INTERCEPT  6.1289156
#> 2 Common shape Exponential          1 TX(Intervention) -0.7908096
#> 3 Common shape Exponential          2        INTERCEPT  6.0663108
#> 4 Common shape Exponential          2 TX(Intervention) -0.6928566
#> 5 Common shape Exponential          3        INTERCEPT  6.0120960
#> 6 Common shape Exponential          3 TX(Intervention) -0.6119670

Details on conversions

To illustrate the conversions will fit a full set of models to the data.

psm_PFS_all <- runPSM(data=PFS_data,
                     time_var="AVAL",
                     event_var="event",
                     model.type= c("Common shape", 
                                   "Independent shape", 
                                   "Separate"),
                     distr = c('exp',
                               'weibull',
                               'gompertz',
                               'lnorm',
                               'llogis',
                               'gengamma',
                               'gamma',
                               'genf'),
                     strata_var = "ARMCD",
                     int_name="A",
                     ref_name = "B")

# only supplying x
PFS_conv_all <- convSTEM(x = psm_PFS_all)

# To see what the converted parameters are can look at stem_param
PFS_conv_all$stem_param %>%
  group_by(Model, Dist) %>%
  summarise(Params = paste(Param, collapse = ", ")) %>%
  knitr::kable()

Model	Dist	Params
Common shape	Exponential	INTERCEPT, TX(Intervention)
Common shape	Gamma	INTERCEPT, TX(Intervention), SCALE
Common shape	Generalized Gamma	INTERCEPT, TX(Intervention), SCALE, SHAPE
Common shape	Gompertz	INTERCEPT, TX(Intervention), SCALE
Common shape	Log Logistic	INTERCEPT, TX(Intervention), SCALE
Common shape	Log Normal	INTERCEPT, TX(Intervention), SCALE
Common shape	Weibull	INTERCEPT, TX(Intervention), SCALE
Independent shape - Intervention	Exponential	INTERCEPT
Independent shape - Intervention	Gamma	INTERCEPT, SCALE
Independent shape - Intervention	Generalized Gamma	INTERCEPT, SCALE, SHAPE
Independent shape - Intervention	Gompertz	INTERCEPT, SCALE
Independent shape - Intervention	Log Logistic	INTERCEPT, SCALE
Independent shape - Intervention	Log Normal	INTERCEPT, SCALE
Independent shape - Intervention	Weibull	INTERCEPT, SCALE
Independent shape - Reference	Exponential	INTERCEPT
Independent shape - Reference	Gamma	INTERCEPT, SCALE
Independent shape - Reference	Generalized Gamma	INTERCEPT, SCALE, SHAPE
Independent shape - Reference	Gompertz	INTERCEPT, SCALE
Independent shape - Reference	Log Logistic	INTERCEPT, SCALE
Independent shape - Reference	Log Normal	INTERCEPT, SCALE
Independent shape - Reference	Weibull	INTERCEPT, SCALE
Separate - Intervention	Exponential	INTERCEPT
Separate - Intervention	Gamma	INTERCEPT, SCALE
Separate - Intervention	Generalized Gamma	INTERCEPT, SCALE, SHAPE
Separate - Intervention	Gompertz	INTERCEPT, SCALE
Separate - Intervention	Log Logistic	INTERCEPT, SCALE
Separate - Intervention	Log Normal	INTERCEPT, SCALE
Separate - Intervention	Weibull	INTERCEPT, SCALE
Separate - Reference	Exponential	INTERCEPT
Separate - Reference	Gamma	INTERCEPT, SCALE
Separate - Reference	Generalized Gamma	INTERCEPT, SCALE, SHAPE
Separate - Reference	Gompertz	INTERCEPT, SCALE
Separate - Reference	Log Logistic	INTERCEPT, SCALE
Separate - Reference	Log Normal	INTERCEPT, SCALE
Separate - Reference	Weibull	INTERCEPT, SCALE

Conversion of parameters

Note in general independent shape models were not estimated by STEM macro so are converted for backwards compatibility as if if they were estimated by separate models. This has implications for how AIC and BIC should be interpreted in these cases.

Conversion of Exponential models

flexsurvPlus uses the parameter rate ($b$). For common shape, independent shape and separate models these can be denoted as $b_R$ for reference and $b_I$ for intervention.

The SAS STEM macro reports INTERCEPT and TX(INTERVENTION) which are converted as shown below.

Seperate models

Reference arm
- INTERCEPT = $-\log(b_R)$
Intervention arm
- INTERCEPT = $-\log(b_I)$

Common shape models

INTERCEPT = $-\log(b_R)$
TX(INTERVENTION) = $-(\log(b_I) - \log(b_R))$

Excel formula

To derive survival in Excel the following formula are used:

lambda = EXP(-INTERCEPT) and/or
lambda = EXP(-(INTERCEPT+TX(INTERVENTION)))
Survival = EXP(-lambda*time)

Conversion of Weibull models

flexsurvPlus uses the parameters scale ($b$) and shape ($a$). For common shape, independent shape and separate models these can be denoted as $b_R, a_R$ for reference and $b_I, a_I$ for intervention. For common shape models $a_R=a_I$.

The SAS STEM macro reports INTERCEPT, TX(INTERVENTION) and SCALE which are converted as shown below.

Seperate models

Reference arm
- INTERCEPT = $\log(b_R)$
- SCALE = $\frac{1}{a_R}$
Intervention arm
- INTERCEPT = $\log(b_I)$
- SCALE = $\frac{1}{a_I}$

Common shape models

INTERCEPT = $\log(b_R)$
TX(INTERVENTION) = $\log(b_I) - \log(b_R)$
SCALE = $\frac{1}{a_R}$

Excel formula

To derive survival in Excel the following formula are used:

lambda = EXP(-INTERCEPT/SCALE) and/or
lambda = EXP(-(INTERCEPT+TX(INTERVENTION)/SCALE))
gamma = 1/SCALE
Survival = EXP(-lambda*time^gamma)

Conversion of Gompertz models

flexsurvPlus uses the parameters rate ($b$) and shape ($a$). For common shape, independent shape and separate models these can be denoted as $b_R, a_R$ for reference and $b_I, a_I$ for intervention. For common shape models $a_R=a_I$.

The SAS STEM macro reports INTERCEPT, TX(INTERVENTION) and SCALE which are converted as shown below.

Seperate models

Reference arm
- INTERCEPT = $-\log(b_R)$
- SCALE = $a_R$
Intervention arm
- INTERCEPT = $-\log(b_I)$
- SCALE = $a_I$

Common shape models

INTERCEPT = $-\log(b_R)$
TX(INTERVENTION) = $-(\log(b_I) - \log(b_R))$
SCALE = $a_R$

Excel formula

To derive survival in Excel the following formula are used:

lambda = EXP(-INTERCEPT) and/or
lambda = EXP(-(INTERCEPT+TX(INTERVENTION)))
gamma = SCALE
Survival = EXP((lambda/gamma)*(1-EXP(gamma*time)))

Conversion of Log-logistic models

The SAS STEM macro reports INTERCEPT, TX(INTERVENTION) and SCALE which are converted as shown below.

Seperate models

Reference arm
- INTERCEPT = $\log(b_R)$
- SCALE = $\frac{1}{a_R}$
Intervention arm
- INTERCEPT = $\log(b_I)$
- SCALE = $\frac{1}{a_I}$

Common shape models

INTERCEPT = $-\log(b_R)$
TX(INTERVENTION) = $\log(b_I) - \log(B_R)$
SCALE = $\frac{1}{a_R}$

Excel formula

To derive survival in Excel the following formula are used:

lambda = EXP(-INTERCEPT/SCALE) and/or
lambda = EXP(-(INTERCEPT+TX(INTERVENTION)/SCALE))
gamma = 1/SCALE
Survival = 1 / (1 + lambda*time^gamma)

Conversion of Log-normal models

flexsurvPlus uses the parameters meanlog ($\mu$) and sdlog ($\sigma$). For common shape, independent shape and separate models these can be denoted as $\mu_R, \sigma_R$ for reference and $\mu_I, \sigma_I$ for intervention. For common shape models $\sigma_R=\sigma_I$.

The SAS STEM macro reports INTERCEPT, TX(INTERVENTION) and SCALE which are converted as shown below.

Seperate models

Reference arm
- INTERCEPT = $\mu_R$
- SCALE = $\sigma_R$
Intervention arm
- INTERCEPT = $\mu_I$
- SCALE = $\sigma_I$

Common shape models

INTERCEPT = $\mu_R$
TX(INTERVENTION) = $\mu_I - \mu_R$
SCALE = $\sigma_R$

Excel formula

To derive survival in Excel the following formula are used:

lambda = INTERCEPT and/or
lambda = INTERCEPT+TX(INTERVENTION)
gamma = SCALE
Survival = 1-NORMDIST(((LN(time)-lambda)/gamma),0,1,TRUE)

Conversion of Generalized Gamma models

flexsurvPlus uses the parameters mu ($\mu$), sigma ($\sigma$) and $Q$. For common shape, independent shape and separate models these can be denoted as $\mu_R, \sigma_R, Q_R$ for reference and $\mu_I, \sigma_I, Q_I$ for intervention. For common shape models $\sigma_R=\sigma_I$ and $Q_R=$Q_I$.

The SAS STEM macro reports INTERCEPT, TX(INTERVENTION), SCALE and SHAPE which are converted as shown below.

Seperate models

Reference arm
- INTERCEPT = $\mu_R$
- SCALE = $\sigma_R$
- SHAPE = $Q_R$
Intervention arm
- INTERCEPT = $\mu_I$
- SCALE = $\sigma_I$
- SHAPE = $Q_I$

Common shape models

INTERCEPT = $\mu_R$
TX(INTERVENTION) = $\mu_I - \mu_R$
SCALE = $\sigma_R$
SHAPE = $Q_R$

Excel formula

To derive survival in Excel the following formula are used:

lambda = (EXP(-INTERCEPT)^(SHAPE/SCALE))/(SHAPE^2) and/or
lambda = (EXP(-(INTERCEPT+TX(INTERVENTION))^(SHAPE/SCALE))/(SHAPE^2)
gamma = 1/(SHAPE^2)
delta = SHAPE/SCALE
Survival = IF(gamma>0, 1-GAMMADIST(lambda*time^(delta),gamma,1,TRUE), 1-( 1-GAMMADIST(lambda*time^(delta),gamma,1,TRUE)))

Conversion of Gamma models

flexsurvPlus uses the parameters Shape ($a$) and Rate ($b$). For common shape, independent shape and separate models these can be denoted as $a_R, b_R$ for reference and $a_I, b_I$ for intervention. For common shape models $a_R=a_I$.

The SAS STEM macro reports INTERCEPT, TX(INTERVENTION) and SCALE which are converted as shown below. This is equivalent to the parameters used for the Generalized Gamma when the constraint that $\sigma = Q$ or identically that SCALE = SHAPE is applied.

Seperate models

Reference arm
- INTERCEPT = $-\log(\frac{b_R}{a_R})$
- SCALE = $\frac{1}{\sqrt{a_R}}$
Intervention arm
- INTERCEPT = $-\log(\frac{b_I}{a_I})$
- SCALE = $\frac{1}{\sqrt{a_I}}$

Common shape models

INTERCEPT = $-\log(\frac{b_R}{a_R})$
TX(INTERVENTION) = $-(\log(b_I) - \log(b_R))$
SCALE = $\frac{1}{\sqrt{a_R}}$

Excel formula

To derive survival in Excel the following formula are used:

lambda = (EXP(-INTERCEPT))/(SCALE^2) and/or
lambda = (EXP(-(INTERCEPT+TX(INTERVENTION)))/(SCALE^2)
gamma = 1/(SCALE^2)
Survival = IF(gamma>0, 1-GAMMADIST(lambda*time,gamma,1,TRUE), 1- (1-GAMMADIST(lambda*time,gamma,1,TRUE)))

Conversion of AIC and BIC

As the existing SAS STEM macro estimated models with log(time) as a response variable while flexsurv and flexsurvPlus estimate models with time as the response variable there are differences in the log-likelihood between the two software packages. These differences do not affect the parameter estimates or ranking of fit but do affect the AIC and BIC reported by a constant.

This constant is the sum of the events log(time). As such can convert by adding this constant to the maximum log-likelihood and by extension double the sum of the events log(time) to AIC or BIC.


# This constant is estimated from the sum of the log of times for patients who have an event

PFS_data %>%
  filter(event == 1) %>% # select events only
  transmute(log_event_time = log(AVAL)) %>% # difference in log time
  summarise(2 * sum(log_event_time)) 
#>   2 * sum(log_event_time)
#> 1                4274.312

# So for common shape models (using all data) the difference is 4274.312

# Can be seen in results from convSTEM here
modsum <- PFS_conv_all$stem_modsum %>%
  transmute(Model, Dist, AIC, AIC_SAS, BIC, BIC_SAS) 

# note as the separate and common shape models use different data these are not comparable
modsum %>%
  mutate(delta_AIC = AIC - AIC_SAS,
         delta_BIC = AIC - AIC_SAS)
#>                      Model              Dist      AIC   AIC_SAS      BIC
#> 1             Common shape       Exponential 5600.660 1326.3479 5609.089
#> 2             Common shape           Weibull 5545.222 1270.9094 5557.866
#> 3             Common shape          Gompertz 5564.003 1289.6905 5576.647
#> 4             Common shape        Log Normal 5606.451 1332.1382 5619.094
#> 5             Common shape      Log Logistic 5566.512 1292.1995 5579.156
#> 6             Common shape Generalized Gamma 5546.841 1272.5287 5563.699
#> 7             Common shape             Gamma 5546.203 1271.8911 5558.847
#> 8  Separate - Intervention       Exponential 3023.176  671.5601 3026.697
#> 9  Separate - Intervention           Weibull 2990.943  639.3272 2997.986
#> 10 Separate - Intervention          Gompertz 3005.220  653.6042 3012.263
#> 11 Separate - Intervention        Log Normal 3021.443  669.8278 3028.486
#> 12 Separate - Intervention      Log Logistic 3002.733  651.1172 3009.776
#> 13 Separate - Intervention Generalized Gamma 2991.950  640.3347 3002.514
#> 14 Separate - Intervention             Gamma 2990.152  638.5363 2997.195
#> 15    Separate - Reference       Exponential 2577.485  654.7878 2581.006
#> 16    Separate - Reference           Weibull 2556.271  633.5741 2563.314
#> 17    Separate - Reference          Gompertz 2560.755  638.0579 2567.798
#> 18    Separate - Reference        Log Normal 2582.939  660.2420 2589.982
#> 19    Separate - Reference      Log Logistic 2563.469  640.7722 2570.512
#> 20    Separate - Reference Generalized Gamma 2558.162  635.4655 2568.727
#> 21    Separate - Reference             Gamma 2557.768  635.0706 2564.810
#> 22       Independent shape       Exponential 5600.660 1326.3479 5609.089
#> 23       Independent shape           Weibull 5547.214 1272.9013 5564.072
#> 24       Independent shape          Gompertz 5565.974 1291.6621 5582.833
#> 25       Independent shape      Log Logistic 5566.202 1291.8894 5583.060
#> 26       Independent shape             Gamma 5547.919 1273.6069 5564.778
#> 27       Independent shape        Log Normal 5604.382 1330.0698 5621.241
#> 28       Independent shape Generalized Gamma 5550.112 1275.8001 5575.400
#>      BIC_SAS delta_AIC delta_BIC
#> 1  1334.7771  4274.312  4274.312
#> 2  1283.5533  4274.312  4274.312
#> 3  1302.3343  4274.312  4274.312
#> 4  1344.7821  4274.312  4274.312
#> 5  1304.8433  4274.312  4274.312
#> 6  1289.3872  4274.312  4274.312
#> 7  1284.5349  4274.312  4274.312
#> 8   675.0816  2351.615  2351.615
#> 9   646.3702  2351.615  2351.615
#> 10  660.6471  2351.615  2351.615
#> 11  676.8707  2351.615  2351.615
#> 12  658.1602  2351.615  2351.615
#> 13  650.8991  2351.615  2351.615
#> 14  645.5792  2351.615  2351.615
#> 15  658.3092  1922.697  1922.697
#> 16  640.6170  1922.697  1922.697
#> 17  645.1009  1922.697  1922.697
#> 18  667.2849  1922.697  1922.697
#> 19  647.8151  1922.697  1922.697
#> 20  646.0299  1922.697  1922.697
#> 21  642.1136  1922.697  1922.697
#> 22 1334.7771  4274.312  4274.312
#> 23 1289.7598  4274.312  4274.312
#> 24 1308.5206  4274.312  4274.312
#> 25 1308.7478  4274.312  4274.312
#> 26 1290.4653  4274.312  4274.312
#> 27 1346.9282  4274.312  4274.312
#> 28 1301.0878  4274.312  4274.312

Roche

2023-05-02

Introduction

Read in the data

Fitting models

Converting to a STEM format

The output of convSTEM

stem_param

stem_cov

stem_modsum

stem_boot

Details on conversions

Conversion of parameters

Conversion of Exponential models

Seperate models

Common shape models

Excel formula

Conversion of Weibull models

Seperate models

Common shape models

Excel formula

Conversion of Gompertz models

Seperate models

Common shape models

Excel formula

Conversion of Log-logistic models

Seperate models

Common shape models

Excel formula

Conversion of Log-normal models

Seperate models

Common shape models

Excel formula

Conversion of Generalized Gamma models

Seperate models

Common shape models

Excel formula

Conversion of Gamma models

Seperate models

Common shape models

Excel formula

Conversion of AIC and BIC