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Detailed Function Presentation

PDRobust

This vignette demonstrates validation, prediction, diagnostics, and treatment effect estimation using the bundled data.

data("BiSample") -> Mapping() -> DataCheck() -> DataStandard() -> prediction / diagnostic / analysis functions

1. Load the built-in package data

library(PDRobust)
data("BiSample", package = "PDRobust")
head(BiSample)
#>   id time    Pi S1 S0 S A Y1 Y0 Y    X1     X2     X3 X4 X5 X6
#> 1  1    0 0.987  1  1 1 1  0  1 0 1.479 -0.168  0.873  0  1  1
#> 2  1    1 0.987  1  1 1 1  0  0 0 1.479 -0.168  0.873  0  1  1
#> 3  1    2 0.987  1  1 1 1  0  0 0 1.479 -0.168  0.873  0  1  1
#> 4  2    0 0.777  1  1 1 1  0  0 0 0.267  0.350 -1.438  1  1  1
#> 5  2    1 0.777  1  1 1 1  0  0 0 0.267  0.350 -1.438  1  1  1
#> 6  2    2 0.777  1  1 1 1  0  0 0 0.267  0.350 -1.438  1  1  1

2. Define roles and analysis settings with `Mapping()`

mapping <- Mapping(
  id = "id",
  time = "time",
  treatment = "A",
  survival = "S",
  outcome = "Y",
  baseline_time = 0,
  cutoff_time = 2,
  covariates = c("X1", "X3", "X4", "X5", "X6"),
  interest_vars = c("X1", "X4"),
  y_type = "B"
)

print(mapping)
#> PDRobust data mapping and analysis settings.
#>   ID: id
#>   Time: time
#>   Treatment: A
#>   Survival: S
#>   Outcome: Y
#>   Baseline time: 0
#>   Cutoff time: 2
#>   Mapped covariates: X1, X3, X4, X5, X6
#>   Interest variables: X1, X4
#>   Outcome type: B (binary)

3. Validate the raw data with `DataCheck()`

check <- DataCheck(BiSample, mapping, strict = FALSE)
names(check)           
#> [1] "valid"                      "ready_for_analysis"        
#> [3] "manual_resolution_required" "can_standardize"           
#> [5] "checks"                     "settings"                  
#> [7] "diagnostics"

check$valid
#> [1] TRUE
check$ready_for_analysis
#> [1] TRUE
check$manual_resolution_required
#> [1] FALSE
check$can_standardize
#> [1] TRUE

The itemized report is in check$checks; supporting details are in check$diagnostics.

4. Standardize the panel with `DataStandard()`

pd_data <- DataStandard(BiSample, mapping, drop =TRUE)
head(pd_data)
#>   id time    Pi S1 S0 S A Y1 Y0 Y    X1     X2     X3 X4 X5 X6
#> 1  1    0 0.987  1  1 1 1  0  1 0 1.479 -0.168  0.873  0  1  1
#> 2  1    1 0.987  1  1 1 1  0  0 0 1.479 -0.168  0.873  0  1  1
#> 3  1    2 0.987  1  1 1 1  0  0 0 1.479 -0.168  0.873  0  1  1
#> 4  2    0 0.777  1  1 1 1  0  0 0 0.267  0.350 -1.438  1  1  1
#> 5  2    1 0.777  1  1 1 1  0  0 0 0.267  0.350 -1.438  1  1  1
#> 6  2    2 0.777  1  1 1 1  0  0 0 0.267  0.350 -1.438  1  1  1

Imperfect dataset

For imperfect dataset, we have:

data("ImperfectConSample", package = "PDRobust")
head(ImperfectConSample)
#>   patient_id visit_month alive_status treatment clinical_outcome     X1     X2
#> 1    PT-0171           0            1         1            4.598  1.452 -2.075
#> 2    PT-0100           6            0         1               NA  1.473 -0.758
#> 3    PT-0056           0            1         0            8.806 -2.722 -0.735
#> 4    PT-0034           6            1         0           13.851 -1.471  0.278
#> 5    PT-0164          12            1         1            9.643 -1.272 -1.881
#> 6    PT-0058           0            1         1           10.341 -0.534 -0.842
#>       X3 X4 X5 X6
#> 1 -0.147  0  1  1
#> 2  0.608  0  1  1
#> 3  0.424  1  1  0
#> 4 -0.158  0  0  0
#> 5 -3.333  0  1  0
#> 6 -0.092  0  1  0

con_mapping <- Mapping(
  id = "patient_id",
  time = "visit_month",
  treatment = "treatment",
  survival = "alive_status",
  outcome = "clinical_outcome",
  baseline_time = 0,
  cutoff_time = 12,
  covariates = c("X1", "X2", "X3", "X4", "X5", "X6"),
  interest_vars = c("X1", "X2"),
  y_type = "C"
)

con_check <- DataCheck(ImperfectConSample, con_mapping, strict = FALSE)

con_check$valid
#> [1] FALSE
con_check$ready_for_analysis
#> [1] FALSE
con_check$manual_resolution_required
#> [1] FALSE
con_check$can_standardize
#> [1] TRUE

con_data <- DataStandard(ImperfectConSample, con_mapping, drop = TRUE)
head(con_data)
#>   patient_id visit_month alive_status treatment clinical_outcome     X1     X2
#> 1          1           0            1         1           10.803  0.168  0.421
#> 2          1           1            1         1           12.006  0.168  0.421
#> 3          1           2            1         1            7.833  0.168  0.421
#> 4          2           0            1         0            4.101 -2.400 -0.324
#> 5          2           1            1         0            5.508 -2.400 -0.324
#> 6          2           2            0         0               NA -2.400 -0.324
#>       X3 X4 X5 X6
#> 1 -0.557  1  1  1
#> 2 -0.557  1  1  1
#> 3 -0.557  1  1  1
#> 4 -0.391  0  0  0
#> 5 -0.391  0  0  0
#> 6 -0.391  0  0  0

print(dim(ImperfectConSample))
#> [1] 599  11
print(dim(con_data))
#> [1] 588  11

names(attributes(con_data))
#> [1] "names"               "row.names"           "class"              
#> [4] "pd_mapping"          "pd_original_mapping" "pd_check"           
#> [7] "pd_standardization"

attr_standard <- attributes(con_data)
attr_standard$pd_standardization$time_map
#>   raw_time standardized_time
#> 1        0                 0
#> 2        6                 1
#> 3       12                 2
head(attr_standard$pd_standardization$id_map)
#>    raw_id standardized_id
#> 1 PT-0005               1
#> 2 PT-0006               2
#> 3 PT-0007               3
#> 4 PT-0008               4
#> 5 PT-0009               5
#> 6 PT-0010               6

5.1 Prediction functions and Diagnostics

ps_fo <- A ~ X1 + X3 + X4 + X5 + X6
prin_fo <- S ~ (X1 + X3 + X4 + X5 + X6 ) * A
out_fo <- Y ~ (X1 + X3 + X4 + X5 + X6) * A + S

Propensity score model

ps <- PSPred(
  ps_fo = ps_fo,
  fit_dat = pd_data,
  pred_dat = pd_data,
  mapping = mapping
)
           
head(ps)
#> [1] 0.987 0.987 0.987 0.873 0.873 0.873

ps_diagnostic <- PSDiag(data = pd_data,
                        ps_fo = ps_fo)

print(ps_diagnostic)
#> Exposure-model balance diagnostics before and after weighting.
#>  covariate adjustment   smd
#>         X1     Before 0.679
#>         X3     Before 0.615
#>         X4     Before 0.025
#>         X5     Before 0.545
#>         X6     Before 0.152
#>         X1      After 0.081
#>         X3      After 0.084
#>         X4      After 0.049
#>         X5      After 0.153
#>         X6      After 0.020

Absolute standardized mean differences before and after propensity-score weighting.

Principal score model

p0 <- PrinPred(
  prin_fo = prin_fo,
  fit_dat = pd_data,
  pred_dat = pd_data,
  a = 0,
  mapping = mapping
)

head(p0)
#> [1] 1.000 0.985 0.971 1.000 0.990 0.979

principal_diagnostic <- PrinSDiag(
  data = pd_data, 
  ps_fo = ps_fo, 
  prin_fo = prin_fo)

print(principal_diagnostic)
#> Principal-score standardized diagnostic statistics.
#>  covariate statistic
#>         X1    -0.575
#>         X3    -0.511
#>         X4    -0.374
#>         X5     1.006
#>         X6     0.656

Standardized principal-score balance statistics for the selected covariates.

Outcome model

mu1 <- OutPred(
  out_fo = out_fo,
  fit_dat = pd_data,
  pred_dat = pd_data,
  a = 1,
  mapping = mapping
)

head(mu1)
#> [1] 0.228 0.228 0.228 0.255 0.255 0.255

set.seed(12345)
sensitivity <- SA(
  data  = pd_data,
  ps_fo = ps_fo,
  prin_fo = prin_fo,
  out_fo = out_fo,
  ratiovec = c(0.05,0.1, 0.2)
)
print(sensitivity)
#> Outcome-noise sensitivity estimates across variance-ratio scenarios.
#>  ratiovec time Intercept     X1     X4
#>      0.05    0     0.107 -0.083 -0.317
#>      0.10    0     0.046 -0.085 -0.283
#>      0.20    0     0.173 -0.084 -0.407
#>      0.05    1    -0.029 -0.049  0.324
#>      0.10    1    -0.006 -0.064  0.487
#>      0.20    1     0.159  0.083  0.203
#>      0.05    2     0.249  0.153 -0.642
#>      0.10    2     0.375  0.314 -0.860
#>      0.20    2     0.084  0.070 -0.322
#>   Scenarios: 3

Estimated effect-modification coefficients over time at different outcome-noise variance ratios.

Principal-stratum profiling with `QR()`

principal_profile <- QR(
  data = pd_data,
  prin_fo = prin_fo,
  quantile_level = c(0.25, 0.50, 0.75)
)

print(principal_profile)
#> Principal-stratum weighted means and quantiles.
#> Weighted means:
#>    X1    X4 
#> 0.117 0.500 
#> 
#> Weighted quantiles (NA for binary variables):
#> $X1
#>  q0.25  q0.50  q0.75 
#> -0.517  0.130  0.728 
#> 
#> $X4
#> q0.25 q0.50 q0.75 
#>    NA    NA    NA
principal_profile$data
#>   covariate  mean quantile estimate binary
#> 1        X1 0.117     0.25   -0.517  FALSE
#> 2        X1 0.117     0.50    0.130  FALSE
#> 3        X1 0.117     0.75    0.728  FALSE
#> 4        X4 0.500     0.25       NA   TRUE
#> 5        X4 0.500     0.50       NA   TRUE
#> 6        X4 0.500     0.75       NA   TRUE

Treatment-group odds ratios

or_control <- ORCI(
  data = pd_data,
  formula = S ~ X1 + X3 + X4,
  a = 0,
  conf_level = 0.95
)

print(or_control)
#> Treatment-group-specific survival odds ratios and confidence intervals.
#>  covname estcoef lowerbd upperbd
#>       X1   2.044   1.111   3.761
#>       X3   0.565   0.301   1.059
#>       X4   2.213   0.748   6.549

Cutoff survival odds ratios and confidence intervals within treatment group zero.

5.2 Heterogeneous treatment effect

The five bootstrap replications below are only for a fast demonstration. Substantive standard errors and confidence intervals require more replications and an assessment of their stability. Use B = 0 for point estimates alone.

set.seed(12345)
separate_hte <- HTESepT(
  data = pd_data,
  ps_fo = ps_fo,
  prin_fo = prin_fo,
  out_fo = out_fo,
  target_time = c(1, 2),
  B = 5,
  conf_level = 0.95,
  max_attempts = NULL,
  verbose = TRUE
)

separate_hte$summary
#>   time covariate estimate    SD LowerBound UpperBound
#> 1    1 Intercept   -0.019 0.122     -0.259      0.220
#> 2    1        X1   -0.063 0.280     -0.611      0.486
#> 3    1        X4    0.345 0.300     -0.243      0.932
#> 4    2 Intercept    0.212 0.064      0.087      0.338
#> 5    2        X1    0.166 0.193     -0.213      0.546
#> 6    2        X4   -0.506 0.556     -1.596      0.584
separate_hte$forest_plot

Time-specific treatment-effect model coefficients and demonstration bootstrap confidence intervals.

head(separate_hte$boot_mat)
#>       1_Intercept        1_X1      1_X4 2_Intercept        2_X1        2_X4
#> boot1  0.07044230  0.20360933 0.1404987  0.15163733  0.04579371 -0.73561676
#> boot2 -0.12408163 -0.02886817 0.6331085  0.20827059 -0.11123892 -1.51657044
#> boot3  0.07315448  0.20847100 0.1417911  0.04808113 -0.08855529 -0.94695185
#> boot4 -0.19742717 -0.43617102 0.7375801  0.15990027  0.21257140 -0.60646106
#> boot5  0.01576182  0.20472683 0.1451984  0.08346920  0.33674388  0.01799855

pooled_hte <- HTEAllT(
  data = pd_data,
  ps_fo = ps_fo,
  prin_fo = prin_fo,
  out_fo = out_fo,
  B = 0,
  verbose = FALSE
)
pooled_hte$summary
#>          term estimate SD LowerBound UpperBound
#> 1   Intercept    0.102 NA         NA         NA
#> 2          X1    0.020 NA         NA         NA
#> 3          X4   -0.153 NA         NA         NA
#> 4 Time Effect    0.004 NA         NA         NA
pooled_hte$forest_plot

Pooled treatment-effect model point estimates; bootstrap intervals are not calculated in this example.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.