# Introduction

With the psfmi package you can pool Cox regression models by using
the following pooling methods: RR (Rubin’s Rules), D1, D2, and MPR (Median R Rule). You can also use forward or backward selection from the pooled model. This vignette show you examples of how to apply these procedures.

# Examples

## Pooling without BW and method D1

If you set p.crit at 1 than no selection of variables takes place. Either using direction = “FW” or direction = “BW” will produce the same result.


library(psfmi)
pool_coxr <- psfmi_coxr(data=lbpmicox, nimp=5, impvar="Impnr",
formula = Surv(Time, Status) ~ Duration + Radiation + Onset +
Function + Age + Previous + Tampascale + JobControl +
JobDemand + Social + factor(Expect_cat), p.crit=1,
method="D1", direction = "BW")

pool_coxr$RR_model #>$Step 1 - no variables removed -
#>                   term     estimate   std.error  statistic       df    p.value
#> 1             Duration -0.007738082 0.003989357 -1.9396814 178.7494 0.05399243
#> 2            Radiation -0.074924387 0.153336031 -0.4886287 178.9424 0.62570287
#> 3                Onset -0.093736647 0.175892468 -0.5329202 179.0136 0.59474977
#> 4             Function  0.043959177 0.016917684  2.5984159 175.2854 0.01016263
#> 5                  Age -0.008853266 0.007712097 -1.1479713 177.7066 0.25252344
#> 6             Previous -0.098349421 0.199199997 -0.4937220 178.0134 0.62211113
#> 7           Tampascale -0.023267973 0.014089917 -1.6513918 133.5549 0.10100803
#> 8           JobControl -0.008379513 0.008329969 -1.0059477 178.6831 0.31580101
#> 9            JobDemand -0.021840998 0.015512484 -1.4079626 178.3078 0.16088320
#> 10              Social -0.051348486 0.024912588 -2.0611462 178.3036 0.04074068
#> 11 factor(Expect_cat)2  0.243295714 0.231183479  1.0523923 177.6191 0.29404919
#> 12 factor(Expect_cat)3  0.227055353 0.200259380  1.1338063 178.6187 0.25839523
#>           HR lower.EXP upper.EXP
#> 1  0.9922918 0.9845108 1.0001342
#> 2  0.9278136 0.6855705 1.2556522
#> 3  0.9105225 0.6435046 1.2883376
#> 4  1.0449397 1.0106267 1.0804177
#> 5  0.9911858 0.9762151 1.0063861
#> 6  0.9063322 0.6117408 1.3427877
#> 7  0.9770006 0.9501492 1.0046109
#> 8  0.9916555 0.9754881 1.0080908
#> 9  0.9783958 0.9488992 1.0088093
#> 10 0.9499476 0.9043761 0.9978154
#> 11 1.2754457 0.8082175 2.0127772
#> 12 1.2548993 0.8452496 1.8630856
pool_coxr$multiparm #>$Step 1 - no variables removed -
#>                    p-values D1 F-statistic
#> Duration           0.052418576   3.7623639
#> Onset              0.594088831   0.2840039
#> Function           0.009371567   6.7517650
#> Age                0.250982797   1.3178380
#> Previous           0.621503127   0.2437614
#> Tampascale         0.099111558   2.7270949
#> JobControl         0.314440908   1.0119309
#> JobDemand          0.159143091   1.9823588
#> Social             0.039289895   4.2483236
#> factor(Expect_cat) 0.485351826   0.7228839

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## Pooling with FW and method MPR


library(psfmi)
pool_coxr <- psfmi_coxr(data=lbpmicox, nimp=5, impvar="Impnr",
formula = Surv(Time, Status) ~ Duration + Radiation + Onset +
Function + Age + Previous + Tampascale + JobControl +
JobDemand + Social + factor(Expect_cat), p.crit=0.05,
method="D1", direction = "FW")
#> Entered at Step 1 is - Function
#> Entered at Step 2 is - Social
#> Entered at Step 3 is - Duration
#>
#> Selection correctly terminated,
#> No new variables entered the model

pool_coxr$RR_model_final #>$Final model
#>       term     estimate   std.error statistic       df      p.value        HR
#> 1 Duration -0.007605055 0.003742491 -2.032084 188.0122 0.0435521399 0.9924238
#> 2 Function  0.056490633 0.015414714  3.664722 188.0122 0.0003219893 1.0581167
#> 3   Social -0.051992380 0.022611457 -2.299382 188.0122 0.0225821316 0.9493361
#>   lower.EXP upper.EXP
#> 1 0.9851240 0.9997776
#> 2 1.0264257 1.0907861
#> 3 0.9079217 0.9926396
pool_coxr$multiparm_final #>$Step 2 - selected - Duration
#>                    p-value D1
#> Duration            0.0421452
#> Onset               0.5294033
#> Age                 0.2989933
#> Previous            0.7136713
#> Tampascale          0.1555227
#> JobControl          0.5565327
#> JobDemand           0.1341280
#> factor(Expect_cat)  0.6103930
pool_coxr$predictors_in #> Duration Radiation Onset Function Age Previous Tampascale JobControl #> Step 1 0 0 0 1 0 0 0 0 #> Step 2 0 0 0 0 0 0 0 0 #> Step 3 1 0 0 0 0 0 0 0 #> Included 1 0 0 1 0 0 0 0 #> JobDemand Social factor(Expect_cat) #> Step 1 0 0 0 #> Step 2 0 1 0 #> Step 3 0 0 0 #> Included 0 1 0 Back to Examples ## Pooling with FW including interaction terms and method D1 Pooling Cox regression models over 5 imputed datasets with backward selection using a p-value of 0.05 and as method D1 including interaction terms with a categorical predictor and forcing the predictor Tampascale in the models during backward selection.  library(psfmi) pool_coxr <- psfmi_coxr(data=lbpmicox, nimp=5, impvar="Impnr", formula = Surv(Time, Status) ~ Duration + Radiation + Onset + Function + Age + Previous + Tampascale + factor(Expect_cat) + factor(Satisfaction) + Tampascale:Radiation + factor(Expect_cat):Tampascale, keep.predictors = "Tampascale", p.crit=0.05, method="D1", direction = "FW") #> Entered at Step 1 is - Function #> Entered at Step 2 is - Duration #> #> Selection correctly terminated, #> No new variables entered the model pool_coxr$RR_model_final
#> $Final model #> term estimate std.error statistic df p.value HR #> 1 Duration -0.008309329 0.003753484 -2.213765 187.9452 0.028047868 0.9917251 #> 2 Tampascale -0.016998788 0.013360456 -1.272321 177.6436 0.204921997 0.9831449 #> 3 Function 0.050217190 0.016427330 3.056930 187.0360 0.002563622 1.0514994 #> lower.EXP upper.EXP #> 1 0.9844091 0.9990955 #> 2 0.9575624 1.0094108 #> 3 1.0179701 1.0861332 pool_coxr$multiparm_final
#> $Step 1 - selected - Duration #> p-value D1 #> Duration 0.02684499 #> Radiation 0.49765169 #> Onset 0.47699469 #> Age 0.18893166 #> Previous 0.46140973 #> factor(Expect_cat) 0.57323599 #> factor(Satisfaction) 0.78635590 #> Radiation*Tampascale 0.23337740 #> Tampascale*factor(Expect_cat) 0.34684004 pool_coxr$predictors_in
#>          Duration Radiation Onset Function Age Previous Tampascale
#> Step 1          0         0     0        1   0        0          1
#> Step 2          1         0     0        0   0        0          1
#> Included        1         0     0        1   0        0          1
#> Step 1                    0                    0                    0
#> Step 2                    0                    0                    0
#> Included                  0                    0                    0
#>          Tampascale*factor(Expect_cat)
#> Step 1                               0
#> Step 2                               0
#> Included                             0

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## Pooling with BW including spline coefficients and method D1

Pooling Cox regression models over 5 imputed datasets with backward selection using a p-value of 0.05 and as method D1 including a restricted cubic spline predictor and forcing Tampascale in the models during backward selection.


library(psfmi)

pool_coxr <- psfmi_coxr(data=lbpmicox, nimp=5, impvar="Impnr",
formula = Surv(Time, Status) ~ Duration + Radiation + Onset +
Function + Previous + rcs(Tampascale, 3) +
keep.predictors = "Tampascale",
p.crit=0.05, method="D1", direction = "BW")
#> Removed at Step 1 is - factor(Satisfaction)
#> Removed at Step 2 is - Radiation*rcs(Tampascale,3)
#> Removed at Step 3 is - Onset
#> Removed at Step 4 is - Radiation
#> Removed at Step 5 is - Previous
#>
#> Selection correctly terminated,
#> No more variables removed from the model

pool_coxr$RR_model_final #>$Step 6
#>                            term    estimate  std.error statistic       df
#> 1                      Duration -0.00834864 0.00375033 -2.226108 186.9008
#> 2                      Function  0.05529708 0.01668254  3.314668 184.6679
#> 3  rcs(Tampascale, 3)Tampascale -0.06563800 0.02724068 -2.409558 129.2769
#> 4 rcs(Tampascale, 3)Tampascale'  0.05942661 0.02982168  1.992732 106.0096
#>       p.value        HR lower.EXP upper.EXP
#> 1 0.027201742 0.9916861 0.9843763 0.9990502
#> 2 0.001104361 1.0568545 1.0226366 1.0922174
#> 3 0.017380618 0.9364698 0.8873345 0.9883259
#> 4 0.048860903 1.0612279 1.0003023 1.1258642
pool_coxr$multiparm_final #>$Step 6
#>                    p-values D1 F-statistic
#> Duration          0.0260069717    4.955557
#> Function          0.0009181754   10.987023
#> rcs(Tampascale,3) 0.0522892728    2.971050
pool_coxr$predictors_in #> # A tibble: 3 × 1 #> value #> <chr> #> 1 Duration #> 2 Function #> 3 rcs(Tampascale,3) Back to Examples ## Pooling with FW including spline coefficients and method MPR Pooling Cox regression models over 5 imputed datasets with forward selection using a p-value of 0.05 and as method MPR including a restricted cubic spline predictor and forcing Tampascale in the models during forward selection.  library(psfmi) pool_coxr <- psfmi_coxr(data=lbpmicox, nimp=5, impvar="Impnr", formula = Surv(Time, Status) ~ Duration + Radiation + Onset + Function + Previous + rcs(Tampascale, 3) + factor(Satisfaction) + rcs(Tampascale, 3):Radiation, keep.predictors = "Tampascale", p.crit=0.05, method="MPR", direction = "FW") #> Entered at Step 1 is - Function #> Entered at Step 2 is - Duration #> #> Selection correctly terminated, #> No new variables entered the model pool_coxr$RR_model_final
#> $Final model #> term estimate std.error statistic df #> 1 Duration -0.00834864 0.00375033 -2.226108 186.9008 #> 2 rcs(Tampascale, 3)Tampascale -0.06563800 0.02724068 -2.409558 129.2769 #> 3 rcs(Tampascale, 3)Tampascale' 0.05942661 0.02982168 1.992732 106.0096 #> 4 Function 0.05529708 0.01668254 3.314668 184.6679 #> p.value HR lower.EXP upper.EXP #> 1 0.027201742 0.9916861 0.9843763 0.9990502 #> 2 0.017380618 0.9364698 0.8873345 0.9883259 #> 3 0.048860903 1.0612279 1.0003023 1.1258642 #> 4 0.001104361 1.0568545 1.0226366 1.0922174 pool_coxr$multiparm_final
#> $Step 1 - selected - Duration #> P-value #> Duration 0.02280326 #> Radiation 0.46220293 #> Onset 0.41857220 #> Previous 0.64851606 #> factor(Satisfaction) 0.58075823 #> Radiation*rcs(Tampascale,3) 0.75488109 pool_coxr$predictors_in
#>          Duration Radiation Onset Function Previous factor(Satisfaction)
#> Step 1          0         0     0        1        0                    0
#> Step 2          1         0     0        0        0                    0
#> Included        1         0     0        1        0                    0
#> Step 1                   1                           0
#> Step 2                   1                           0
#> Included                 1                           0

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## Pooling with BW for a stratified Cox model

Pooling Cox regression models over 5 imputed datasets with backward selection using a p-value of 0.05 and as method MPR for a stratified Cox model.


library(psfmi)
pool_coxr <- psfmi_coxr(data=lbpmicox, nimp=5, impvar="Impnr",
formula = Surv(Time, Status) ~ Duration + Onset +
Function + Previous + rcs(Tampascale, 3) +
p.crit=0.05, method="MPR", direction = "BW")
#> Removed at Step 1 is - factor(Satisfaction)
#> Removed at Step 2 is - Onset
#> Removed at Step 3 is - Previous
#>
#> Selection correctly terminated,
#> No more variables removed from the model

pool_coxr$RR_model_final #>$Step 4
#>                            term     estimate   std.error statistic        df
#> 1                      Duration -0.008484749 0.003738762 -2.269401 186.85272
#> 2                      Function  0.055437188 0.017461177  3.174883 184.30915
#> 3  rcs(Tampascale, 3)Tampascale -0.064744168 0.027417178 -2.361445 124.61432
#> 4 rcs(Tampascale, 3)Tampascale'  0.061363612 0.030289959  2.025873  97.02152
#>       p.value        HR lower.EXP upper.EXP
#> 1 0.024386480 0.9915511 0.9842648 0.9988915
#> 2 0.001757088 1.0570026 1.0212095 1.0940503
#> 3 0.019754160 0.9373072 0.8878009 0.9895742
#> 4 0.045523544 1.0632855 1.0012474 1.1291675
pool_coxr$multiparm_final #>$Step 4
#>                   p-value MPR
#> Duration          0.024176044
#> Function          0.001305273
#> rcs(Tampascale,3) 0.037329200
pool_coxr$formula_step #>$Step 1 - removal - factor(Satisfaction)
#> Surv(Time, Status) ~ Duration + Onset + Function + Previous +
#>     factor(Satisfaction) + rcs(Tampascale, 3) + strata(Radiation)
#> <environment: 0x00000182fa18a788>
#>
#> $Step 2 - removal - Onset #> Surv(Time, Status) ~ Duration + Onset + Function + Previous + #> rcs(Tampascale, 3) + strata(Radiation) #> <environment: 0x00000182fa18a788> #> #>$Step 3 - removal - Previous
#> Surv(Time, Status) ~ Duration + Function + Previous + rcs(Tampascale,
#> \$Step 4 - removal - ended
#> <environment: 0x00000182fa18a788>