Seoul- AAAP

Introduction

For the sake of continuity and uniformity, the analysis of the addition of the time pressure factor was done in the same manner as the analyses done so far, within the framework of the survival analysis of the “crossing times” as defined earlier and correlations of the difference between the two groups and the level of difficulty of the scenario. The button press data of the participants at each vehicle crossing was now divided into two for presses without or with time pressure. Therefore, in practice, the analysis became an analysis with two explanatory factors: the five-level scenario factor and the two-level time pressure factor.

The analysis will be done in the following steps. In the first section, the “interaction” analysis will be done in two ways: comparing the effect of time pressure in each scenario and vice versa, the scenario’s impact in each situation of time pressure. In the second section, the analysis of the main effects will be done, i.e., the effect of the scenario factor “on average” on the time pressure situations and the effect of the time pressure factor “on average” on all scenarios. The third section will be for finding the relationship between the difficulty of the scenario, the time pressure situation, and the crossing patterns.

Interaction

Time Pressure within each scenario

SCENARIO 1

TIME
----

Call: survfit(formula = Surv(Time, Case) ~ TP, data = Dat.1_all)

        n events median 0.95LCL 0.95UCL
TP=NO  60     59      9       5       9
TP=YES 60     59      6       4       7

Call:
survdiff(formula = Surv(Time, Case) ~ TP, data = Dat.1_all)

        N Observed Expected (O-E)^2/E (O-E)^2/V
TP=NO  60       59     62.9     0.245     0.835
TP=YES 60       59     55.1     0.280     0.835

 Chisq= 0.8  on 1 degrees of freedom, p= 0.4

Cum gap time
------------

Call: survfit(formula = Surv(Cum_gap_time, Case) ~ TP, data = Dat.1_all)

        n events median 0.95LCL 0.95UCL
TP=NO  60     59   19.3   10.18    19.3
TP=YES 60     59   12.4    7.67    14.3

Call:
survdiff(formula = Surv(Cum_gap_time, Case) ~ TP, data = Dat.1_all)

        N Observed Expected (O-E)^2/E (O-E)^2/V
TP=NO  60       59     62.9     0.245     0.835
TP=YES 60       59     55.1     0.280     0.835

 Chisq= 0.8  on 1 degrees of freedom, p= 0.4

     Cross_Score Gap_Score Stop_Score_Gap Cross_Score_Gap Med_Time Med_CGT
S1.1   0.3318082  8.235468       4.286381        3.949087        9  19.325
S2.1   0.3318082  8.235468       4.286381        3.949087        6  12.425

SCENARIO 2

TIME
----

Call: survfit(formula = Surv(Time, Case) ~ TP, data = Dat.2_all)

        n events median 0.95LCL 0.95UCL
TP=NO  57     51      5       5       7
TP=YES 63     60      5       5       7

Call:
survdiff(formula = Surv(Time, Case) ~ TP, data = Dat.2_all)

        N Observed Expected (O-E)^2/E (O-E)^2/V
TP=NO  57       51     52.8    0.0594     0.186
TP=YES 63       60     58.2    0.0538     0.186

 Chisq= 0.2  on 1 degrees of freedom, p= 0.7

Cum gap time
------------

Call: survfit(formula = Surv(Cum_gap_time, Case) ~ TP, data = Dat.2_all)

        n events median 0.95LCL 0.95UCL
TP=NO  57     51   9.15    9.15    14.8
TP=YES 63     60   9.15    9.15    14.8

Call:
survdiff(formula = Surv(Cum_gap_time, Case) ~ TP, data = Dat.2_all)

        N Observed Expected (O-E)^2/E (O-E)^2/V
TP=NO  57       51     52.8    0.0594     0.186
TP=YES 63       60     58.2    0.0538     0.186

 Chisq= 0.2  on 1 degrees of freedom, p= 0.7

     Cross_Score Gap_Score Stop_Score_Gap Cross_Score_Gap Med_Time Med_CGT
S1.2   0.3537461   7.37293       3.258095        4.114835        5    9.15
S2.2   0.3537461   7.37293       3.258095        4.114835        5    9.15

SCENARIO 3

TIME
----

Call: survfit(formula = Surv(Time, Case) ~ TP, data = Dat.3_all)

         n events median 0.95LCL 0.95UCL
TP=NO  118    112      7       7       7
TP=YES 122    120      7       6       7

Call:
survdiff(formula = Surv(Time, Case) ~ TP, data = Dat.3_all)

         N Observed Expected (O-E)^2/E (O-E)^2/V
TP=NO  118      112      127      1.81      7.17
TP=YES 122      120      105      2.19      7.17

 Chisq= 7.2  on 1 degrees of freedom, p= 0.007

Cum gap time
------------

Call: survfit(formula = Surv(Cum_gap_time, Case) ~ TP, data = Dat.3_all)

         n events median 0.95LCL 0.95UCL
TP=NO  118    112     16    16.0      16
TP=YES 122    120     16    12.7      16

Call:
survdiff(formula = Surv(Cum_gap_time, Case) ~ TP, data = Dat.3_all)

         N Observed Expected (O-E)^2/E (O-E)^2/V
TP=NO  118      112      127      1.81      7.17
TP=YES 122      120      105      2.19      7.17

 Chisq= 7.2  on 1 degrees of freedom, p= 0.007

     Cross_Score Gap_Score Stop_Score_Gap Cross_Score_Gap Med_Time Med_CGT
S1.2   0.3537461   7.37293       3.258095        4.114835        5    9.15
S2.2   0.3537461   7.37293       3.258095        4.114835        5    9.15

SCENARIO 4

TIME
----

Call: survfit(formula = Surv(Time, Case) ~ TP, data = Dat.4_all)

         n events median 0.95LCL 0.95UCL
TP=NO  120    115      5       5       7
TP=YES 120    119      5       5       6

Call:
survdiff(formula = Surv(Time, Case) ~ TP, data = Dat.4_all)

         N Observed Expected (O-E)^2/E (O-E)^2/V
TP=NO  120      115      132      2.12      7.93
TP=YES 120      119      102      2.73      7.93

 Chisq= 7.9  on 1 degrees of freedom, p= 0.005

Cum gap time
------------

Call: survfit(formula = Surv(Cum_gap_time, Case) ~ TP, data = Dat.4_all)

         n events median 0.95LCL 0.95UCL
TP=NO  120    115   8.45    8.45    15.0
TP=YES 120    119   8.45    8.45    11.4

Call:
survdiff(formula = Surv(Cum_gap_time, Case) ~ TP, data = Dat.4_all)

         N Observed Expected (O-E)^2/E (O-E)^2/V
TP=NO  120      115      132      2.12      7.93
TP=YES 120      119      102      2.73      7.93

 Chisq= 7.9  on 1 degrees of freedom, p= 0.005

     Cross_Score Gap_Score Stop_Score_Gap Cross_Score_Gap Med_Time Med_CGT
S1.4   0.2525662   8.04388       3.443119        4.600761        5    8.45
S2.4   0.2525662   8.04388       3.443119        4.600761        5    8.45

SCENARIO 5

TIME
----

Call: survfit(formula = Surv(Time, Case) ~ TP, data = Dat.5_all)

         n events median 0.95LCL 0.95UCL
TP=NO  120    102      9       9       9
TP=YES 120    116      7       6       9

Call:
survdiff(formula = Surv(Time, Case) ~ TP, data = Dat.5_all)

         N Observed Expected (O-E)^2/E (O-E)^2/V
TP=NO  120      102    131.9      6.79      25.4
TP=YES 120      116     86.1     10.40      25.4

 Chisq= 25.4  on 1 degrees of freedom, p= 5e-07

Cum gap time
------------

Call: survfit(formula = Surv(Cum_gap_time, Case) ~ TP, data = Dat.5_all)

         n events median 0.95LCL 0.95UCL
TP=NO  120    102   19.4    19.4    19.4
TP=YES 120    116   13.5    11.1    19.4

Call:
survdiff(formula = Surv(Cum_gap_time, Case) ~ TP, data = Dat.5_all)

         N Observed Expected (O-E)^2/E (O-E)^2/V
TP=NO  120      102    131.9      6.79      25.4
TP=YES 120      116     86.1     10.40      25.4

 Chisq= 25.4  on 1 degrees of freedom, p= 5e-07

     Cross_Score Gap_Score Stop_Score_Gap Cross_Score_Gap Med_Time Med_CGT
S1.5  0.06689682  7.279143       5.629801        1.649341        9    19.4
S2.5  0.06689682  7.279143       5.629801        1.649341        7    13.5

All Scenraios in one figure

In Figure X, you can see the estimates of survival (according to cum gap time) of each time pressure group (blue with, red without) and in each scenario. In Table Y, you can see the median crossing times in each scenario and time pressure group, as well as the difficulty level scores of each scenario. It can be seen from Figure X and Table Y that in three scenarios, statistically significant differences were found between the two-time pressure groups, and by implementing the Fisher method to combine the P-values, we will get \(\chi(5)\)=36, p<0.001. In the group with time pressure, the decision to cross takes less time, meaning they decide to cross earlier.

Scenario within Time Pressure

Time Pressure = N0

TIME
----

Call: survfit(formula = Surv(Time, Case) ~ Scenario, data = temp)

             n events median 0.95LCL 0.95UCL
Scenario=1  60     59      9       5       9
Scenario=2  57     51      5       5       7
Scenario=3 118    112      7       7       7
Scenario=4 120    115      5       5       7
Scenario=5 120    102      9       9       9

Call:
survdiff(formula = Surv(Time, Case) ~ Scenario, data = temp)

             N Observed Expected (O-E)^2/E (O-E)^2/V
Scenario=1  60       59     54.7     0.336     0.539
Scenario=2  57       51     34.4     8.010    11.675
Scenario=3 118      112    103.5     0.705     1.298
Scenario=4 120      115     93.8     4.809     8.636
Scenario=5 120      102    152.7    16.812    38.123

 Chisq= 45  on 4 degrees of freedom, p= 4e-09


    Pairwise comparisons using Log-Rank test 

data:  temp and Scenario 

  1       2       3       4      
2 0.06428 -       -       -      
3 0.89303 0.03728 -       -      
4 0.87274 0.20525 0.11183 -      
5 0.00089 3.0e-09 1.4e-06 7.0e-08

P value adjustment method: BH

Cum gap time
------------

Call: survfit(formula = Surv(Cum_gap_time, Case) ~ Scenario, data = temp)

             n events median 0.95LCL 0.95UCL
Scenario=1  60     59  19.33   10.18    19.3
Scenario=2  57     51   9.15    9.15    14.8
Scenario=3 118    112  16.00   16.00    16.0
Scenario=4 120    115   8.45    8.45    15.0
Scenario=5 120    102  19.40   19.40    19.4

Call:
survdiff(formula = Surv(Cum_gap_time, Case) ~ Scenario, data = temp)

             N Observed Expected (O-E)^2/E (O-E)^2/V
Scenario=1  60       59     49.8   1.68696  2.21e+00
Scenario=2  57       51     32.4  10.71357  1.32e+01
Scenario=3 118      112    112.2   0.00023  3.66e-04
Scenario=4 120      115     82.6  12.70719  1.82e+01
Scenario=5 120      102    162.0  22.24047  4.33e+01

 Chisq= 57.3  on 4 degrees of freedom, p= 1e-11


    Pairwise comparisons using Log-Rank test 

data:  temp and Scenario 

  1       2       3       4      
2 0.081   -       -       -      
3 0.427   3.8e-05 -       -      
4 0.946   0.139   4.0e-05 -      
5 6.8e-07 6.2e-07 7.5e-06 1.1e-08

P value adjustment method: BH

Time Pressure = Yes

TIME
----

Call: survfit(formula = Surv(Time, Case) ~ Scenario, data = temp)

             n events median 0.95LCL 0.95UCL
Scenario=1  60     59      6       4       7
Scenario=2  63     60      5       5       7
Scenario=3 122    120      7       6       7
Scenario=4 120    119      5       5       6
Scenario=5 120    116      7       6       9

Call:
survdiff(formula = Surv(Time, Case) ~ Scenario, data = temp)

             N Observed Expected (O-E)^2/E (O-E)^2/V
Scenario=1  60       59     62.7   0.21649   0.36492
Scenario=2  63       60     53.2   0.87314   1.35395
Scenario=3 122      120    119.4   0.00289   0.00543
Scenario=4 120      119    103.7   2.27106   4.14219
Scenario=5 120      116    135.1   2.69014   5.47699

 Chisq= 8.8  on 4 degrees of freedom, p= 0.07


    Pairwise comparisons using Log-Rank test 

data:  temp and Scenario 

  1    2    3    4   
2 0.43 -    -    -   
3 0.78 0.56 -    -   
4 0.43 0.89 0.29 -   
5 0.60 0.12 0.25 0.05

P value adjustment method: BH

Cum gap time
------------

Call: survfit(formula = Surv(Cum_gap_time, Case) ~ Scenario, data = temp)

             n events median 0.95LCL 0.95UCL
Scenario=1  60     59  12.43    7.67    14.3
Scenario=2  63     60   9.15    9.15    14.8
Scenario=3 122    120  16.00   12.70    16.0
Scenario=4 120    119   8.45    8.45    11.4
Scenario=5 120    116  13.50   11.15    19.4

Call:
survdiff(formula = Surv(Cum_gap_time, Case) ~ Scenario, data = temp)

             N Observed Expected (O-E)^2/E (O-E)^2/V
Scenario=1  60       59     57.7    0.0302    0.0382
Scenario=2  63       60     54.7    0.5175    0.6529
Scenario=3 122      120    129.4    0.6810    1.0615
Scenario=4 120      119     95.5    5.7824    8.1276
Scenario=5 120      116    136.8    3.1492    5.1039

 Chisq= 11.6  on 4 degrees of freedom, p= 0.02

The two time pressure groups in one figure

Main Effects

Scenrio

Time

Call: survfit(formula = Surv(Time, Case) ~ Scenario, data = Dat_all)

             n events median 0.95LCL 0.95UCL
Scenario=1 120    118      6       5       9
Scenario=2 120    111      5       5       7
Scenario=3 240    232      7       7       7
Scenario=4 240    234      5       5       6
Scenario=5 240    218      9       8       9

Call:
survdiff(formula = Surv(Time, Case) ~ Scenario, data = Dat_all)

             N Observed Expected (O-E)^2/E (O-E)^2/V
Scenario=1 120      118    116.7    0.0138    0.0225
Scenario=2 120      111     85.8    7.3975   11.0045
Scenario=3 240      232    222.2    0.4328    0.7982
Scenario=4 240      234    197.8    6.6357   11.9431
Scenario=5 240      218    290.5   18.0928   38.8060

 Chisq= 47.3  on 4 degrees of freedom, p= 1e-09


    Pairwise comparisons using Log-Rank test 

data:  Dat_all and Scenario 

  1      2       3       4      
2 0.0388 -       -       -      
3 0.9000 0.0388  -       -      
4 0.3433 0.3433  0.0388  -      
5 0.0043 9.7e-09 2.8e-06 9.7e-09

P value adjustment method: BH

Cum gap time

Call: survfit(formula = Surv(Cum_gap_time, Case) ~ Scenario, data = Dat_all)

             n events median 0.95LCL 0.95UCL
Scenario=1 120    118  12.43   10.18    19.3
Scenario=2 120    111   9.15    9.15    14.8
Scenario=3 240    232  16.00   16.00    16.0
Scenario=4 240    234   8.45    8.45    11.4
Scenario=5 240    218  19.40   16.05    19.4

Call:
survdiff(formula = Surv(Cum_gap_time, Case) ~ Scenario, data = Dat_all)

             N Observed Expected (O-E)^2/E (O-E)^2/V
Scenario=1 120      118    106.0     1.364     1.744
Scenario=2 120      111     84.6     8.207    10.143
Scenario=3 240      232    240.7     0.311     0.488
Scenario=4 240      234    178.9    16.957    24.005
Scenario=5 240      218    302.8    23.750    42.304

 Chisq= 59.4  on 4 degrees of freedom, p= 4e-12


    Pairwise comparisons using Log-Rank test 

data:  Dat_all and Scenario 

  1       2       3       4      
2 0.11523 -       -       -      
3 0.36534 0.00011 -       -      
4 0.66168 0.36534 8.9e-07 -      
5 3.0e-06 3.4e-06 7.6e-05 2.4e-09

P value adjustment method: BH

The two plots together

Time Pressure

Time

Call: survfit(formula = Surv(Time, Case) ~ TP, data = Dat_all)

         n events median 0.95LCL 0.95UCL
TP=NO  475    439      7       7       7
TP=YES 485    474      6       5       7

Call:
survdiff(formula = Surv(Time, Case) ~ TP, data = Dat_all)

         N Observed Expected (O-E)^2/E (O-E)^2/V
TP=NO  475      439      508      9.27      29.1
TP=YES 485      474      405     11.61      29.1

 Chisq= 29.1  on 1 degrees of freedom, p= 7e-08

Cum gap time

Call: survfit(formula = Surv(Cum_gap_time, Case) ~ TP, data = Dat_all)

         n events median 0.95LCL 0.95UCL
TP=NO  475    439   15.0   15.00    16.0
TP=YES 485    474   11.4    9.25    13.5

Call:
survdiff(formula = Surv(Cum_gap_time, Case) ~ TP, data = Dat_all)

         N Observed Expected (O-E)^2/E (O-E)^2/V
TP=NO  475      439      516      11.4      29.7
TP=YES 485      474      397      14.7      29.7

 Chisq= 29.7  on 1 degrees of freedom, p= 5e-08

The two plots together

Section 3

Correlation analysis

Scatter plots and Pearson’s correlation matrix

	Cross_Score	Gap_Score	Stop_Score_Gap	Cross_Score_Gap	Med_Time	Med_CGT
Cross_Score	1.0000	0.3190	-0.8740	0.8711	-0.8569	-0.8508
Gap_Score	0.3190	1.0000	-0.2032	0.5235	-0.4319	-0.3530
Stop_Score_Gap	-0.8740	-0.2032	1.0000	-0.9406	0.9473	0.9840
Cross_Score_Gap	0.8711	0.5235	-0.9406	1.0000	-0.9740	-0.9787
Med_Time	-0.8569	-0.4319	0.9473	-0.9740	1.0000	0.9818
Med_CGT	-0.8508	-0.3530	0.9840	-0.9787	0.9818	1.0000

          Cross_Score Gap_Score Stop_Score_Gap Cross_Score_Gap Med_Time_N
Scenrio 1  0.33180825  8.235468       4.286381        3.949087          9
Scenrio 2  0.35374610  7.372930       3.258095        4.114835          5
Scenrio 3  0.11052311  7.895862       5.240555        2.655307          7
Scenrio 4  0.25256623  8.043880       3.443119        4.600761          5
Scenrio 5  0.06689682  7.279143       5.629801        1.649341          9
          Med_Time_Y Med_CGT_N Med_CGT_Y      Chi_Y        PV_Ym      Chi_N
Scenrio 1          6    19.325    12.425  0.8354752 3.606941e-01  0.8354752
Scenrio 2          5     9.150     9.150  0.1861448 6.661448e-01  0.1861448
Scenrio 3          7    16.000    16.000  7.1705398 7.411047e-03  7.1705398
Scenrio 4          5     8.450     8.450  7.9315285 4.858074e-03  7.9315285
Scenrio 5          7    19.400    13.500 25.4078535 4.640252e-07 25.4078535
                  PV_N Med_Time Med_CGT
Scenrio 1 3.606941e-01        6  12.425
Scenrio 2 6.661448e-01        5   9.150
Scenrio 3 7.411047e-03        7  16.000
Scenrio 4 4.858074e-03        5   8.450
Scenrio 5 4.640252e-07        9  19.400

P-values of the correlation matrix

	Cross_Score	Gap_Score	Stop_Score_Gap	Cross_Score_Gap	Med_Time	Med_CGT
Cross_Score	NA	0.3004	0.0263	0.0272	0.0318	0.0338
Gap_Score	0.5831	NA	0.3715	0.1826	0.2339	0.2800
Stop_Score_Gap	-3.1148	-0.3594	NA	0.0086	0.0072	0.0012
Cross_Score_Gap	3.0724	1.0642	-4.7992	NA	0.0025	0.0019
Med_Time	-2.8789	-0.8294	5.1206	-7.4502	NA	0.0015
Med_CGT	-2.8042	-0.6535	9.5748	-8.2485	8.9416	NA

LMM analysis

The purpose of the analysis in this subsection is to see if the estimate of the median crossing time in each scenario and time pressure situation depends on the difficulty level of the scenario and the time pressure situation. The model used is LMM, the median estimator is the dependent variable, and the level of difficulty (continuous) and the blood moisture condition (binary) are the independent variables. The scenario itself was taken as a random factor.

Time and Cross_Score_Gap
------------------------

Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Med_Time_N ~ Cross_Score_Gap * TP + (1 | Scenario)
   Data: reg_dat

REML criterion at convergence: 26.7

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-0.7937 -0.4330 -0.1411  0.1394  1.7659 

Random effects:
 Groups   Name        Variance Std.Dev.
 Scenario (Intercept) 0.4394   0.6628  
 Residual             1.2390   1.1131  
Number of obs: 10, groups:  Scenario, 5

Fixed effects:
                      Estimate Std. Error      df t value Pr(>|t|)   
(Intercept)            10.6024     1.9045  5.6152   5.567  0.00177 **
Cross_Score_Gap        -1.0614     0.5346  5.6152  -1.986  0.09756 . 
TPYES                  -2.0536     2.3141  3.0000  -0.887  0.44021   
Cross_Score_Gap:TPYES   0.3104     0.6495  3.0000   0.478  0.66535   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

           R2m       R2c
[1,] 0.4514223 0.5950282

Time and Stop_Score_Gap
-----------------------

Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Med_Time_N ~ Stop_Score_Gap * TP + (1 | Scenario)
   Data: reg_dat

REML criterion at convergence: 24

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.1805 -0.3171 -0.0403  0.1463  1.9951 

Random effects:
 Groups   Name        Variance Std.Dev.
 Scenario (Intercept) 0.000    0.000   
 Residual             1.133    1.064   
Number of obs: 10, groups:  Scenario, 5

Fixed effects:
                     Estimate Std. Error      df t value Pr(>|t|)  
(Intercept)            0.6796     2.2568  6.0000   0.301   0.7735  
Stop_Score_Gap         1.4458     0.5046  6.0000   2.865   0.0286 *
TPYES                  1.2223     3.1916  6.0000   0.383   0.7150  
Stop_Score_Gap:TPYES  -0.5083     0.7137  6.0000  -0.712   0.5030  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
optimizer (nloptwrap) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')

           R2m       R2c
[1,] 0.6064078 0.6064078

Med_CGT_N and Cross_Score_Gap
-----------------------------

Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Med_CGT_N ~ Cross_Score_Gap * TP + (1 | Scenario)
   Data: reg_dat

REML criterion at convergence: 38.3

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-0.66171 -0.47134 -0.16759  0.07015  1.54288 

Random effects:
 Groups   Name        Variance Std.Dev.
 Scenario (Intercept) 5.354    2.314   
 Residual             7.091    2.663   
Number of obs: 10, groups:  Scenario, 5

Fixed effects:
                      Estimate Std. Error     df t value Pr(>|t|)   
(Intercept)             24.944      5.186  5.063   4.810  0.00468 **
Cross_Score_Gap         -3.088      1.456  5.063  -2.121  0.08667 . 
TPYES                   -6.294      5.536  3.000  -1.137  0.33818   
Cross_Score_Gap:TPYES    1.100      1.554  3.000   0.708  0.52999   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

         R2m       R2c
[1,] 0.46047 0.6925876

Med_CGT_N and Stop_Score_Gap
----------------------------

Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Med_CGT_N ~ Stop_Score_Gap * TP + (1 | Scenario)
   Data: reg_dat

REML criterion at convergence: 35.2

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-0.8110 -0.5101 -0.1397  0.0827  1.7909 

Random effects:
 Groups   Name        Variance Std.Dev.
 Scenario (Intercept) 0.8961   0.9466  
 Residual             6.5243   2.5543  
Number of obs: 10, groups:  Scenario, 5

Fixed effects:
                     Estimate Std. Error     df t value Pr(>|t|)  
(Intercept)            -3.849      5.777  5.914  -0.666    0.530  
Stop_Score_Gap          4.189      1.292  5.914   3.243    0.018 *
TPYES                   4.159      7.660  3.000   0.543    0.625  
Stop_Score_Gap:TPYES   -1.537      1.713  3.000  -0.897    0.436  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

           R2m       R2c
[1,] 0.6530961 0.6949904

In Figure XX you can see the medians of the crossing times (Cum gap time) depending on the difficulty of the scenario, Figure XX.A Cross_Score_Gap index and Figure B.XX Stop_Score_Gap index. These two figures show that the median response time increases with the difficulty of the scenario (similar to diagram X). Although it was not statistically significant, the difference between the two levels of time pressure also increases with the difficulty of the scenario.

An alternative way to analyze the Survival curves using (Cox’s) Proportional hazards model

Sir David Cox observed that if the proportional hazards assumption holds (or, is assumed to hold) then it is possible to estimate the effect parameter(s), denoted \(\hat{\beta}\) below, without any consideration of the full hazard function. This approach to survival data is called application of the Cox proportional hazards model^[1], sometimes abbreviated to Cox model or to proportional hazards model^[2].

Let \(X_i= (X_{1,i}, X_{2,i},...,X_{p,i})\) be the realized values of the \(p*\) covariates for subject \(i\). The hazard function for the Cox proportional hazards model has the form

\[ \begin{split} \Lambda(t|X_i) & =\Lambda_0(t)\exp\left(\beta_1 X_{1,i}+\beta_2 X_{2,i}+...+ \beta_p X_{p,i} \right) \\ & = \Lambda_0(t)\exp\left(X_i\beta\right) \end{split} \] [1] Cox, David R (1972). “Regression Models and Life-Tables”. Journal of the Royal Statistical Society, Series B. 34 (2): 187–220. JSTOR 2985181. MR 0341758.

[2] Kalbfleisch, John D.; Schaubel, Douglas E. (10 March 2023). “Fifty Years of the Cox Model”. Annual Review of Statistics and Its Application. 10 (1): 1–23. Bibcode:2023AnRSA..10….1K. doi:10.1146/annurev-statistics-033021-014043. ISSN 2326-8298.