Delving into Causal Discovery in Health-Related Quality of Life Questionnaires
<p>The seven synthetic directed acyclic graphs (numbered (1)–(7)) corresponding to the seven hypothetical health-related quality of life questionnaires. The letters represent the questions in each HRQoL questionnaire.</p> "> Figure 2
<p>The mean relative Hamming distance (HD) is displayed across the different sample sizes (number of participants) considered for each of the five algorithms. The notations DAG #1, 2, 3, 4, 5, 6, and 7 correspond to the seven synthetic directed acyclic graphs that are described in <a href="#sec2dot2dot1-algorithms-17-00138" class="html-sec">Section 2.2.1</a> and are displayed in <a href="#algorithms-17-00138-f001" class="html-fig">Figure 1</a>.</p> "> Figure 3
<p>The mean relative structural Hamming distance (SHD) is displayed across the different sample sizes (number of participants) considered for each of the five algorithms. The notations DAG #1, 2, 3, 4, 5, 6, and 7 correspond to the seven synthetic directed acyclic graphs that are described in <a href="#sec2dot2dot1-algorithms-17-00138" class="html-sec">Section 2.2.1</a> and are displayed in <a href="#algorithms-17-00138-f001" class="html-fig">Figure 1</a>.</p> "> Figure 4
<p>Serialization of a fragment of a health-related quality of life questionnaire as a Resource Description Framework Turtle.</p> "> Figure 5
<p>Serialization of a sample hypothetical patient and their responses to two questions as a Resource Description Framework Turtle.</p> "> Figure 6
<p>A sample cause–effect graph in Resource Description Framework Turtle format, corresponding to DAG #6 (see <a href="#algorithms-17-00138-f001" class="html-fig">Figure 1</a>). The red nodes represent specific questions in DAG #6 (namely, the questions Q, R, S, T, U, V, W, X, Y, and Z), while the cyan nodes represent the respective hypothetical facets and second-level domains of the questions. The labels over the edges reflect the respective semantics including the cause–effect relationships between questions. For instance, over the edge that connects questions S and T, the label “is cause of” shows that question S is the cause of question T. Moreover, question S has a facet of “Self-esteem” that belongs to the second-level domain “Psychological”.</p> "> Figure 7
<p>A sample cause–effect graph corresponding to DAG #6 (<a href="#algorithms-17-00138-f001" class="html-fig">Figure 1</a>), generated by SemSpect. The numbers in parenthesis indicate the counts of respective entities (e.g., the bigger cluster in the middle contains 26 questions). The node in red corresponds each time to the selected node for investigation, while the arrows next to the predicates indicate the directionality of the respective properties; for instance, the sample questionnaire (red node) contains 26 questions in total.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
2.1. Directed Acyclic Graph
2.2. Methodology
2.2.1. Synthetic Directed Acyclic Graphs
2.2.2. Simulations
- Grow–Shrink (GS) [60], employing the “gs” function: This is based on the Grow–Shrink Markov blanket, which is a Markov blanket detection algorithm.
- Incremental Association (IA) [61], employing the “iamb” function: This is based on the Markov blanket detection algorithm of the same name.
- Interleaved Incremental Association (Inter-IA) [62], employing the “inter.iamb” function: This is a variant of the IA algorithm, which differentiates in using gradual forward selection to avoid false positives in the Markov blanket detection phase.
- Fast Incremental Association (Fast-IA), employing the “fast.iamb” function: This is another variant of the IA algorithm that employs speculative stepwise forward selection to reduce the number of conditional independence tests.
- The mean HD between the estimated and the true DAG across the 1000 iterations.
- The mean relative HD across the 1000 iterations, defined as the mean HD between the estimated and the true DAG, divided by the number of edges of the true DAG.
- The number of the cases where the HD between the estimated and the true DAG was zero across the 1000 iterations.
- The mean SHD between the estimated and the true DAG across the 1000 iterations.
- The mean relative SHD across the 1000 iterations, defined as the mean SHD between the estimated and the true DAG, divided by the number of edges of the true DAG.
- The number of cases where the SHD between the estimated and the true DAG was zero across the 1000 iterations.
2.2.3. Shareability and Interoperability
2.2.4. Available Resources
3. Results
3.1. Simulation Findings
3.2. Resource Description Framework Knowledge Graph
3.2.1. Representing Questionnaires and Responses
- ○
- The excerpt shown in the figure only includes three sample hypothetical questions for illustration purposes. The representation of an actual HRQoL questionnaire would include all the questions.
- ○
- In order to also represent the order of questions in the questionnaire, every question contains information about the previous one via predicate “:isAfter”.
- ○
- The association of questions to facets (see Section 2.2.3) is materialized via DDI-RDF predicate “disco:concept”.
- ○
- The association of facets to domains is materialized via SKOS predicate “skos:broader”, which represents a narrower–broader interrelationship.
3.2.2. Representing Cause–Effect Relationships
4. Discussion
4.1. Causal Discovery
4.2. Knowledge Representation via Semantic KGs
4.3. Impact, Limitations, and Future Work
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
PC | DAG # | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|---|
# of nodes | 5 | 10 | 11 | 15 | 21 | 26 | 26 | |
Sample size n | # of edges | 5 | 9 | 11 | 16 | 17 | 21 | 19 |
100 | HD | 2.01 | 2.70 | 4.89 | 8.84 | 7.12 | 8.86 | 7.66 |
rHD | 0.40 | 0.30 | 0.44 | 0.55 | 0.42 | 0.42 | 0.40 | |
0’s in HD | 13 | 11 | 0 | 0 | 0 | 0 | 0 | |
SHD | 3.33 | 5.41 | 8.60 | 12.99 | 10.78 | 14.56 | 11.89 | |
rSHD | 0.67 | 0.60 | 0.78 | 0.81 | 0.63 | 0.69 | 0.63 | |
0’s in SHD | 5 | 3 | 0 | 0 | 0 | 0 | 0 | |
500 | HD | 0.52 | 0.60 | 1.25 | 1.85 | 2.33 | 2.14 | 1.82 |
rHD | 0.10 | 0.07 | 0.11 | 0.12 | 0.14 | 0.10 | 0.10 | |
0’s in HD | 532 | 491 | 226 | 107 | 45 | 84 | 142 | |
SHD | 0.95 | 1.16 | 4.05 | 5.62 | 6.24 | 5.42 | 3.91 | |
rSHD | 0.19 | 0.13 | 0.37 | 0.35 | 0.37 | 0.26 | 0.21 | |
0’s in SHD | 526 | 479 | 85 | 19 | 8 | 20 | 48 | |
1000 | HD | 0.18 | 0.21 | 0.50 | 0.56 | 1.63 | 1.50 | 1.48 |
rHD | 0.04 | 0.02 | 0.05 | 0.04 | 0.10 | 0.07 | 0.08 | |
0’s in HD | 832 | 805 | 603 | 561 | 157 | 220 | 220 | |
SHD | 0.30 | 0.42 | 1.72 | 3.14 | 4.85 | 3.28 | 2.92 | |
rSHD | 0.06 | 0.05 | 0.16 | 0.20 | 0.29 | 0.16 | 0.15 | |
0’s in SHD | 828 | 797 | 378 | 171 | 46 | 141 | 149 | |
2000 | HD | 0.10 | 0.11 | 0.20 | 0.30 | 0.97 | 1.26 | 1.35 |
rHD | 0.02 | 0.01 | 0.02 | 0.02 | 0.06 | 0.06 | 0.07 | |
0’s in HD | 909 | 896 | 820 | 747 | 373 | 270 | 231 | |
SHD | 0.12 | 0.19 | 0.68 | 2.02 | 3.32 | 2.20 | 2.49 | |
rSHD | 0.02 | 0.02 | 0.06 | 0.13 | 0.20 | 0.10 | 0.13 | |
0’s in SHD | 905 | 888 | 716 | 325 | 144 | 252 | 211 | |
5000 | HD | 0.10 | 0.12 | 0.22 | 0.28 | 0.77 | 1.26 | 1.40 |
rHD | 0.02 | 0.01 | 0.02 | 0.02 | 0.05 | 0.06 | 0.07 | |
0’s in HD | 903 | 889 | 807 | 757 | 456 | 272 | 226 | |
SHD | 0.11 | 0.18 | 0.37 | 1.07 | 2.29 | 2.12 | 2.37 | |
rSHD | 0.02 | 0.02 | 0.03 | 0.07 | 0.13 | 0.10 | 0.12 | |
0’s in SHD | 903 | 889 | 803 | 573 | 299 | 271 | 226 | |
10,000 | HD | 0.10 | 0.12 | 0.22 | 0.33 | 0.78 | 1.27 | 1.36 |
rHD | 0.02 | 0.01 | 0.02 | 0.02 | 0.05 | 0.06 | 0.07 | |
0’s in HD | 905 | 885 | 801 | 712 | 445 | 249 | 232 | |
SHD | 0.12 | 0.23 | 0.33 | 0.59 | 1.60 | 2.06 | 2.39 | |
rSHD | 0.02 | 0.03 | 0.03 | 0.04 | 0.09 | 0.10 | 0.13 | |
0’s in SHD | 905 | 885 | 801 | 692 | 390 | 249 | 232 |
GS | DAG # | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|---|
# of nodes | 5 | 10 | 11 | 15 | 21 | 26 | 26 | |
Sample size n | # of edges | 5 | 9 | 11 | 16 | 17 | 21 | 19 |
100 | HD | 1.48 | 2.27 | 4.42 | 9.04 | 8.62 | 11.89 | 10.02 |
rHD | 0.30 | 0.25 | 0.40 | 0.56 | 0.51 | 0.57 | 0.53 | |
0’s in HD | 49 | 17 | 0 | 0 | 0 | 0 | 0 | |
SHD | 3.60 | 5.68 | 8.76 | 13.37 | 11.62 | 16.65 | 14.41 | |
rSHD | 0.72 | 0.63 | 0.80 | 0.84 | 0.68 | 0.79 | 0.76 | |
0’s in SHD | 28 | 1 | 0 | 0 | 0 | 0 | 0 | |
500 | HD | 0.31 | 0.40 | 1.15 | 2.22 | 3.17 | 4.83 | 3.58 |
rHD | 0.06 | 0.04 | 0.10 | 0.14 | 0.19 | 0.23 | 0.19 | |
0’s in HD | 714 | 645 | 241 | 65 | 11 | 2 | 18 | |
SHD | 1.03 | 2.45 | 3.69 | 7.73 | 6.28 | 10.37 | 7.58 | |
rSHD | 0.21 | 0.27 | 0.34 | 0.48 | 0.37 | 0.49 | 0.40 | |
0’s in SHD | 703 | 283 | 38 | 2 | 0 | 0 | 0 | |
1000 | HD | 0.14 | 0.18 | 0.50 | 0.70 | 1.92 | 3.07 | 2.26 |
rHD | 0.03 | 0.02 | 0.05 | 0.04 | 0.11 | 0.15 | 0.12 | |
0’s in HD | 870 | 832 | 580 | 498 | 94 | 52 | 116 | |
SHD | 0.37 | 1.05 | 1.71 | 3.76 | 4.44 | 6.16 | 4.32 | |
rSHD | 0.07 | 0.12 | 0.16 | 0.24 | 0.26 | 0.29 | 0.23 | |
0’s in SHD | 866 | 602 | 228 | 101 | 3 | 20 | 62 | |
2000 | HD | 0.13 | 0.17 | 0.32 | 0.38 | 1.23 | 2.16 | 1.67 |
rHD | 0.03 | 0.02 | 0.03 | 0.02 | 0.07 | 0.10 | 0.09 | |
0’s in HD | 877 | 841 | 731 | 679 | 264 | 145 | 195 | |
SHD | 0.35 | 0.54 | 0.96 | 1.28 | 3.25 | 3.26 | 2.59 | |
rSHD | 0.07 | 0.06 | 0.09 | 0.08 | 0.19 | 0.16 | 0.14 | |
0’s in SHD | 877 | 789 | 565 | 444 | 43 | 130 | 175 | |
5000 | HD | 0.15 | 0.18 | 0.26 | 0.35 | 0.94 | 1.55 | 1.39 |
rHD | 0.03 | 0.02 | 0.02 | 0.02 | 0.06 | 0.07 | 0.07 | |
0’s in HD | 857 | 820 | 769 | 701 | 414 | 203 | 225 | |
SHD | 0.41 | 0.52 | 0.54 | 0.55 | 2.02 | 2.13 | 1.97 | |
rSHD | 0.08 | 0.06 | 0.05 | 0.03 | 0.12 | 0.10 | 0.10 | |
0’s in SHD | 857 | 816 | 760 | 674 | 268 | 201 | 220 | |
10,000 | HD | 0.11 | 0.18 | 0.31 | 0.36 | 0.75 | 1.37 | 1.26 |
rHD | 0.02 | 0.02 | 0.03 | 0.02 | 0.04 | 0.07 | 0.07 | |
0’s in HD | 889 | 836 | 732 | 687 | 475 | 245 | 275 | |
SHD | 0.29 | 0.48 | 0.63 | 0.50 | 1.50 | 1.76 | 1.67 | |
rSHD | 0.06 | 0.05 | 0.06 | 0.03 | 0.09 | 0.08 | 0.09 | |
0’s in SHD | 889 | 831 | 727 | 680 | 375 | 326 | 345 |
IA | DAG # | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|---|
# of nodes | 5 | 10 | 11 | 15 | 21 | 26 | 26 | |
Sample size n | # of edges | 5 | 9 | 11 | 16 | 17 | 21 | 19 |
100 | HD | 1.54 | 2.21 | 4.32 | 8.06 | 7.85 | 11.03 | 9.93 |
rHD | 0.31 | 0.25 | 0.39 | 0.50 | 0.46 | 0.53 | 0.52 | |
0’s in HD | 44 | 25 | 0 | 0 | 0 | 0 | 0 | |
SHD | 3.66 | 5.68 | 8.72 | 12.79 | 11.17 | 16.72 | 14.32 | |
rSHD | 0.73 | 0.63 | 0.79 | 0.80 | 0.66 | 0.80 | 0.75 | |
0’s in SHD | 25 | 2 | 0 | 0 | 0 | 0 | 0 | |
500 | HD | 0.27 | 0.37 | 1.05 | 1.73 | 2.79 | 4.14 | 3.01 |
rHD | 0.05 | 0.04 | 0.10 | 0.11 | 0.16 | 0.20 | 0.16 | |
0’s in HD | 747 | 665 | 280 | 124 | 23 | 15 | 37 | |
SHD | 0.89 | 2.29 | 3.49 | 7.35 | 5.97 | 9.96 | 7.00 | |
rSHD | 0.18 | 0.25 | 0.32 | 0.46 | 0.35 | 0.47 | 0.37 | |
0’s in SHD | 736 | 290 | 46 | 5 | 1 | 0 | 2 | |
1000 | HD | 0.10 | 0.20 | 0.50 | 0.60 | 1.95 | 2.85 | 2.11 |
rHD | 0.02 | 0.02 | 0.05 | 0.04 | 0.11 | 0.14 | 0.11 | |
0’s in HD | 898 | 819 | 589 | 553 | 122 | 36 | 118 | |
SHD | 0.30 | 1.10 | 1.80 | 3.50 | 4.56 | 6.06 | 4.14 | |
rSHD | 0.06 | 0.12 | 0.16 | 0.22 | 0.27 | 0.29 | 0.22 | |
0’s in SHD | 898 | 581 | 255 | 111 | 10 | 12 | 50 | |
2000 | HD | 0.12 | 0.18 | 0.32 | 0.40 | 1.22 | 2.30 | 1.63 |
rHD | 0.02 | 0.02 | 0.03 | 0.03 | 0.07 | 0.11 | 0.09 | |
0’s in HD | 887 | 837 | 713 | 655 | 271 | 69 | 202 | |
SHD | 0.34 | 0.62 | 0.94 | 1.29 | 3.14 | 4.26 | 2.53 | |
rSHD | 0.07 | 0.07 | 0.09 | 0.08 | 0.18 | 0.20 | 0.13 | |
0’s in SHD | 887 | 787 | 532 | 395 | 176 | 60 | 180 | |
5000 | HD | 0.14 | 0.21 | 0.34 | 0.41 | 1.04 | 2.00 | 1.18 |
rHD | 0.03 | 0.02 | 0.03 | 0.03 | 0.06 | 0.10 | 0.06 | |
0’s in HD | 867 | 808 | 694 | 665 | 325 | 90 | 250 | |
SHD | 0.36 | 0.57 | 0.69 | 0.58 | 2.06 | 3.38 | 2.17 | |
rSHD | 0.07 | 0.06 | 0.06 | 0.04 | 0.12 | 0.16 | 0.11 | |
0’s in SHD | 867 | 799 | 687 | 643 | 200 | 86 | 194 | |
10,000 | HD | 0.12 | 0.18 | 0.33 | 0.43 | 1.05 | 1.90 | 1.13 |
rHD | 0.02 | 0.02 | 0.03 | 0.03 | 0.06 | 0.09 | 0.06 | |
0’s in HD | 879 | 837 | 715 | 638 | 352 | 121 | 305 | |
SHD | 0.30 | 0.48 | 0.63 | 0.60 | 1.60 | 2.30 | 1.63 | |
rSHD | 0.06 | 0.05 | 0.06 | 0.04 | 0.09 | 0.11 | 0.09 | |
0’s in SHD | 879 | 834 | 713 | 633 | 308 | 113 | 310 |
Inter-IA | DAG # | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|---|
# of nodes | 5 | 10 | 11 | 15 | 21 | 26 | 26 | |
Sample size n | # of edges | 5 | 9 | 11 | 16 | 17 | 21 | 19 |
100 | HD | 1.52 | 2.70 | 4.89 | 7.90 | 7.12 | 10.34 | 8.68 |
rHD | 0.30 | 0.30 | 0.44 | 0.49 | 0.42 | 0.49 | 0.46 | |
0’s in HD | 63 | 11 | 0 | 0 | 0 | 0 | 0 | |
SHD | 3.65 | 5.41 | 8.60 | 12.74 | 10.78 | 16.46 | 14.19 | |
rSHD | 0.73 | 0.60 | 0.78 | 0.80 | 0.63 | 0.78 | 0.75 | |
0’s in SHD | 35 | 3 | 0 | 0 | 0 | 0 | 0 | |
500 | HD | 0.27 | 0.60 | 1.25 | 1.69 | 2.33 | 2.83 | 2.05 |
rHD | 0.05 | 0.07 | 0.11 | 0.11 | 0.14 | 0.13 | 0.11 | |
0’s in HD | 742 | 491 | 226 | 176 | 45 | 37 | 99 | |
SHD | 0.93 | 1.16 | 4.05 | 7.34 | 6.24 | 8.53 | 5.85 | |
rSHD | 0.19 | 0.13 | 0.37 | 0.46 | 0.37 | 0.41 | 0.31 | |
0’s in SHD | 737 | 479 | 85 | 10 | 8 | 0 | 6 | |
1000 | HD | 0.14 | 0.21 | 0.50 | 0.55 | 1.63 | 1.94 | 1.50 |
rHD | 0.03 | 0.02 | 0.05 | 0.03 | 0.10 | 0.09 | 0.08 | |
0’s in HD | 875 | 805 | 603 | 584 | 157 | 77 | 208 | |
SHD | 0.38 | 0.42 | 1.72 | 3.40 | 4.85 | 4.76 | 3.31 | |
rSHD | 0.08 | 0.05 | 0.16 | 0.21 | 0.29 | 0.23 | 0.17 | |
0’s in SHD | 871 | 797 | 378 | 103 | 46 | 22 | 85 | |
2000 | HD | 0.14 | 0.11 | 0.20 | 0.38 | 0.97 | 1.94 | 1.28 |
rHD | 0.03 | 0.01 | 0.02 | 0.02 | 0.06 | 0.09 | 0.07 | |
0’s in HD | 865 | 896 | 820 | 684 | 373 | 83 | 249 | |
SHD | 0.40 | 0.19 | 0.68 | 1.27 | 3.32 | 3.63 | 1.97 | |
rSHD | 0.08 | 0.02 | 0.06 | 0.08 | 0.20 | 0.17 | 0.10 | |
0’s in SHD | 865 | 888 | 716 | 421 | 144 | 69 | 228 | |
5000 | HD | 0.13 | 0.12 | 0.22 | 0.42 | 0.77 | 1.83 | 1.32 |
rHD | 0.03 | 0.01 | 0.02 | 0.03 | 0.05 | 0.09 | 0.07 | |
0’s in HD | 877 | 889 | 807 | 649 | 456 | 113 | 247 | |
SHD | 0.35 | 0.18 | 0.37 | 0.67 | 2.29 | 3.10 | 1.88 | |
rSHD | 0.07 | 0.02 | 0.03 | 0.04 | 0.13 | 0.15 | 0.10 | |
0’s in SHD | 877 | 889 | 803 | 611 | 299 | 110 | 241 | |
10,000 | HD | 0.14 | 0.12 | 0.22 | 0.40 | 0.78 | 1.58 | 1.33 |
rHD | 0.03 | 0.01 | 0.02 | 0.03 | 0.05 | 0.08 | 0.07 | |
0’s in HD | 864 | 885 | 801 | 669 | 445 | 179 | 241 | |
SHD | 0.35 | 0.23 | 0.33 | 0.59 | 1.60 | 2.38 | 1.81 | |
rSHD | 0.07 | 0.03 | 0.03 | 0.04 | 0.09 | 0.11 | 0.10 | |
0’s in SHD | 864 | 885 | 801 | 656 | 390 | 177 | 238 |
Fast-IA | DAG # | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|---|
# of nodes | 5 | 10 | 11 | 15 | 21 | 26 | 26 | |
Sample size n | # of edges | 5 | 9 | 11 | 16 | 17 | 21 | 19 |
100 | HD | 3.82 | 6.75 | 9.51 | 13.87 | 11.98 | 13.69 | 11.61 |
rHD | 0.76 | 0.75 | 0.86 | 0.87 | 0.70 | 0.65 | 0.61 | |
0’s in HD | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
SHD | 4.23 | 7.21 | 10.23 | 14.26 | 13.10 | 16.28 | 14.36 | |
rSHD | 0.85 | 0.80 | 0.93 | 0.89 | 0.77 | 0.78 | 0.76 | |
0’s in SHD | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
500 | HD | 2.85 | 3.09 | 5.04 | 7.81 | 5.04 | 6.78 | 6.81 |
rHD | 0.57 | 0.34 | 0.46 | 0.49 | 0.30 | 0.32 | 0.36 | |
0’s in HD | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
SHD | 3.77 | 5.18 | 8.12 | 11.34 | 7.45 | 12.22 | 12.29 | |
rSHD | 0.75 | 0.58 | 0.74 | 0.71 | 0.44 | 0.58 | 0.65 | |
0’s in SHD | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1000 | HD | 2.82 | 3.09 | 5.06 | 7.64 | 4.89 | 6.56 | 6.58 |
rHD | 0.56 | 0.34 | 0.46 | 0.48 | 0.29 | 0.31 | 0.35 | |
0’s in HD | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
SHD | 3.67 | 4.60 | 7.54 | 10.56 | 6.72 | 11.11 | 10.56 | |
rSHD | 0.74 | 0.51 | 0.69 | 0.66 | 0.40 | 0.53 | 0.56 | |
0’s in SHD | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
2000 | HD | 0.09 | 0.96 | 1.14 | 1.90 | 1.23 | 2.17 | 1.26 |
rHD | 0.02 | 0.11 | 0.10 | 0.12 | 0.07 | 0.10 | 0.07 | |
0’s in HD | 915 | 182 | 151 | 63 | 279 | 55 | 266 | |
SHD | 0.14 | 3.43 | 3.94 | 5.29 | 2.98 | 4.93 | 1.84 | |
rSHD | 0.03 | 0.38 | 0.36 | 0.33 | 0.18 | 0.23 | 0.10 | |
0’s in SHD | 915 | 176 | 117 | 32 | 86 | 50 | 238 | |
5000 | HD | 0.08 | 1.06 | 1.21 | 1.85 | 1.00 | 1.76 | 1.26 |
rHD | 0.02 | 0.12 | 0.11 | 0.12 | 0.06 | 0.08 | 0.07 | |
0’s in HD | 918 | 75 | 90 | 49 | 368 | 122 | 260 | |
SHD | 0.11 | 3.83 | 3.99 | 4.84 | 1.90 | 3.78 | 1.63 | |
rSHD | 0.02 | 0.43 | 0.36 | 0.30 | 0.11 | 0.18 | 0.09 | |
0’s in SHD | 918 | 75 | 89 | 48 | 262 | 122 | 258 | |
10,000 | HD | 0.12 | 0.22 | 0.30 | 0.36 | 0.90 | 1.53 | 1.31 |
rHD | 0.02 | 0.02 | 0.03 | 0.02 | 0.05 | 0.07 | 0.07 | |
0’s in HD | 882 | 804 | 740 | 688 | 388 | 211 | 249 | |
SHD | 0.34 | 0.56 | 0.61 | 0.50 | 1.39 | 2.15 | 1.76 | |
rSHD | 0.07 | 0.06 | 0.06 | 0.03 | 0.08 | 0.10 | 0.09 | |
0’s in SHD | 882 | 799 | 726 | 669 | 333 | 206 | 248 |
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Cause Domain | Effect Domain | Count |
---|---|---|
Environment | Physical health | 3 |
Environment | Psychological | 2 |
Environment | Social relationships | 2 |
Physical health | Environment | 1 |
Physical health | Social relationships | 1 |
Psychological | Environment | 1 |
Psychological | Social relationships | 1 |
Social relationships | Environment | 1 |
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Ganopoulou, M.; Kontopoulos, E.; Fokianos, K.; Koparanis, D.; Angelis, L.; Kotsianidis, I.; Moysiadis, T. Delving into Causal Discovery in Health-Related Quality of Life Questionnaires. Algorithms 2024, 17, 138. https://doi.org/10.3390/a17040138
Ganopoulou M, Kontopoulos E, Fokianos K, Koparanis D, Angelis L, Kotsianidis I, Moysiadis T. Delving into Causal Discovery in Health-Related Quality of Life Questionnaires. Algorithms. 2024; 17(4):138. https://doi.org/10.3390/a17040138
Chicago/Turabian StyleGanopoulou, Maria, Efstratios Kontopoulos, Konstantinos Fokianos, Dimitris Koparanis, Lefteris Angelis, Ioannis Kotsianidis, and Theodoros Moysiadis. 2024. "Delving into Causal Discovery in Health-Related Quality of Life Questionnaires" Algorithms 17, no. 4: 138. https://doi.org/10.3390/a17040138