Background
Methods
The log-rank split-rule
The log-rank score split-rule
Random survival forests algorithm
Conditional inference trees and forests
Model evaluation
Simulation study
Simulated time-to-event datasets
Time-to-event datasets with binary covariates
Properties of simulated time-to-event datasets | ||||
---|---|---|---|---|
Type of covariates | Datasets | Sample size | % of censoring | Nature of the |
hazard | ||||
Binary | Data 1 | 100 | 80 | Increasing |
Data 2 | 100 | 50 | Decreasing | |
Data 3 | 250 | 20 | Constant | |
Data 4 | 1000 | 80 | Increasing | |
Data 5 | 1500 | 50 | Decreasing | |
Data 6 | 2000 | 20 | Constant | |
Polytomous | Data 1 | 100 | 20 | Increasing |
Data 2 | 100 | 80 | Constant | |
Data 3 | 250 | 50 | Decreasing | |
Data 4 | 1000 | 20 | Increasing | |
Data 5 | 1500 | 80 | Constant | |
Data 6 | 2000 | 50 | Decreasing | |
Binary & polytomous | Data 1 | 1000 | 20 | Increasing |
Data 2 | 100 | 80 | Decreasing | |
Data 3 | 250 | 50 | Constant | |
Data 4 | 1000 | 20 | Increasing | |
Data 5 | 1500 | 80 | Decreasing | |
Data 6 | 2000 | 50 | Constant | |
Interactions | Data 1 | 100 | 20 | Increasing |
Data 2 | 100 | 50 | Decreasing | |
Data 3 | 1000 | 20 | Increasing | |
Data 4 | 1500 | 50 | Decreasing |
Time-to-event datasets with polytomous covariates
Time-to-event datasets with binary and polytomous covariates
Time-to-event datasets with covariate interactions
Results on simulated datasets
Real data application
Dataset 1
Explanatory variables
Characteristics | Dead N(%) | Alive N(%) | Total | Characteristics | Dead N(%) | Alive N(%) | Total |
---|---|---|---|---|---|---|---|
Mother’s education level | Mother’s occupation | ||||||
Illiterate Mothers | 344(7.7) | 4149(92.3) | 4493 | Not-working | 93(6.9) | 1260(93.1) | 1353 |
Mother completed primary | 119(6.4) | 1749(93.6) | 1868 | Sales and Services | 110 (6.5) | 1589 (93.5) | 1699 |
Secondary and higher | 14(4.2) | 317(95.8) | 331 | Agriculture | 274(7.5) | 3366(92.5) | 3640 |
Partner’s level of education | Births in past 5 years | ||||||
Illiterate Father | 266(7.7) | 3180(92.3) | 3446 | 1-Birth | 93(4.5) | 1982(95.5) | 2075 |
Father completed primary | 170(6.9) | 2287(93.1) | 2457 | 2-Birth | 227(6.5) | 3288(93.5) | 3515 |
Secondary and higher | 41(5.2) | 748(94.8) | 789 | 3-Births | 140(13.6) | 887(86.4) | 1027 |
Birth status | 4-Births | 17(22.7) | 58(77.3) | 75 | |||
Singleton births | 431(6.7) | 6048(93.3) | 6479 | Births in past 1 year | |||
Multiple births (Twins) | 46(21.5) | 167(78.5) | 213 | No-births | 309(6.8) | 4212(93.2) | 4521 |
Sex of the child | 1-Birth | 163(7.6) | 1971(92.4) | 2134 | |||
Males | 258(7.8) | 3067(92.2) | 3325 | 2-Births | 5(13.5) | 32(86.5) | 37 |
Females | 212(6.3) | 3155(93.7) | 3367 | Children Under 5 in Household | |||
Type of place of residence | No-child | 101(34.9) | 188(65.1) | 289 | |||
Urban | 81(5.8) | 1308(94.2) | 1389 | 1-Child | 178(10.5) | 1511(89.5) | 1689 |
Rural | 396(7.5) | 4907(92.5) | 5303 | 2-Children | 146(4.9) | 2831(95.1) | 2977 |
Wealth index | 3-Children | 35(2.5) | 1349(97.5) | 1384 | |||
Poorest | 131(7.5) | 1623(92.5) | 1754 | 4-Children | 17(4.8) | 336(95.2) | 353 |
Poorer | 112(8.5) | 1205(91.5) | 1317 | Mother’s age group | |||
Middle | 86(7.2) | 1109(92.8) | 1195 | Less than 20 years | 29(8.9) | 296(91.1) | 325 |
Richer | 72(6.9) | 969(93.1) | 1041 | 20-29 years | 235(6.5) | 3376(93.5) | 3611 |
Richest | 76(5.5) | 1309(94.5) | 1385 | 30-39 years | 164(7.4) | 2054(92.6) | 2218 |
Children ever born | 40 years +
| 49(7.9) | 489(90.1) | 538 | |||
One child | 20(3.3) | 581(96.7) | 601 | Birth order number | |||
Two children | 81(7.1) | 1065(92.9) | 1146 | First child | 95(7.6) | 1154(92.4) | 1249 |
Three children | 67(6.6) | 953(93.4) | 1020 | Second to Third child | 117(5.6) | 1974(94.4) | 2091 |
Four and more | 309(7.9) | 3616(92.1) | 3925 | 4
th
-6
th
child | 149(7.1) | 1949(92.9) | 2098 |
Birth order number |
t
h
+child | 116(9.3) | 1138(90.7) | 1254 | |||
First child | 95(7.6) | 1154(92.4) | 1249 | Sex of household head | |||
Second to Third child | 117(5.6) | 1974(94.4) | 2091 | Male | 341(6.7) | 4771(93.3) | 5112 |
4
th
-6
th
child | 149(7.1) | 1949(92.9) | 2098 | Female | 136(8.6) | 1444(91.4) | 1580 |
t
h
+child | 116(9.2) | 1138(90.8) | 1254 | Source of drinking water | |||
Religion | Piped water | 76(5.9) | 1204(94.1) | 1280 | |||
Catholics | 217(7.4) | 2722(92.6) | 2939 | Borehole | 216(7.3) | 2731(92.7) | 2947 |
Muslims | 69(7.5) | 852(92.5) | 921 | Well | 93(6.9) | 1261(93.1) | 1354 |
Other Christians | 187(6.8) | 2571(93.2) | 2758 | Surface/Rain/Pond/Lake/tank | 70(8.5) | 756(91.5) | 826 |
Others | 4(5.4) | 70(94.6) | 74 | Other | 22(7.7) | 263(92.3) | 285 |
Type of toilet facility | Age at first birth | ||||||
Flush toilet | 5(4.1) | 116(95.9) | 121 | Less than 20 years | 347(7.5) | 4291(92.5) | 4638 |
Pitlatrine | 376(6.9) | 5031(93.1) | 5407 | 20-29 years | 127(6.3) | 1899(93.7) | 2026 |
No-facility | 96(8.2) | 1068(91.8) | 1164 | 30-39 years | 3(12.0) | 22(88.0) | 25 |
Dataset 2
Explanatory variable
Characteristics | Dead N(%) | AliveN (%) | Total | Characteristics | Dead N(%) | Alive N(%) | Total |
---|---|---|---|---|---|---|---|
Age at diagnosis | Ethionamide | ||||||
Below 30 | 35(81.3) | 8(18.6) | 43 | Not prescribed | 25(64.10) | 14(35.89) | 39 |
Above 30 | 43(68.25) | 20(31.75) | 63 | Prescribed | 54(79.41) | 14(20.59) | 68 |
Gender | Ofloxacin | ||||||
Females | 41(83.67) | 8(16.33) | 49 | Not prescribed | 48(70.59) | 20(29.41) | 68 |
Males | 38(65.52) | 20(34.48) | 58 | Prescribed | 31(79.49) | 8(20.51) | 39 |
smoking status | Ofloxacin and moxifloxacin | ||||||
No | 28(65.12) | 15(34.88) | 43 | Not prescribed | 72(72.73) | 27(27.27) | 99 |
Yes | 38(79.17) | 10(20.83) | 48 | Prescribed | 7(87.50) | 1(12.50) | 8 |
HIV plus ART status | Amikacin | ||||||
HIV -ve | 46(73.02) | 17(26.98) | 63 | Not prescribed | 76(73.79) | 27(26.21) | 103 |
HIV +ve ART | 24(68.57) | 11(31.43) | 35 | Prescribed | 3(75.00) | 1(25.00) | 4 |
HIV +ve no ART | 9 (100.00) | 0 (0.00) | 9 | Capreomycin | |||
Cohort | Not prescribed | 8(88.98) | 1(11.11) | 9 | |||
B | 54(83.08) | 11(16.92) | 65 | Prescribed | 71(72.45) | 27(27.55) | 98 |
N | 12(80.00) | 3(20.00) | 15 | Dapsone | |||
S | 13(48.15) | 14(51.85) | 27 | Not prescribed | 43(67.19) | 21(32.81) | 64 |
Race | Prescribed | 36(83.72) | 7(16.28) | 43 | |||
Blacks | 34(64.15) | 19(35.85) | 53 | Augmentin | |||
Mixed ancestry | 45(83.33) | 9(16.67) | 54 | Not prescribed | 28(66.67) | 14(33.33) | 42 |
Drugs used | Prescribed | 51(78.46) | 14(21.54) | 65 | |||
Isoniazid | Clofazamine | ||||||
Not prescribed | 57(83.82) | 11(16.18) | 68 | Not prescribed | 70(82.35) | 15(17.65) | 85 |
Prescribed | 22(56.41) | 17(43.59) | 39 | Prescribed | 9(40.91) | 13(59.09) | 22 |
Etambutol | Azithromycin | ||||||
Not prescribed | 39(66.10) | 20(33.89) | 59 | Not prescribed | 75(76.53) | 23(23.47) | 98 |
Prescribed | 40(83.33) | 8(16.67) | 48 | Prescribed | 4(44.44) | 5(55.56) | 9 |
Pyrazinainamide | Amoxicillin | ||||||
Not prescribed | 14(58.33) | 10(41.67) | 24 | Not prescribed | 49(71.01) | 20(28.99) | 69 |
Prescribed | 65(78.3) | 18(21.69) | 83 | Prescribed | 30(78.95) | 8(21.05) | 38 |
Clarithromycin | |||||||
Not prescribed | 19(70.37) | 8(29.63) | 27 | ||||
Prescribed | 60(75.00) | 20(25.00) | 80 |