Information for 4505 patients who met the inclusion criteria was extracted from SEER database. Of those patients, 100 patients with 0 survival time were excluded and 4405 were included for final analysis. Descriptive characteristics were summarized into Table 1. The median age of these patients was 30 years old, and 19.09% of them were older than 60 years. About half of the patients were male (57.05%). The minority of the patients had tumors more than 100 mm (4.74%), metastasis (5.93%), III stage (0.61%) and IV stage (8.94%). Furthermore, the majority of the patients experienced surgery (77.80%) and chemotherapy (67.17%), while few cases (14.10%) underwent radiation.
Table 1
Basic characteristics of osteosarcoma patients from SEER
Covariates | n (%) |
Age, years, median (Q1, Q3) | 30.00(19.00, 54.00) |
>60 years | 841(19.09%) |
<=60 years | 3564(80.91%) |
Sex, Male | 2513(57.05%) |
Year of diagnosis | |
1970s ~ 1980 s | 803(18.23%) |
1990s ~ 2000 s | 3602(81.77%) |
Race | |
White and black | 4015(91.15%) |
others | 390(8.85%) |
Tumor Size | |
< 100 mm | 655(14.87%) |
> 100 mm | 209(4.74%) |
unknown | 3541(80.39%) |
Extend of disease | |
Confined | 283(6.42%) |
Local Invasion | 887(20.14%) |
Metastasis | 261(5.93%) |
Unknown | 2974(67.51%) |
AJCC | |
I | 207(4.70%) |
II | 886(20.11%) |
III | 27(0.61%) |
IV | 394(8.94%) |
Unknown | 2891(65.63%) |
Surgery, yes | 3427(77.80%) |
Radiation, yes | 621(14.10%) |
Chemotherapy, yes | 2959(67.17%) |
Outcome | |
All-cause death | |
Alive | |
Q1, the first quartile, Q3, the third quartile |
AJCC, American Joint Committee on Cancer for staging. |
Assumption tests of proportional hazard and the homogeneity of censoring mechanism of all covariates on 10 covariates were summarized into Table 2. Dichotomous age, diagnosis year, race, the extend of disease, surgery status and radiation status met proportional hazard assumption, while others failed to pass the test. Dichotomous age, sex, race and radiation met the homogeneity of censoring mechanism, and the resting 7 covariates failed, which implied IPCW regression with group-specified weights was preferable to IPCW regression with individual weights.
Table 2
Assumption test of proportional hazard and homogeneity of censoring mechanism
Covariates | Proportional hazard assumption | Homogeneity of censoring mechanism |
KM curves | ln (-ln(S(t))) vs ln(t) Curves | Graphical analysis | Log-rank test |
Age(continuous) | - | - | - | - |
Age(binary) | ✓ | ✓ | ✓ | ✓ |
Sex | ✕ | ✕ | ✓ | ✓ |
Year of diagnosis | ✓ | ✓ | ✕ | ✕ |
Race | ✓ | ✓ | ✓ | ✓ |
Tumor size | ✕ | ✕ | ✕ | ✕ |
Extend of disease | ✓ | ✓ | ✕ | ✕ |
AJCC | ✓ | ✕ | ✕ | ✕ |
Surgery | ✓ | ✓ | ✕ | ✕ |
Radiation | ✓ | ✓ | ✓ | ✓ |
Chemotherapy | ✕ | ✕ | ✕ | ✕ |
KM, Kaplan-Meier. AJCC, American Joint Committee on Cancer for staging |
Overall, all covariates were associated with overall survival in univariable analyses (Table 3). In difference analysis, log-rank test, Wilcoxon test and difference in RMST presented similar results at ɑ=0.05 in all covariates but sex. Since sex did not satisfy PH assumption, Wilcoxon test was more appropriate and showed no statistical difference in overall survival between male and female patients. Difference in RMST, however, claimed male patients would live shorter by 24.31 months than female ones significantly (p = 0.004). In regressions, PV regressions exhibited similar effect estimates and conclusion to difference estimation in RMST from Kaplan-Meier method; similar effect estimates of covariates were shown in IPCW regression with group-specified weights, but sex, race and chemotherapy turned to be insignificant, p = 0.42 and p = 0.35, respectively.
Table 3
univariable analysis based on conventional survival analysis and restricted mean survival time
Covariates | Difference analysis | Regression |
Survival rate | Difference in RMST a | Cox regression b | RMST-based regression |
| Log-rank | Wilcoxon | | | PV regression a | IPCW regression (individual weights) a | IPCW regression (group-specified weight) a |
| | | | | | | |
Age (continuous) | - | - | - | 1.13, < 0.001 | -4.09, < 0.001 | -4.35, < 0.001 | - |
Age(binary) | | | | | | | |
>60 years | < 0.001 | < 0.001 | -146.64, < 0.001 | 3.82, < 0.001 | -147.29, < 0.001 | -137.17, < 0.001 | -146.43, < 0.001 |
<=60 years | - | - | ref | ref | ref | ref | ref |
Sex | | | | | | | |
Male | 0.005 | 0.058 | -24.31, 0.004 | 1.12, 0.005 | -24.22, 0.004 | -60.12, 0.46 | -23.98, 0.42 |
Female | - | - | ref | ref | ref | ref | ref |
Year of diagnosis | | | | | | | |
1970s ~ 1980 s | < 0.001 | < 0.001 | -26.89, < 0.001 | 1.32, < 0.001 | -28.03, < 0.001 | 178.96, < 0.001 | -26.27, < 0.001 |
1990s ~ 2000 s | - | - | ref | ref | ref | ref | ref |
Race | | | | | | | |
White and black | 0.005 | 0.006 | -41.67, 0.01 | 1.24, 0.005 | -39.76, 0.005 | -165.32, 0.274 | -41.80, 0.35 |
others | - | - | ref | ref | ref | ref | ref |
Tumor Size | < 0.001* | < 0.001* | < 0.001 | | | | |
> 100 mm | - | - | -50.03, < 0.001 | 1.32, < 0.001 | -58.56, < 0.001 | -33.62, 0.010 | -50.02, 0.07 |
unknown | - | - | -36.45, < 0.001 | 1.42, < 0.001 | -39.35, < 0.001 | 72.64, < 0.001 | -37.02, < 0.001 |
< 100 mm(reference) | - | - | - | ref | ref | ref | ref |
Extend of disease | < 0.001* | < 0.001* | < 0.001* | | | | |
Metastasis | - | - | -164.09, < 0.001 | 6.34, < 0.001 | -183.43, < 0.001 | -113.45, < 0.001 | -164.05, < 0.001 |
Local Invasion | - | - | -60.15, < 0.001 | 1.98, < 0.001 | -71.54, < 0.001 | -22.99, < 0.001 | -60.18, < 0.001 |
Unknown | - | - | -82.28, < 0.001 | 2.50, < 0.001 | -93.62, < 0.001 | 2.21, < 0.001 | -82.94, < 0.001 |
Confined | - | - | ref | ref | ref | ref | ref |
AJCC | < 0.001* | < 0.001* | < 0.001* | | | | |
IV | - | - | -76.92, < 0.001 | 15.36, < 0.001 | -68.27, < 0.001 | -70.48, < 0.001 | -77.06, < 0.001 |
III | - | - | -45.31, < 0.001 | 6.511, < 0.001 | -41.12, < 0.001 | -51.98, < 0.001 | -45.77, < 0.001 |
II | - | - | -28.72, < 0.001 | 3.99, < 0.001 | -23.05, < 0.001 | -34.50, < 0.001 | -28.89, < 0.001 |
Unknown | - | - | -39.58, < 0.001 | 5.62, < 0.001 | -33.66, < 0.001 | -16.99, < 0.001 | -39.49, < 0.001 |
I | - | - | ref | ref | ref | ref | ref |
Surgery, yes | < 0.001 | < 0.001 | 121.41, < 0.001 | 0.37, < 0.001 | 121.11, < 0.001 | 18.17, 0.88 | 121.05, < 0.001 |
Radiation, yes | < 0.001 | < 0.001 | -133.53, < 0.001 | 2.54, < 0.001 | -134.41, < 0.001 | -29.15, 0.73 | -133.39, < 0.001 |
Chemotherapy, yes | < 0.001 | < 0.001 | 16.26, 0.048 | 0.85, < 0.001 | 17.04, 0.05 | -137.623, 0.001 | 16.06, 0.27 |
RMST, restricted mean survival time. IPCW, inverse probability of censored weighting. AJCC, American Joint Committee on Cancer for staging |
a Presented as point estimation of coefficient (difference in RMST) and corresponding p value |
b Presented as point estimation of hazard ratio and corresponding p value |
* Overall test for categorical covariates with more than 2 groups. |
coefficients estimated by IPCW regression with group-specified weights were quite different from those estimated by IPCW regression with individual weights ignoring homogeneity of censoring mechanism, for instance, radiation variable held the homogeneity of censoring mechanism, and estimated coefficient was − 133.39 in IPCW regression with group-specified weights and − 29.15 in IPCW regression with individual weights. Surgery variable broke the assumption and estimated coefficients were 121.05 and 18.17, respectively. Two IPCW methods were sensitive to weights and produce unstable estimation.
It was noticeable that difference analysis and IPCW regression with group-specified weights were no longer applicable when age was included as a continuous variable. At this point, PV regression indicated that the average survival time was reduced by 4.09 months for each additional year in age (p < 0.001). Meanwhile, similar regression coefficient, 4.35, was acquired by IPCW regression with individual weights.
In Fig. 2, differences in RMST estimated by Kaplan-Meier method were almost equal to those by PV regressions and IPCW regression with group-specified weights (Y = 1.04X + 0.24, R2 = 0.99; Y = 1.00X-0.14, R2 = 1.00, respectively), but were different from those by IPCW regression with individual weights (Y = 0.37X − 18.47, R² = 0.09). In addition, the relationship between HR estimated by COX regressions and coefficients estimated by PV regressions was illustrated in Fig. 3. when covariates met PH assumption, a well-fitted logarithmic relationship was observed (coefficients = -109.3✕ln (HR) − 0.8343, R² = 0.9702); But if PH assumption was not met, goodness of fit declined markedly (coefficients = -16.02✕ln (HR) – 15.06, R² = 0.39). Because coefficients from PV regressions agreed with those from IPCW regression with group-specified weights, there is no further plot in univariable analyses.
All covariates were included in multivariable regressions. IPCW regression with group-specified weights was limited. P values were highly consistent between COX regressions and PV regressions, but changed chaotically and greatly in IPCW regression with individual weights (Table 4). For simplification, negative difference in RMST was defined as survival time lost (STL) and positive difference was defined as survival time gain (STG). The overall survival was independently associated with age (HR:1.03, STL: 3.86), sex (HR:1.18, STL:24.23), diagnosis in 1970 ~ 1980s (HR: 1.39, STL:27.49), > 100 mm tumor size (HR:1.48, STL:49.56), metastasis and local invasion, higher AJCC staging, surgery (HR:0.58, STG:35.55), radiation (HR:1.46, STL:44.65) and chemotherapy (HR:1.26, STL:49.49).
Table 4
multivariable analysis based on cox proportional hazard regression and restricted mean survival time based regression.
Parameter | Cox regression | Pseudo-Value regression | IPCW regression (individual weights) |
HR | p | Beta (95% CI), months | p | Beta (95% CI), months | p |
Age (continuous) | 1.03(1.03,1.03) | < 0.001 | -3.86(-4.20,-3.53) | < 0.001 | -2.58(-3.12,-2.04) | < 0.001 |
Sex, male | 1.18(1.08,1.28) | < 0.001 | -24.23(-38.02,-10.45) | < 0.001 | -18.34(-47.03,10.35) | 0.21 |
Year of diagnosis | | | | | | |
1970s ~ 1980 s | 1.39(1.23,1.57) | < 0.001 | -27.49(-1.80,-53.19) | 0.036 | -197.65(-227.40,-167.91) | < 0.001 |
1990s ~ 2000 s | ref | | ref | | ref | |
Race | | | | | | |
White and black | 1.02(0.88,1.19) | 0.79 | 11.00(-12.32,34.32) | 0.355 | -14.67(-55.39,26.05) | 0.48 |
other | ref | | ref | | ref | |
Tumor Size | | | | | | |
> 100 mm | 1.48(1.21,1.80) | < 0.001 | -49.56(-85.01,-14.12) | 0.006 | -15.01(-29.61,-0.42) | 0.044 |
unknown | 1.12(0.97,1.31) | 0.126 | -11.51(-37.92,14.90) | 0.393 | -5.23(-19.48,9.03) | 0.472 |
< 100 mm(reference) | ref | | ref | | ref | |
EOD | | | | | | |
Metastasis | 4.47(3.49,5.73) | < 0.001 | -202.47(-237.54,-167.39) | < 0.001 | -22.48(-45.64,0.69) | 0.057 |
Local Invasion | 1.66(1.33,2.07) | < 0.001 | -89.60(-121.37,-57.83) | < 0.001 | 0.95(-13.51,15.41) | 0.897 |
Unknown | 1.81(1.43,2.29) | < 0.001 | -113.22(-147.32,-79.11) | < 0.001 | 38.59(23.69,53.49) | < 0.001 |
Confined | ref | | ref | | ref | |
AJCC staging | | | | | | |
IV | 11.44(7.29,17.93) | < 0.001 | -174.21(-201.43,-146.99) | < 0.001 | 25.90(-4.87,56.68) | 0.099 |
III | 4.81(2.48,9.36) | < 0.001 | -105.87(-179.12,-32.62) | 0.005 | 21.26(-7.95,50.47) | 0.154 |
II | 3.56(2.28,5.56) | < 0.001 | -61.97(-86.77,-37.17) | < 0.001 | 20.22(-4.02,44.47) | 0.102 |
Unknown | 4.21(2.71,6.54) | < 0.001 | -89.53(-114.75,-64.31) | < 0.001 | 75.49(56.17,94.81) | < 0.001 |
I | ref | | ref | | ref | |
Surgery, yes | 0.58(0.53,0.64) | < 0.001 | 35.55(18.57,52.53) | < 0.001 | 53.15(17.20,89.10) | 0.004 |
Radiation, yes | 1.46(1.32,1.62) | < 0.001 | -44.65(-62.19,-27.11) | < 0.001 | -4.95(-58.00,48.09) | 0.855 |
Chemotherapy, yes | 1.26(1.14,1.39) | < 0.001 | -49.49(-67.41,-31.57) | < 0.001 | -55.42(-94.40,-16.45) | 0.005 |
The relationship between HR and coefficients estimated by PV regressions were also fitted. Figure 4 showed that the slope of logarithmic transformed HR on coefficients from PV regressions changed slightly from − 109.3 to -128.2 with stably high goodness of fit (R2 = 0.92) when covariates meeting PH assumption, and the slope changed dramatically from − 16.02 to -57.92 but obtained increased goodness of fit (R2 = 0.91) when covariates broke PH assumption. However, no significant and stable relationship was observed between HR and coefficients estimated by IPCW regression with individual weights in Fig. 5.