Point Level Analysis

4.3.1.1 MCMC Convergence from Trace Plots

We began by checking MCMC convergence by considering the trace plots for each model for the four chosen states in the point analysis. The plots shown in Appendix

4.4 show that mixing is good and there is evidence for satisfactory convergence. We next look at autocorrelation in the latent field, and then check the information content in the data by plotting the priors against the posterior for each parameter. The idea of these plots is that the data should move the prior somewhat; if the prior and posterior are too similar, then there is little information in the data on this particular parameter.

4.3.1.2 Model Comparison

We compared three possible models for the baseline hazard using WAIC; Table

4.3 shows these values. The model with the smallest WAIC value is considered to have the best fit. In all four of the chosen states, the model using a Weibull

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distribution to describe the baseline hazard function yielded the smallest WAIC value.

State WAIC

Weibull Exponential B-spline Kelantan 2428.152 2434.033 2430.226

Kedah 4125.213 4145.084 4130.128

Kuala Lumpur 2472.562 2475.856 2473.387 Sarawak 4149.445 4153.215 4149.778

Table 4.3: Table comparing the WAIC values of models with Weibull, Expo-

nential and B-spline distributed baseline hazard functions, by state

Table 4.4 and Table 4.5 summarise the parameter effects described by the spatial survival model for the four states chosen for the point level analysis. Age slightly increased the risk of death for colorectal cancer and the association was signifi- cantly found in Kedah and Sarawak states. Sex was not significantly associated with the risk of death from colorectal cancer in any of the four states chosen in this study. Being of Malay race was found to increase the risk of death from colorectal cancer. We found that patients that had higher education level had a decrease in the risk of death from colorectal cancer, in particular those with tertiary education (degree) had the lowest risk of death from colorectal cancer. However, in Kedah, we noted that those with secondary level education had more than twice the risk of death than patients with no formal education.

Regarding smoking status, our evidence was mixed regarding the deviation of the effect. In Kelantan, being a former smoker, active smoker or having missing smoking status resulted in lower risk of death from colorectal cancer than the non smoking group, but the effect was not significant. In contrast, in Kuala Lumpur and Sarawak, former smokers and active smokers had more risk of death from colorectal cancer compared to those who do not smoke. However, it was found to

be significant in the smoker group for Sarawak only. Former smoker group and missing smoking status positively affect the risk of death in Kedah but the effect was not significant.

Colorectal cancer patients diagnosed with Stage IV cancer had the highest risk of death from colorectal cancer in all states except Kuala Lumpur, where those at Stage III at diagnosis had higher risk of death than Stage IV, but the effect was not significant. The group with missing stage also had high risk of death in all states but the effect was only significant in the state of Kedah.

The site of cancer did not significantly affect survival of colorectal cancer in any of the states in our study. Tumours graded moderately or poorly differentiated, or without a grading, were all at increased risk of death from colorectal cancer compared to those graded as well differentiated. The presence of distant metastases also had positive association with colorectal cancer survival even after controlling for spatial correlation. However, the effect was only significant in Kuala Lumpur and Kedah. Patients that underwent ‘other’ treatment had the lowest survival of all treatment groups after accounting for correlation in space, but this was found to be significant in Kuala Lumpur only. Diabetes mellitus was not significantly associated with survival in colorectal cancer once adjusted for correlation on space.

Overall, when the spatial location is taken into account, cancer staging and tu- mour differentiation play an important role in affecting survival in colorectal cancer where the risk of death increased with higher cancer staging and poorer differentia- tion of the tumour. On the other hand, high education level (tertiary) significantly reduced the risk of death from colorectal cancer in these four selected states. Other factors found to be significantly affecting the risk of death in certain states, after controlling for spatial location, were the patient’s age, race, the presence of dis- tance metastases and treatment modalities received by the patients. Patients’ sex,

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smoking status and diabetes status did not significantly affect the hazard of death in colorectal cancer patients in all selected states in the model.

Table 4.4: Table of parameter estimates from the fitted model for four states in

Malaysia. Significant estimates (those whose credible interval does not contain 1) are given in bold font for ease of identification.

Kelantan(N=268) KLumpur(N=290) Kedah(N=556) Sarawak(N=588)

Variable Med(95% CRI) Med(95% CRI) Med(95% CRI) Med(95% CRI)

Age 0.99 (0.98, 1.01) 1.01 (0.98, 1.03) 1.02 (1.01, 1.03) 1.01 (1.00, 1.03) Sex Female Male 1.14 (0.71, 1.85) 0.94 (0.53, 1.63) 1.17 (0.86, 1.61) 0.81 (0.61, 1.08) Race Non Malay Malay 1.17 (0.61, 2.29) 1.31 (0.75, 2.36) 1.47 (1.08, 2.06) 1.47 (1.02, 2.07) Education Nil Primary 0.38 (0.16, 0.94) 0.37 (0.14, 0.93) 1.36 (0.75, 2.45) 1.17 (0.69, 1.97) Secondary 0.18 (0.08, 0.43) 0.33 (0.11, 0.92) 2.38 (1.26, 4.63) 0.94 (0.54, 1.59) Tertiary 0.13 (0.05, 0.36) 0.06 (0.01, 0.45) 0.52 (0.18, 1.37) 0.43 (0.17, 0.98) Missing 0.46 (0.23, 1.01) 0.76 (0.36, 1.52) 2.65 (1.49, 4.73) 0.92 (0.61, 1.44) Smoking status Non Smoker Former Smoker 0.90 (0.48, 1.77) 1.25 (0.58, 2.96) 1.65 (0.96, 2.68) 1.88 (1.15, 2.92) Active smoker 0.72 (0.30, 1.55) 1.89 (0.82, 4.49) 0.94 (0.60, 1.49) 1.07 (0.68,1.76) Missing 0.77 (0.44, 1.36) 0.88 (0.47, 1.62) 1.06 (0.71, 1.57) 1.16 (0.81, 1.63) Staging Stage I Stage II 0.47 (0.12, 2.09) 2.79 (0.97, 10.7) 0.85 (0.35, 2.35) Stage III 3.30 (1.35, 8.69) 1.50(0.41, 6.19) 3.20 (1.15, 11.8) 1.34 (0.60, 3.65) Stage IV 6.59 (2.58, 19.14) 1.31 (0.36, 5.51) 7.11 (2.62, 27.1) 3.19 (1.38, 8.48) Not staged 1.22 (0.39, 4.05) 0.81 (0.16, 4.19) 2.62 (0.87, 9.79) 1.68 (0.71, 4.85) Missing 6.53 (2.69, 17.66) 1.31 (0.39, 5.02) 4.29 (1.56, 15.5) 1.85 (0.83, 4.91) Cancer Site Colon Rectum 0.88 (0.51, 1.45) 1.27 (0.57, 2.64) 0.85 (0.55, 1.38) 1.14 (0.73, 1.7) Rectosigmoid 1.10 (0.67, 1.73) 0.82 (0.45, 1.39) 1.25 (0.95, 1.69) 1.20 (0.89, 1.63)

Table 4.5: Table of parameter estimates from the fitted model for four states in

Malaysia. Significant estimates (those whose credible interval does not contain 1) are given in bold font for ease of identification.

Kelantan(N=268) KLumpur(N=290) Kedah(N=556) Sarawak(N=588)

Variable Med(95% CRI) Med(95% CRI) Med(95% CRI) Med(95% CRI)

Tumor grade Moderate 2.18 (1.02, 5.88) 2.74 (1.08, 8.00) 1.48 (0.83, 2.77) 1.98 (1.11, 3.64) Poor 2.24 (0.54, 8.88) 7.38 (1.49, 48.0) 1.94 (0.69, 4.92) 4.92 (2.03, 12.4) Missing 3.10 (1.31, 8.26) 3.38 (1.31, 11.7) 1.88 (1.06, 3.70) 2.82 (1.48, 5.42) Metastasis No Yes 1.08 (0.64, 1.82) 2.50 (1.30, 5.02) 1.58 (1.08, 2.29) 1.44(0.98, 2.16) Missing 0.86 (0.38, 2.12) 2.12 (0.85, 5.36) 1.41 (0.83, 2.47) 1.36 (0.85, 2.28) Treatment Surgery Alone Surg,Chemo,radio 0.59 (0.37, 0.95) 1.15 (0.63, 2.21) 0.71 (0.481, 1.03) 0.90 (0.64, 1.26) Radio,Chemo 1.50 (0.57, 3.42) 2.52 (0.99, 6.33) 0.62 (0.29, 1.27) 1.06 (0.67, 1.69 ) Other 1.97 (0.496, 3.69) 4.75 (1.54, 15.02) 1.83(0.95, 3.63) 1.37 (0.19, 5.12) Unknown 1.37 (0.62, 2.84) 1.76 (0.71, 4.52) 0.89 (0.56, 1.40) 1.75 (1.01, 2.94) Diabetes No Diabetes 1.46 (0.87, 2.31) 1.21 (0.66, 2.24) 0.84 (0.60, 1.19) 1.01 (0.68, 1.48) Missing 0.57 (0.30, 1.01) 0.91 (0.42, 1.95) 0.91 (0.54, 1.56) 0.98 (0.35, 2.22) σ 0.55 (0.33, 0.88) 1.32 (0.92, 1.88) 0.54 (0.311, 0.83) 0.38 (0.20, 0.65) φ 5010 (2285, 11241) 776 (495, 1309) 3839 (1617, 8458) 16384 (5828, 44570)

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