Forecasting the Incidence of Breast, Colorectal and Bladder Cancers in North of Iran Using Time Series Models; Comparing Bayesian, ARIMA and Bootstrap Approaches

  1. Ghasem Janbabaee ,
  2. Aliasghar Nadi-Ghara ,
  3. Mahdi Afshari ,
  4. Somayeh Rahimi Moghadam ,
  5. Majid Yaghoubi Ashrafi ,
  6. Mohsen Aarabi ,
  7. Akbar Hedayatizadeh-Omran ,
  8. Reza Alizadeh-Navaei ,
  9. Mohammad Eslami Jouybari ,
  10. Mahmood Moosazadeh

Vol 4 No 1 (2021)

DOI 10.31557/apjec.2021.4.1.3-7


Introduction: Cancers are the second cause of death worldwide. Prevalence and incidence of cancers is getting increased by aging and population growth. This study aims to predict the incidence of breast, colorectal and bladder cancers in north of Iran until 2020 using time series models.
Methods: The number of breast, colorectal and bladder cancer cases from April 2014 to March 2016 was extracted. The time variable was each month of the study years and using the number of daily registered cancers in each month, the time series of the monthly incident cases was designed. Then, three methods of time series analysis including Box Jenkins, Bayesian and Bootstrap were applied for predicting the incidence of the above cancers until March 2020.
Results: The number of bladder cancer cases in March 2014 was 6 cases. This study showed that the number of breast cancer cases in March 2020 will be increased to 15, 15 and 26 cases based on ARIMA, Bootstrap and Bayesian methods respectively. In addition, the incident cases of breast cancer, will be increased from 32 in 2014 to 65 (ARIMA method), 47 (Bootstrap method) and 364 (Bayesian method). The corresponding figure for colorectal cancer was 30, 30 and 95 respectively.
Conclusion: The increasing trend of breast, bladder and colorectal cancers will be continued which is considerable based on the Bayesian method results. Considering the limited reliable data used in a short time, it seems that the forecasting results of this model is acceptable.


Cancers are the second cause of death worldwide [1]. The increasing trend of cancer, is associated with aging and population growth [2, 3]. Cancers significantly act in individual and social levels and cause a wide network of physical, mental, familial and social problems [4].

Breast cancer is the most common cancers among women and the second top cancers among all types of malignancies. The standardized incidence of breast cancer among Iranian women has been increased from 15.96 per 100,000 in 2003 to 28.25 per 100,000 in 2009 [5, 6]. Colorectal cancer is the third prevalent cancers worldwide with approximately 150,000 new cases annually. In Iran, during 2003- 2008, the age standardized incidence of colorectal cancer has been increased from 5.47 to 11.12 per 100,000 in women and from 5.56 to 12.7 per 100,000 in men [7, 8]. Bladder cancer is one of the other common cancers especially among men. According to the results of a meta-analysis, the standardized incidence of this cancer among Iranian men and women has been estimated as of 10.92 per 100,000 and 2.80 per 100,000 respectively [9].

Control of cancer, as one of the three man health priorities in Iran, requires designing a clear road map for all stakeholders. The present global facts show the importance of approach to this strategy. For example, the treatment costs of cancer is 19% higher than the costs of cardiovascular disorders. Meanwhile, one-third to half of the cancer associated deaths which are occurred in the low-middle income countries are preventable by early diagnosis and treatment. The growth of knowledge of public health helps policymakers plan suitable evidence based strategies. Therefore, it is better to draw the future perspective of cancer based on the present situation and associated factors such as changes in population and risk factors [10].

Time series is one of the most common used techniques applied in the futures studies including a set of observations of a specified variable sorting based on time. In general, the aim of time series studies is determination of the probable models of data generating and predicting their quantities in the future. These techniques facilitate the statistical analysis of the variables according to the time [11]. In a time series study investigating the previous behavior of the series, the best model engaged in the data generation is detected. Therefore, assuming the similar behaviors in the future, the upcoming amounts of the series is predicted. Such analyses are attributed to dependent data which are associated with each other during the time. Such dependence between the sequential observations is the basic principle of the time series analysis [12]. This study aims to forecast the incidence of breast cancer, colorectal cancer and bladder cancer in the northern part of Iran (Mazandaran province) until 2020 using different approaches of time series analysis.

Materials and Methods

This cross sectional study was carried out based on the recorded data. The monthly number of the incident cases of bladder cancer, breast cancer and colorectal cancer from April 2014 to March 2016 were extracted. Note that only the information of the recent two years were completely available, just 24 time points were established. Sampling was conducted based on consensus method.

The main source of data was the cancer registry of Mazandaran University of Medical Sciences, Sari, Iran (IR.MAZUMS.REC.96.2730). The data extraction was conducted without patients’ names.

Three methods of analysis including Box Jenkins, Bayesian and Bootstrap were applied for prediction of the breast, colorectal and bladder cancers until March 2020. The time variable in this time series analysis was each of the months of the study years. Considering the daily number of the incident cancers registered in each month, the time series model of the monthly incident cases was designed.

Modeling approaches

In the time series modeling based on the Box-Jenkins model, to investigate the nature of data, time series graphs were designed including ACF (autocorrelation function) and PACF (partial autocorrelation function). The type of these series was assessed in term of static or instability of the mean, variance and trend detection. Model making was first begun by detecting an experimental ARIMA model through real data analysis. Then, the unknown parameters of the model (p, d, q) were estimated using ACF and PACF graphs. The final model was designed using ARIMA method. Goodness of fit of the model was assessed using AIC, Box Ljung test as well as evaluation of the model residuals (Q-Q plot).

For each observation, the Q-Q plot shows the observed (X axis) and expected (Y axis when the sample data are normally distributed) values. In the case of normal distributed data, all points will be collected around a direct line.

In the Bootstrap approach, for each series, 1000 sampling was performed according to the selected rank in the ARIMA model. Then, the model goodness of fit was applied on all ranks of the sampling and finally, the number of cancer cases was predicted for the future. In the Bayesian approach, the probable trend of each series was investigated using bsts package. Then, the posterior distributions were selected using appropriate prior distributions and the forecasting was conducted for the next 48 months.

The statistical analyses were performed using R version 3.5.3 software. The tseries part of the forecast package was used for Box-Jenkins and Bootstrap modeling and the bsts part of the package was applied for the Bayesian approach modeling.


All bladder cancer cases were 367 patients varied between 6 cases in April to 25 cases in August 2014 (appendix 1). The relevant distributions were 18 in March to 38 in February.

The model parameters were estimated from ACF and PACF models after differentiation. As illustrated in the graphs of appendix3&4, the p & q parameters were estimated as 1. Considering the graphs in the appendix 2-4, the ARIMA (p=1, q=1 and d=1) seems to be the best models. I.e. the model includes both autoregressive and moving average components (ARIMA [(p, q, d) (1,1,1)]). This model had also the least AIC (149.45). It should be noted that Ljung-Box test was applied for assessment the ARIMA model for forecasting the bladder cancer incidence and the statistics showed that the final selected model is appropriate (X-squared=0.015718, p-value=0.900). The residuals were normally distributed indicating the effectiveness of the model (appendix 5).

As illustrated in the graph in the appendix 6, the average monthly number of the bladder cancer incident cases in north of Iran in 2020 will be 15 per month. The graph in appendix 7 illustrates the results of forecasting following 1000 Bootstrap sampling based on the ARIMA model. The results of the bladder cancer new cases based on Bayesian approach was estimated as of 30 cases per month in 2020 (Table 1, graph appendix 8).

Table 1. The Incident Cases of Breast, Bladder and Colorectal Cancer Predicted for March 2020.

Id Year Month   Bladder cancer     Breast cancer     Colorectal cancer  
      ARIMA Bootstrap Bayesian ARIMA Bootstrap Bayesian ARIMA Bootstrap Bayesian
1 2016 Apr 17.4155 15.3452 15.22746 48.6689 46.65132 71.2487 27.76202 30.11558 35.66455
2 2016 May 15.86397 15.38567 15.43442 73.10882 47.02884 78.27944 30.33082 30.17676 37.06692
3 2016 Jun 15.43291 15.36696 15.65411 61.24121 46.86865 84.45937 30.00476 30.16285 38.06237
4 2016 Jul 15.31315 15.38314 16.15532 67.00392 46.94276 90.59722 30.04615 30.17653 39.68993
5 2016 Aug 15.27987 15.37182 16.09151 64.20565 46.90941 96.8571 30.04089 30.1757 40.89032
6 2016 Sep 15.27063 15.38183 16.87119 65.56444 46.9222 103.1941 30.04156 30.17555 42.34386
7 2016 Oct 15.26806 15.37402 17.21513 64.90463 46.9194 109.7253 30.04147 30.18029 42.73563
8 2016 Nov 15.26735 15.38058 17.50012 65.22502 46.91715 115.9209 30.04149 30.17425 44.73483
9 2016 Dec 15.26715 15.37524 17.48442 65.06945 46.92206 122.8926 30.04148 30.1825 46.10567
10 2017 Jan 15.2671 15.3797 18.01552 65.14499 46.91598 129.8191 30.04148 30.17319 46.88251
11 2017 Feb 15.26708 15.37598 18.26541 65.10831 46.92263 135.709 30.04148 30.18374 48.33736
12 2017 Mar 15.26708 15.37913 18.4448 65.12612 46.9159 141.835 30.04148 30.17244 49.29929
13 2017 Apr 15.26707 15.37645 18.73475 65.11747 46.92255 148.6321 30.04148 30.18447 50.67441
14 2017 May 15.26707 15.37874 19.02945 65.12167 46.91613 154.9006 30.04148 30.17195 51.66125
15 2017 Jun 15.26707 15.37677 19.62755 65.11963 46.92228 162.2598 30.04148 30.18492 53.09373
16 2017 Jul 15.26707 15.37848 20.13925 65.12062 46.91644 167.9198 30.04148 30.17162 53.83005
17 2017 Aug 15.26707 15.37699 19.94702 65.12014 46.92197 174.4505 30.04148 30.18519 55.342
18 2017 Sep 15.26707 15.3783 20.1321 65.12037 46.91675 180.5774 30.04148 30.17142 56.60753
19 2017 Oct 15.26707 15.37715 20.55032 65.12026 46.92168 187.4819 30.04148 30.18537 58.29652
20 2017 Nov 15.26707 15.37816 20.99356 65.12032 46.91703 193.3027 30.04148 30.17129 59.06646
21 2017 Dec 15.26707 15.37727 21.5669 65.12029 46.92141 200.0601 30.04148 30.18547 60.0318
22 2018 Jan 15.26707 15.37806 22.03783 65.1203 46.91729 205.6375 30.04148 30.1712 61.92887
23 2018 Feb 15.26707 15.37735 22.20908 65.1203 46.92117 211.9153 30.04148 30.18554 62.75577
24 2018 Mar 15.26707 15.37798 22.44532 65.1203 46.91751 217.1927 30.04148 30.17115 64.37054
25 2018 Apr 15.26707 15.37742 22.85164 65.1203 46.92096 224.5392 30.04148 30.18558 65.05909
26 2018 May 15.26707 15.37792 23.13887 65.1203 46.91771 229.8751 30.04148 30.17112 66.47356
27 2018 Jun 15.26707 15.37747 23.5565 65.1203 46.92077 235.444 30.04148 30.18561 67.51255
28 2018 Jul 15.26707 15.37787 24.20189 65.1203 46.91789 242.6142 30.04148 30.1711 69.29039
29 2018 Aug 15.26707 15.37752 19.19638 65.1203 46.92061 242.6037 30.04148 30.18562 66.43344
30 2018 Sep 15.26707 15.37784 25.00504 65.1203 46.91805 269.331 30.04148 30.17109 76.58006
31 2018 Oct 15.26707 15.37755 22.2988 65.1203 46.92046 270.681 30.04148 30.18563 74.82842
32 2018 Nov 15.26707 15.37781 28.08278 65.1203 46.91819 260.9105 30.04148 30.17109 80.27744
33 2018 Dec 15.26707 15.37758 34.27281 65.1203 46.92033 275.7888 30.04148 30.18563 73.77579
34 2019 Jan 15.26707 15.37778 32.31013 65.1203 46.91831 289.38 30.04148 30.17108 81.36997
35 2019 Feb 15.26707 15.3776 20.37637 65.1203 46.92021 279.8265 30.04148 30.18563 77.56736
36 2019 Mar 15.26707 15.37777 28.88045 65.1203 46.91842 298.304 30.04148 30.17108 81.50867
37 2019 Apr 15.26707 15.37761 32.16857 65.1203 46.9201 293.4317 30.04148 30.18563 79.81653
38 2019 May 15.26707 15.37775 27.8914 65.1203 46.91852 301.2768 30.04148 30.17108 79.10895
39 2019 Jun 15.26707 15.37763 35.1063 65.1203 46.92001 316.1611 30.04148 30.18563 87.53291
40 2019 Jul 15.26707 15.37774 27.72762 65.1203 46.91861 335.134 30.04148 30.17109 92.57104
41 2019 Aug 15.26707 15.37764 25.63614 65.1203 46.91992 307.0223 30.04148 30.18563 79.99557
42 2019 Sep 15.26707 15.37773 27.2985 65.1203 46.91869 336.092 30.04148 30.17109 94.05782
43 2019 Oct 15.26707 15.37765 30.63707 65.1203 46.91985 330.3854 30.04148 30.18563 93.62512
44 2019 Nov 15.26707 15.37772 29.51558 65.1203 46.91876 338.08 30.04148 30.17109 84.93896
45 2019 Dec 15.26707 15.37765 28.41592 65.1203 46.91978 348.0495 30.04148 30.18563 99.37787
46 2020 Jan 15.26707 15.37771 28.94071 65.1203 46.91883 357.2993 30.04148 30.17109 84.98825
47 2020 Feb 15.26707 15.37766 34.98991 65.1203 46.91972 354.7557 30.04148 30.18562 86.1083
48 2020 Mar 15.26707 15.37771 26.21888 65.1203 46.91888 363.643 30.04148 30.1711 95.24105

Totally 1113 breast cancer cases were investigated minimum and maximum of which were identified in April 2015 (25 cases) and March 2016 (99 cases) respectively (Appendix 9). These cases were distributed from 57 in March to 163 in February. The time series model had instable pattern converted to stable model by one step differentiation (appendix 10). Autoregressive and moving average parameters were estimated as of 1 (appendix 11& 12). Therefore, the ARIMA (p,d,q) (1,1,1) was selected as the best model.

Moreover, the AIC of the model was estimated as of 196.13. The results of Ljung-Box test for the assessment of the ARIMA model showed that the model was appropriate (X-squared=0.014429, p-value=0.9044). According to the graph appendix 13, the residuals were normally distributed.

Graph of the appendix 14 shows the average number of breast cancer cases based on the ARIMA model in 2020 as of 65 cases per month. The corresponding figures for Bootstrap approach (appendix 15) and Bayesian approach (appendix 16) were predicted as of 47 and 358 cases respectively per month (Table 1).

The total number of colorectal cancer cases was 722 minimum and maximum of which were observed in September-October 2015 (21 cases) and April 2014 (86 cases) respectively (appendix 17). These cases were distributed from March (44 cases) to February (86 cases). Note that the time series had instability, one step differentiation was performed (appendix 18). Autoregressive parameter was estimated from the ACF graph (appendix 19) and moving average was estimated from PACF graph (appendix 20), both of which were estimated as of 1 and ARIMA (p,q,d) (1,1,1) was selected as the best model with AIC as of 160.34. Based on the results of the Ljung-Box test (X-squared=0.0063381, p-value=0.936), the selected model was appropriate. In addition, the residuals had normal distribution (appendix 21).

The number of colorectal cancer cases in north of Iran based on the ARIMA model (appendix 22) was estimated as of 30 cases per month. Corresponding incidences for Bootstrap (appendix 23) and Bayesian models (appendix 24) were 30 and 89 cases respectively (Table 1).


In this study, the incidence of breast, colorectal and bladder cancers until March 2020 was predicted using time series analysis based on three modeling approaches (ARIMA, Bootstrap and Bayesian). The results showed that the number of bladder cancer incident cases will be increased from six cases in 2014 to 15, 15 and 26 cases in March 2020 based on ARIMA, Bootstrap and Bayesian approaches. The number of patients diagnose as breast cancer will be increased from 32 to 65, 47 and 364 cases in 2020 based on the above three approaches respectively. In addition, the corresponding incidences for colorectal cancers will be 30, 30 and 95 cases respectively.

Time series models are used in different fields of medical sciences such as forecasting the number of patients, deaths … . In the study conducted by Nikbakht et al, trend of colon cancer in Southeast of Iran until 206 was predicted and showed an increasing trend [13].

Alvaro-Meca et al applied time series models to forecast the mortality of breast cancer in Spain during 1981-2007 and obtained an ARIMA (0,2,0) which was used for 15 years forecasting. Based on the results of that study, an increasing trend of breast cancer mortality for all age groups until 1995 was observed which was then reduced so that the total pattern of death during the 15-year study period was a decreasing trend [14].

Bae et al in 2002 found an increasing trend for all cancers mortality during 1983-2000 based on time series models [15].

Fazeli et al investigated the mortality of breast cancer among four age groups of Iranian women during 1995-2004. They found an increasing trend from 2005 to 2002 and a reducing trend during 2002-2004 [16].

Time series models are widely used in forecasting the cancers [17-18]. Similar to the current study, results of the other forecasting studies are in keeping with the fact that the rate of cancers is increasing. One of the main characteristics of the time series analysis is that such studies are suitable for short time durations so that in the case of long periods, there are more uncertainties [18].

Bayesian theory which has been suggested by Tomas Bayes for the first time, is being used widely in the field of medical sciences [19]. Using Bayesian method during time series analysis has a lot of benefits. When modeling is performed on data with short time period, over fitting may be occurred. Therefore, the designed model can be fit with the current data but cannot precisely predict the new data.

One of the methods for solution of the over fitting is using Bayesian method and prior distribution as a model parameter. In the Bayesian approach, these parameters are considered as random variables and are applied to detect the posterior distribution and more precise estimates [20-24]. In the case of low prior data, the Bayesian approach is an appropriate method for prediction [25]. Ribes et al predicted the cancer incidence until 2020 using Bayesian approach. They reported that the incidence of cancer in 2020 will reach to 26455 in men and 18345 in women indicating 22.5% and 24.5% increase among men and women respectively [26]. That is similar to the results of the present study.

One of the limitations of the current study is that the information of just 24 months (2014-2015) was completely available. It should be noted that at least 50 time points are required for a precise time series analysis. To overcome this limitation in the ARIMA model, 1000 sampling was performed using Bootstrap approach before forecasting. As another limitation of our study, the time of cancer onset is ignored by the Bootstrapping while time series are time dependent. Moreover, the ARIMA model has a short forecasting domain and in the long time predictions, the confidence intervals will be wide. Such limitation can be resolved by the Byesian method.

In conclusion, our study predicted an increasing trend for breast, bladder and colorectal cancers in northern part of Iran. We also found higher estimations based on the Bayesian approach.


This study was financially supported by Mazandaran University of Medical Sciences, Sari, Iran. The authors thank to the research deputy as well as cancer research and registry centers of the university by their kindly cooperation.


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Author Details

Ghasem Janbabaee
Affiliation not stated

Aliasghar Nadi-Ghara
Affiliation not stated

Mahdi Afshari
Affiliation not stated

Somayeh Rahimi Moghadam
Affiliation not stated

Majid Yaghoubi Ashrafi
Affiliation not stated

Mohsen Aarabi
Affiliation not stated

Akbar Hedayatizadeh-Omran
Affiliation not stated

Reza Alizadeh-Navaei
Affiliation not stated

Mohammad Eslami Jouybari
Affiliation not stated

Mahmood Moosazadeh
Affiliation not stated

How to Cite

Janbabaee, G., Nadi-Ghara, A., Afshari, M., Rahimi Moghadam, S., Ashrafi, M. Y., Aarabi, M., Hedayatizadeh-Omran, A., Alizadeh-Navaei, R., Eslami Jouybari, M., & Moosazadeh, M. (2021). Forecasting the Incidence of Breast, Colorectal and Bladder Cancers in North of Iran Using Time Series Models; Comparing Bayesian, ARIMA and Bootstrap Approaches. Asian Pacific Journal of Environment and Cancer, 4(1), 3-7.
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