A warning threshold for monitoring tuberculosis surveillance data: an alternative to hidden Markov model.

OBJECTIVES: Although hidden Markov model (HMM) is known as a powerful tool for the detection of epidemics based on the historical data, the frequent use of such a model poses some limitation especially when decision-making is required for new observations. This study was aimed to address a warning threshold for monitoring the weekly incidences of tuberculosis as an alternative to HMM. METHODS: We extracted the weekly counts of newly diagnosed patients with sputum smear-positive pulmonary TB from 2005 to 2011 nationwide. To detect unexpected incidences of the disease, two approaches: Serfling and HMM, were applied in presence/absence of linear, seasonal and autoregressive components. Models were subsequently evaluated in terms of goodness of fit, and their results were compared in detection of the disease phases. Then, multiple hypothetical thresholds were constructed based on the estimate of models and the optimal one was revealed through ROC curve analysis. RESULTS: Findings from both adjusted R-square (R~2) and Bayesian information criterion (BIC) presented a higher goodness of fit for periodic autoregressive HMM (BIC = -1323.6; R~2=0.74) than other models. According to ROC analysis, better values for both Youden's index and area under curve (0. 96 and 0. 98 respectively) were obtained by the threshold based on the estimate of periodic autoregressive model. CONCLUSIONS: As the optimal threshold presented in this study is simple in concept and has no limitation in practice, especially for monitoring new observations, we would recommend such a threshold to be used for monitoring of TB incidence data in the surveillance system.

Recurrence in breast cancer. Analysis with frailty model.

OBJECTIVE: To determine the value of known prognostic factors for metastasis in breast cancer by accounting for patient-specific effect of patients who received surgical treatment followed by adjuvant treatment using the frailty model. METHODS: One hundred seventeen women with breast cancer who underwent surgery followed by adjuvant therapy at 3 hospitals in Tehran, Iran between 1995 and 2003 were enrolled in this study. Women with defined breast cancer with no distant metastases at time of diagnosis that have undergone modified radical mastectomy or breast-conserving surgery were enrolled. Tumors were classified according to the Tumor, Node, Metastasis (TNM) system of the American Joint Committee on cancer. Grading was performed according to Scarff-Bloom-Richardson method. Estrogen receptor (ER) was measured by immunohistochemistry method. The patients have been followed regularly by routine clinical laboratory profile, serologic markers (CEA, CA15-3) and para-clinical examinations; furthermore, we have followed missing materials by other access ways such as calling. RESULTS: Median follow up time for patients was 26 months after surgery. During the follow up time 44 (38%) patients developed metastasis and 20 (45%) of these 44 patients experienced the second metastasis. The median disease-free survival for patients in the study was 49.6 month. The median time to experience second metastasis after the first one was 22.5 months. Risk of occurrence of a metastasis in the first year after surgery was 12%. Risk of experience a metastasis up to the second year was 32% and up to fifth years was 69%. Result of fitting a frailty model to data showed that size of tumor, number of positive lymph nodes and histologic grade had a significant effect on the risk of metastasis (p<0.05). Patients with tumor size larger than 5 cm were in higher risk of metastasis compared with others. Increase in the number of positive lymph nodes to more than 10, increased risk of metastasis. Patients with moderate or undifferentiated histologic grade were in higher risk of metastasis to well differentiated patients. Age, family history, lymph node stage, and ER had no significant effect. It was found that there was heterogeneity between patients after adjusting for other covariates because variance of frailty was 0.315. It means that based on the variance of the distribution of frailty, the relative risk of high-risk patients to low-risk patients was 7.2, wherein high-risk group is defined as a cluster at the 95th percentile and low-risk to a cluster of 5th percentile of the frailty distribution. CONCLUSION: Known risk factors describe the risk of metastasis partly and other unknown or unmeasured factors, such as genetics or environmental factors are important to describe the risk of metastasis in breast cancer.