Iranian Journal of

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Background and Objectives: Missing data exist in many studies, e.g. in regression models, and they decrease the model's efficacy. Many methods have been suggested for handling incomplete data: they have generally focused on missing outcome values. But covariate values can also be missing.
Materials and Methods: In this paper we study the missing imputation by the EM algorithm and auxiliary variable and compare the result with case-complete analysis in a logistic regression model dealing with factors that influence the choice of the delivery method.
Our data came from a cross-sectional study of factors associated with the choice of the delivery method in pregnant women. The sample size in this cross-sectional study was 365 and the data were collected through interviews, using questionnaires covering several demographic variables, delivery history, attitude, and some social factors. We used standard deviations to compare the efficiency of the two methods.
Results: The results show that maximum likelihood analysis by EM algorithm is more effective than case-complete analysis.
The problem of missing data is common in surveys and it causes bias and decreased model efficacy. Here we show that the EM algorithm for imputation in logistic regression with missing values for a discrete covariate is more effective than case-complete analysis.
Conclusion: On the other hand if missing values occur for a continuous covariate then we have to use other methods or change the variable into a discrete one.

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Background and Objectives: Logistic regression is one of the most widely used generalized linear models for analysis of the relationships between one or more explanatory variables and a categorical response. Strong correlations among explanatory variables (multicollinearity) reduce the efficiency of model to a considerable degree. In this study we used latent variables to reduce the effects of multicollinearity in the analysis of a case-control study.
Methods: Our data came from a case-control study in which 300 women with breast cancer were compared to 300 controls. Five highly correlated quantitative variables were selected to assess the effect of multicollinearity. First, an ordinary logistic regression model was fitted to the data. Then, to remove the effect of multicollinearity, two latent variables were generated using factor analysis and principal components analysis methods. Parameters of logistic regression were estimated using these latent as explanatory variables. We used the estimated standard errors of the parameters to compare the efficiency of models.
Results: The logistic regression based on five primary variables produced unusual odds ratio estimates for age at first pregnancy (OR=67960, 95%CI: 10184-453503) and for total length of breast feeding (OR=0). On the other hand, the parameters estimated for logistic regression on latent variables generated by both factor analysis and principal components analysis were statistically significant (P<0.003). The standard errors were smaller than with ordinary logistic regression on original variables. The factors and components generated by the two methods explained at least 85% of the total variance.
Conclusions: This research showed that the standard errors of the estimated parameters in logistic regression based on latent variables were considerably smaller than that of model for original variables. Therefore models including latent variables could be more efficient when there is multicollinearity among the risk factors for breast cancer.

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Background & Objectives: Hypertension is one of the most prevalent and important risk factor of cardio-vascular diseases. The aim of this research was to determine relative factors on hypertension in Kohrang.
 Methods: This survey was a population – based case - control study. The study population consisted of 415 patient with hypertension (cases) and 415 controls without any history of cardiovascular and or cerebrovascular diseases & hypertension. A systematic random sampling was used. The chi-square test and conditional logistic regression model was used and the data were analyzed by STATA.
Results: Family history of hypertension, age over 60, no physical activity, bmi≥30 were calculated as risk factors with odds ratio: 2.33 (95% CI 1.58-3.47), 2.01(95% CI 1.24-2.67), 1.8 (95% CI 1.2-2.7), 1.66 (95% CI 1.32-2.07) respectively (p<0.05). Fish consumption, unsaturated fat consumption and literacy were considered as protective factors with an odds ratio: 0.516 (95% CI 0.35-0.69), 0.514 (95% CI 0.36-0.72), 0.28 (95% CI 0.17-0.45) respectively (p<0.01).
Conclusions: The findings of this study highlight to plan appropriate health promotion programmes by health policy makers.

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Background & Objectives: Study trend of observed rates changes provide valuable information for need assessment, plan, reload programs and develop indicators of each country. The main objective of this paper is to determine the changes in tuberculosis incidence rate trend in Iran by applying segmented regression model.
Methods: In this study, segmented Linear Regression employed to analyze the trend of changes in pattern of Tuberculosis incidence rate during past 44 years (1964-2008) in Iran. We used least square method and permutation test and Bayesian Information Criteria to decide which of the two segment regression model and poison regression would be better. Data analyzed by Joinpoint3.4 and SAS9.1 software. Results: According the permutation test, it was detected that there were two breakpoints over 1977 and 1993 years (p=0.0108). Incidence rate of tuberculosis during the first 11 years of review had declined with annual percentage change = -10.1%, for second segment it rose upward with 4.3% increase in per year and for end segment TB incidence rate again declined with annually 4.5%. The average annual change of Tuberculosis incidence rate in Iran for at least 10 years has been estimated -4.5 percentages.
Conclusion: The findings of this study have shown that the incidence rate of Tuberculosis decreased after 1992 that interestingly this decline seems faster than estimated by international TB control program. This indicates that preventive and treatment of Tuberculosis programs have been successful in Iran.

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Background & Objectives: Despite decreasing the trend of coronary artery diseases in developed countries and outstanding improvements in clinical management of these patients, case fatality rate after an acute myocardial infarction (AMI) remains high in both genders. Identifying predicting factors of short-term survival in patients with AMI may play an important role in reducing mortality in these patients.
Methods: In this cohort study, all patients with acute myocardial infarction (AMI) admitted to all hospitals in Isfahan, Iran, during 2000-2008 which registered in Isfahan cardiovascular research Institute were analyzed. We used Cox regression models, uni- and multi-variable analysis. 
Results: Within the study period, 8800 AMI patients (73.6% male) were admitted with mean age of 61.85±12.5, and overall 28-day survival of 90.5%. Relative risk (RR) of death for 50-70 years old patients was 2.5 (CI:2-3.1), for over 70 years old RR=5 (CI:4-6.3), for women RR=1.7 (CI:1.5-1.9), for patients who had not received streptokinase RR=0.9 (CI:0.8-1.1), for inferior MI RR=4.2 (CI:2.2-7.8) and for anterior MI, RR was equal to 7.2 (CI:4-13.3).
Conclusion: Recognizing the predicting factors of short-term survival of AMI patients may help health professionals to provide better healthcare services for more at risk patients, i.e. elderly, women and patients with an anterior MI.

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Background & Objectives: Tuberculosis (TB) is one of the major infectious diseases in Iran and has pulmonary and extra-pulmonary manifestations. Considering the differences in the distribution of the cases across different regions, we decided to study the geographical distribution, epidemiologic characteristics, and disease pattern in Lorestan.

 Methods: This ecologic (descriptive analytical) survey was done in Lorestan between 2002 and 2008. The data was collected from the Health Department of Lorestan University of Medical Sciences and included the history of 1481 patients suffering from TB. The study variables were sex, disease type, residential location, age, and year. The data were analyzed using statistical package SAS 9.2 and descriptive and inferential statistics were applied.

Results: From 1481 registered patients 58.4% were male and 41.6% were female among which 68.74% and 29.98% lived in urban and rural areas and 1.28% were nomads. The mean age of the patients was 41.87. The highest and lowest incidence rates were observed in Khoram Abad (19.38 per 100000) and Azna (7.04 per 100000), respectively. Using Poisson regression, it was observed that the effects of age structure and residency on the incidence rate were significant.

Conclusion: The percentage of nomads was identified as the most important demographic factor in the incidence rate of TB in Lorestan. Allocation of better resources and appropriate training can be effective in controlling and preventing the disease.

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Background & Objectives: Due to the increasing tendency to measure the quality of life in recent years and the extensive quality of life questionnaires, it is important to determine the appropriate method of analyzing data derived from these studies. The aim of the present study was to introduce ordinal logistic regression models as an appropriate method for analyzing the data of quality of life.

Methods: The data was derived from a cross-sectional study on quality of life survey of 938 students. For data analysis, two binary logistic regression models and ordinal logistic regression models were used and the results of these models were compared.

Results: The results of goodness of fit showed that all three models were fitted well. Based on the ordinal logistic regression models, the three variables out of the explanatory variables were statistically associated with the response while based on the binary logistic regression model, after combining two categories of response variable, only two variables were significant. Therefore, combining the categories of the response variable should be avoided as much as possible because it may lead to data loss due to ignoring some of the response categories.

Conclusion: It is concluded that to analyze quality of life data, due to the nature of the response variable, ordinal logistic regression models are recommended considering the fewer parameter estimates and easier interpretation of the results

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  Background & Objectives : The length of stay (LOS) is a useful indicator that can be used according to the objective to improve hospital care performance. The purpose of our study was to find factors affecting infants LOS in NICU at Children's Medical Center, Imam Khomeini Hospital, Tehran University of Medical Sciences, using the Cox multiple hazards regression model.

  Methods : This historical cohort study reviewed 369 medical records of all NICU admitted newborns at Children's Medical Center in 2009. The required data were collected through a data collection form. The Cox multiple hazards regression model was used to determine the factors affecting LOS in infants who were discharged on the physician‘s order.

 Results: The median of stay in NICU was 9 days. Of 369 infants, 272 were discharged with improvement. The results of multiple Cox proportional hazards regression model showed the following factors were associated with LOS in the NICU: prematurity, referral from other hospitals, gastrointestinal diseases and infections, central venous catheterization, mechanical ventilation, and antibiotic therapy (P < 0.05).

  Conclusion : Cox proportional hazards regression model should be used when the dependent variable is time and we have censored data. Improving prenatal health care, constructing NICU in hospitals with high risk labor, reduction of preterm birth risk factors, and improving primary health-care services can help us to reduce LOS in NICU.

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  Background & Objectives : The identification of risk factors and their interactions is important in medical studies. The aim of this study was to identify the interaction of risk factors of cerebral palsy in 1-6 years-old children with classification regression methods.

  Methods : The data of this cross-sectional study which was conducted on 225 children aged 1-6 years was collected during 2008- 2009. Classification regression methods (classification and regression tree (CART), adapting boosting (AdaBoost), bagging, and C4.5 algorithm) were used to identify interactions between risk factors. Data analysis was carried out with R3.0.1 software.

  Results : The identified interactions of the factors by a) the AdaBoost method were (consanguinity: sex, previous pregnancies: vaginal delivery, consanguinity: sex: preterm, history of the disease: preterm: asphyxia, consanguinity: sex: asphyxia, history of the disease: sex: small size relative to gestational age, neonatal infection: asphyxia: small size relative to gestational age, history of the disease: sex: asphyxia, preterm: asphyxia: vaginal delivery) by b) the bagging method were (consanguinity: asphyxia, consanguinity: preterm: asphyxia), by c) the C4.5 algorithm were (asphyxia: preterm, asphyxia: consanguinity: history of the disease: preterm), and by d) the CART method were (asphyxia: consanguinity). The sensitivity and specificity of the AdaBoost method was better than other methods (0.941±0.029 and 0.951±0.030, respectively).

  Conclusion : The AdaBoost method could better recognize and model potential interactions between risk factors of cerebral palsy.

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  Background and Objectives : recent years, considerable attention has been paid to statistical models for classification of medical data according to various diseases and their outcomes. Artificial neural networks have been successfully used for pattern recognition and prediction since they are not based on prior assumptions in clinical studies. This study compared two statistical models, artificial neural network and logistic regression, to predict the survival of patients with breast cancer.

  Methods: Two models were applied on cancer registry data, Kerman, southeast of Iran, to predict survival. The data of 712 breast cancer patients in the age group 15 to 85 years was used in this study. The logistic regression and three-layer perceptron neural network models were compared in terms of predicting the survival. Sensitivity, specificity, prediction accuracy, and the area under ROC curve were used for comparing the two models.

  Results : In this study, the sensitivity and specificity of logistic regression and artificial neural network models were (0.594, 0.70) and (0.621, 0.723), respectively. Prediction accuracy and the area under ROC curve for two models were (0.688, 0.725) and (0.70, 0.725), respectively.

  Conclusion: Although there were insignificant differences in the performance of the two models for predicting the survival of the patients with breast cancer, the corresponding results of artificial neural network were more appropriate for predicting survival in such data.

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Background & Objectives: Bovine Tuberculosis (BTB) is one of the most important zoonoses. Mycobacterium bovis is the responsible agent of BTB in the cattle. The current study was conducted to investigate the determination factors of BTB in dairy farms covered by the tuberculin screening test.

Methods: A herd level case- control study was carried out in 124 (62 cases & 62 controls) dairy farms in the provinces of Tehran, Alborz, Hamedan, Isfahan, Qazvin, Qom, Mazandaran and Semnan. The control farms were individually matched with case farms by farm capacity and distance. Statistical analyses were done by Stata 11.2 using conditional logistic regression.

Results: Proper management of manure (OR=0.12 95% CI: 0.03-0.49), regular flaming of stalls (OR= 0.21 95% CI: 0.04-0.92) and complete fencing around the farm (OR= 0.17 95% CI: 0.03-0.81) decreased while the presence of rodents (rat) (OR= 4.90 95% CI: 1.04-23.01) increased the risk of infection. The interaction among these variables was not statistically significant

Conclusion: According to the results, there is an essential need to pay more attention to rodent control in farms.

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  Background & Objectives : Gastric cancer has a low survival and remains a serious threat to the health of human life, especially in developing countries such as Iran. The present study was performed to estimate the main effective factors in the survival rate of patients with gastric cancer in the Province of Kohgilouyeh & Boyerahmad.

  Methods: All cases of gastric cancer in Kohgiloyeh and Boyerahmad recorded in Provinces of Fars and Kohgiloyeh and Boyerahmad cancer registry were enrolled in this study. The impact of the independent variables on the survival was estimated by single and multivariate Cox regression controlled for the probable confounding variables. Survival analysis was performed using Kaplan Meier curves, the log-rank test, and Wilcoxon test to compare the results. Analysis of the data was performed by SPSS 19, and P-values less than 0.05 were considered significant.

 Results: Among the 348 studied patients, 75.6% were male and the rest (24.4%) were female. In general, in this study, 1, 2, 3, 4, and 5-year survival rate of the patients was 37, 27, 20, 19, and 18%, respectively. By combining these end variables in regression models, three risk groups were identified. In the high risk group, the cumulative survival rate was 0% at the end of the fifth year.

 Conclusion: Execution of the down-staging program through public education, considering the low survival rate in this province seems essential especially for high-risk groups such as farmers, ranchers and regional nomadic populations.

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Background and Objectives: Missing data is a big challenge in the research. According to the type of the study and of the variables, different ways have been proposed to work with these data. This study compared five popular imputation approaches in addressing missing data in the questionnaires.

Methods: In this study, 500 questionnaires were used for self-medication in diabetic patients. Missing in the observations was artificially generated by random selection of questions and then deleting them. Five imputation ways included: 1) the mean of the questions, 2) the mean of the person, 3) the mode of the person, 4) linear regression, and 5) EM algorithm. For each method, the mean and standard deviation were compared with imputation. The Spearman correlation coefficient, the percentage of incorrectly classified and kappa statistic were also calculated.

Results: A kappa higher than 0.81 represented almost perfect agreement at 10% missingness. The EM algorithm showed the highest level of agreement with the results of actual data with a Kappa of 0.886. With increasing missingness to 30%, the EM algorithm and the mean of  the person showed a rather similar agreement with a Kappa of 0.697 and 0.687, respectively.

Conclusion: In this study, the EM algorithm was the most accurate method for handling missing data in all models. The mean of the person method is easy for handling missing data, especially for most non statisticians.

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Background and Objectives: Diabetes is a chronic and common metabolic disease which has no curative treatment. Logistic regression (LR) is a statistical model for the analysis and prediction in multivariate statistical techniques. Discriminant analysis is a method for separating observations in terms of dependent variable levels which can allocate any new observation after making discriminating functions. The aim of this study was to compare and determine the effective variables in type 2 diabetes.

Methods: The data included 5357 persons obtained through a cohort study in Kerman, southeastern Iran, in 2009-11. Diabetes was considered the response variable. The independent variables after deleting colinearity and correlated variables included height, waist circumference, age, gender, occupation, education, drugs, systolic blood pressure, HDL, LDL, drug abuse, activities, and triglyceride. Sensitivity, specificity, accuracy, and ROC curve were applied for determining and comparing the prediction power of the models.

Results: The results in the reduced model with extracted significant variables from the full model, the sensitivity of the LR model and DA was 74% and 22.4%, the specificity of the LR model and DA was 71.1 % and 95.4 %, the prediction accuracy of the LR model and DA was 71.5% and 85.3%, and the ROC curve of the LR model and DA was 80.3% and 80.1%, respectively.Simulation showed the sensitivity, specificity, accuracy, and ROC curve was 99.18%, 98.49%, 98.59%, and 99.9% for the LR model and 92.62%, 99.19%, 98.26%, and 99.56% for DA, respectively.

Conclusion: The results showed that the risk factors of diabetes in the logistic regression reduced model were waist circumference, age, gender, LDL level, systolic pressure, and drugs. Also, the sensitivity of the LR model was more than DA while DA had a higher specificity and prediction accuracy. Comparison of the ROC curve showed that the prediction estimated values were rather similar in both models, but the two models were the same asymptotically.

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Background and Objectives: GTN is a general term for an extensive range of malignant trophoblastic diseases including invasive mole, choriocarcinoma, epithelioid trophoblastic tumors and placental site trophoblastic tumors. The aim of this study was to predict the risk of GTN in patients with molar pregnancy in Tehran.

Methods: All cases with partial and complete mole with a record of at least 4 titers of β-hCG were included in this study. Before and after fitting the appropriate model for calculating the area under the curve of each predictor variable, the type of the relationship (linear or non-linear) was first determined using locally weighted scatter plot smoothing (Lowess Smoother) and fractional polynomial regression‏ (Fracpoly); then, a model tailored to data processing was used for drawing the ROC diagram.

Results: Nonparametric chi-square analysis indicated no significant difference between the components of high-risk molar pregnancy and GTN (P=0.39). Generally, among 201 cases of molar pregnancy, 61 (30%) had one of the components of high-risk molar pregnancy. The ROC curve with an AUC of 0.86 showed that the regression slope of β-hCG with 73% sensitivity and 88% specificity could be used as a predictor.

Conclusion: The serum β-hCG measurement after 21 days of molar pregnancy evacuation and the slope of the linear regression line of β-hCG were found be good tests to distinguish between patients who will benefit from spontaneous disease remission and patients developing GTN.

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In epidemiologic studies, the measurement of characteristics of interest is almost always subject to random measurement error. This error and its effects are usually overlooked by researchers. One of its effects is a widespread statistical phenomenon that is well known as regression to the mean. This phenomenon occurs whenever an extreme group of people is selected from a population based on their measurements of a variable. If a second measurement is taken in this group, the mean of the second measurement will be closer to the mean of the population.  In interventional studies, this increase (decrease) might be regarded as the effect of intervention, when in fact it has had no effect. Ignoring regression to the mean will lead to the erroneous conclusions and interpretation of the results of epidemiologic studies and affects the decisions in evidence-based medicine and planning for preventive and public health measures. This paper highlights the importance of this problem and its effects in epidemiologic studies and the ways to avoid it.

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Background and Objectives: One of the main concerns of heart specialists is the occurrence of restenosis after coronary angioplasty which can lead to coronary artery bypass graft, myocardial infarction, and death. The present study was conducted to investigate the factors affecting the frequency of restenosis during four years in patients of Zanjan. 

Methods: In the present retrospective cohort study, all the patients who underwent angioplasty in Ayatollah Musavi Hospital of Zanjan from April of 2009 to June of 2011 were examined in terms of the frequency of restenosis. According to the patients’ medical records, all the demographic and clinical data of the patients were collected. Since the dependent variable was count in nature and the data were over-dispersed, negative binomial regression was used for modeling.

Results: The incidence of at least one restenosis during four years after angioplasty was calculated to be 43%. According to the negative binomial regression model, the ratio of restenosis in patients suffering from diabetes, unstable angina, chronic kidney disease, and myocardial infarction was 32%, 44%, 66%, and 30% more than other patients, respectively (P<0.05).

Conclusion: In the present study, the effective factors of restenosis were recognized as diabetes, unstable angina, chronic kidney disease, and history of myocardial infarction; hence, assessment and periodic follow-up of these patients are strongly recommended.

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Background and Objectives: Breast cancer is one of the most common malignancies in women which accounts for the highest number of deaths after lung cancer. The aim of the current study was to compare the logistic regression and classification tree models in determining the risk factors and prediction of breast cancer.

Methods: We used from the data of a case-control study conducted on 303 patients with breast cancer and 303 controls. In the first step, we included 16 potential risk factors of breast cancer in both the logistic regression and classification tree models. Then, the area under the ROC curve (AUC), sensitivity, and specificity indexes were used for comparing these models.

Results: From 16 variables included in the models, 5 variables were statistically significant in both models. Sensitivity, specificity, and AUC was 71%, 69%, and 74.7% for the logistic regression and 63.3%, 68.8%, and 71.1% for the classification tree, respectively.

Conclusion: The obtained results suggest that the classification tree has more power for separating patients from healthy people. Menopausal status, number of breast cancer cases in the family, and maternal age at the first live birth were significant indicators in both models.

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Standard methods for estimating exposure effects in longitudinal studies will result in biased estimates of the exposure effect in the presence of time-dependent confounders affected by past exposure.

 In the present review article, we first described the assumptions required for estimating the causal effect in longitudinal studies and their structure regarding various types of exposure and confounders; then, we explained the bias of standard methods in estimating the causal effect.

Two types of bias, i.e. over-adjustment bias and selection bias, occur in estimating the effect of time-varying exposure in the presence of time-dependent confounders affected by previous exposure using standard regression analysis. Standard regression methods cannot sufficiently modify time-dependent confounders and estimate the total causal effect of the exposure.

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Background and Objectives: Changes in ideals and aspirations of childbearing are important factors in fertility behavior. Nowadays, fertility rate reduction below the replacement level and decreased childbearing ideals are the most common fertility challenges in Iran. So, with the decrease in the fertility rate, it is necessary to be aware of the ideal number of children and its determinants in order to adopt suitable population policies contexts. The main objective of this study was to investigate factors affecting the ideal number of children using Poisson regression model.
Methods: In 2012, 389 ever married women aged 15-49 in Semnan Province were selected using two-phase stratified random sampling method and studied through applying a structured questionnaire. To model the ideal number of children by Poisson regression model, marriage duration has taken as offset and the number of children, job status, education level, marriage type, and resident place were considered as predictors. The model was fitted with SPSS software version 22.
Results: All predictors in this study had significant effects on ideal number of children in Semnan (p-value <0.05). Women’s ideal number of children who had 2 or fewer children, were employed, and had university education with consanguineous and rural  marriage was higher than those who had 3 and more children, were unemployed, and had elementary and secondary education with inter-family and urban marriage.
Conclusion: To model the ideal number of children, since it is discrete and count, a Poisson regression model is more efficient as compared to linear regression model.