What are the advantages/disadvantages of the different regression approaches when using epidemiology exposure-response data to estimate cancer cancer potency?

What are the advantages/disadvantages of the different regression approaches (Cox proportional hazards, Poisson, Spline analysis) when using epidemiology exposure-response data to estimate cancer potency? Are there other regression approaches that should be considered?
Bioinformatics Epidemiology
Mohammad Asaduzzaman Chowdhury
One of the most significant statistical approaches used in analytical epidemiology is regression modeling. The effect of one or more explanatory variables (e.g., exposures, subject characteristics, risk factors) on a response variable such as mortality or cancer can be examined using regression models. Adjusted effect estimates that account for potential confounders can be obtained from multiple regression models. Regression methods can be used in all types of epidemiological studies, making them a universal tool for data analysis in epidemiology. Depending on the measurement scale of the response variable and the study design, various regression models have been created. For continuous outcomes, linear regression, logistic regression, Cox regression for time-to-event data, and Poisson regression for frequencies and rates are the most relevant methods. This chapter introduces these regression models in a nontechnical way, using cancer research as an example. In epidemiological studies, regression modeling is one of the most extensively used methods. It provides a tool for discovering statistical connections, which may then be used to study potential causal associations relevant to disease control. Multivariable regression has long been the conventional model, having a single dependent variable (typically disease) and numerous independent variables (predictors). Multivariable regression can be generalized to multivariate regression, with all variables possibly statistically dependent. This provides a much richer modeling framework. We examine and contrast these approaches using a number of basic illustrative cases. While Bayesian network structure discovery is a relative newcomer to the epidemiology literature, it has a long history in computing science. Multivariate analysis in epidemiological studies can help researchers gain a better knowledge of disease processes at the population level, which can lead to more effective disease management and prevention initiatives.
Rafael Carvalho
Tauqeer Hussain Mallhi; The type of regression used depends on the outcome variable. Different independent can be used. They can be continuous, dichotomic or categorical (normally in a categorical variable we define one reference) .
When analyzing continuous variables as independent we consider that each algorism will modify that OR. As an example, in one paper published in 2017, we analyzed factors that interfere with surgical site infection. Analyzing surgery length, in hours, we found that each minute could contribute to the rise in the incidence of Surgical Site Infection. Each hour presented an OR of 1.3, or 30% per hour. 
There is no trouble to do that in statistical programs such as Stata, SPSS and R. Just use the code for logistic regression and put your continuous variable.

Tauqeer Hussain Mallhi
Thanks for the information. Can you please guide me that whether we can use logistic regression when dependent variable is bivariate and independent is continuous?
There are many things to consider in terms of advantages/disadvantages of different regression models - making this a huge question to answer.  However, one of the first things to consider is properties of the response (or dependent or outcome) variable.  Different types of regression models (such as those listed) are based on different probability models that should align with properties of the response variable.  For example, Poisson log-linear regression is a model for responses that are integer counts per some unit effort, while Cox proportional hazard is used to model responses that are survival times.   Before making any choice, it's important to understand the assumptions underlying each model and assess their reasonableness given the problem and data in question.  We tend to assume models are free, but model assumptions insert information into an analysis beyond that contained in the data - and are best justified when consistent the design, the data collected, and the objectives of the research.

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