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Reasons for Using Cox Proportional Hazards in Dr. Neal’s Research
Dr. Neal utilized the Cox Proportional Hazards model in her research due to the fact that Cox Proportional Hazards took into account the time at which fetal death occurred, while a logistic regression did not. Stratified logistic regression can take the time of death into account, but, unlike Cox Proportional Hazards, it does not allow for employing censored data (non-death), which results in that the sample size is greatly reduced, so the test loses much power and becomes unlikely to detect the effect. Cox Proportional Hazards, therefore, permitted Dr. Neal to both take into account the time of death and to use the data about successfully produced babies, thus allowing for not losing the power of the research.
The censored data in Dr. Neal’s research consisted of cases where births were successfully given, whereas the time-to-event was the interval starting at the fifth month of pregnancy (the point at which participants began being studied) and finishing at the time when fetal death took place.
Differences and Similarities between Using Cox Proportional Hazards and the Logistic Regression
Both Cox Proportional Hazards and a logistic regression allow for identifying whether a dichotomous dependent variable can be predicted from a number of independent variables/covariates. Both models also produce a “natural” measure of effect size, a ratio (odds ratio in the logistic regression, hazard ratio in the Cox Proportional Hazards) (Forthofer, Lee, & Hernandez, 2007).
However, Cox Proportional Hazards allows for taking into account the time at which the event reflected in the dependent variable occurred, whereas the logistic regression does not. This gap in logistic regression can be filled if a stratified logistic regression is used, but, unlike Cox Proportional Hazards, the stratified logistic regression will not permit for taking the censored data into account.
Strengths and Limitations of Cox Proportional Hazards and the Logistic Regression
A crucial advantage of Cox Proportional Hazards is that it allows for using censored data (as has already been mentioned), which permits for not losing power due to reduced sample size. In addition, it enables one to take into account the time when an event occurs, as well as to use covariates that also vary in time (Austin, 2012). A disadvantage of this model is that it requires some additional assumptions, e.g., that the researched hazards do not cross, remaining proportional over time instead.
A limitation of the logistic regression is that it does not take into account the time when an outcome occurred (Field, 2013), thus providing a less detailed result. A strength of the logistic regression is tied to this limitation: it is easier to run, for it requires less data to be conducted (Warner, 2013).
The Impact of the Choice of the Test on Statistical and Clinical Results of a Study
Statistically, Cox Proportional Hazards allows for a greater likelihood of detecting an effect when there is one (the above-mentioned statistical power) in comparison to the logistic regression. Clinically, Cox Proportional Hazards permits for identifying at which moment of time there is a greater risk that the event occurs, which cannot be done using a logistic regression and which, for example, might let one understand when an intervention is most crucial if the event is to be prevented.
References
Austin, P. C. Generating survival times to simulate Cox proportional hazards models with time-varying covariates. Statistics in Medicine, 31(29), 3946-3958. n.d. Web.
Field, A. (2013). Discovering statistics using IBM SPSS Statistics (4th ed.). Thousand Oaks, CA: SAGE Publications.
Forthofer, R. N., Lee, E. S., & Hernandez, M. (2007). Biostatistics: A guide to design, analysis, and discovery (2nd ed.). Burlington, MA: Elsevier Academic Press.
Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications.
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