## Data and Research Methodology

Question:

Discuss about the Survival Analysis and Regression Models.

This research is aimed to critically appraise the statistical method used in the selected paper and suggest the alternative analysis if there are any which can be performed. The current review paper has been organized in four different parts. The first is devoted to explain the data and research method used in the study. In the second section the results from the selected paper has been reviewed followed by the major limitation of the paper in the third section. Finally in the fourth section the alternative analysis method has been discussed.

For the study, the researcher has picked up random sample of 211 Japanese women who were born in United States. Also the Japanese women who migrated from Japan to United State were also included in the data set. In the sample respondents in the age group 18 to 49 were included. This is the appropriate age group for the analysis, as the women younger than 198 years and more than 49 years are not expected to face partner violence, except in some cases. Also the author argued that the upper age limit was fixed as the systems of posttraumatic may be different for old females. So, the 211 samples were finally selected after the survey & personal interview. The survey was initially sent out to 407 households, but only few households have responded(Yoshihama & Horrock 2003).

The problem with the data collection in this research paper is that only a certain ethnic group has been selected. The sampling was done on one strata which is Japanese American women. Since, the intimate partner for the samples here could be highly different. Most of the cases it would be a partner from the same ethnic group but few cases may be where the partner is from other ethnic group. So, the way this relationship exists might be little biased in the population. So, it would be difficult to generalize the results from the current study(Teddlie & Yu 2007; Daniel 2011).

Also, the survey has 52% response rate and the women with higher age were the group who has mostly not responded. Response rate could be been increased by offering some rewards in the form of money, gifts or some other form. But this leads to biasness in the surveys. In this case, the participants were given $20 each. Also the research should have focused on increasing the sample size by distributing the questionnaire to more people. The results are considered to be robust if the sample size is large. Also the results from the analysis can be generalized in case of large sample size.

## Results and Limitations

Furthermore, the dependent variable is a dichotomous variable, which flag the respondent whether they have experienced PSTD in their lifetime. In other words the dependent variable will take only the value 1 or 0(George et al. 2014). Also, the time at which they experienced for the first time has been updated for each respondent. Since the researcher is using survival analysis to find out the time the event occurs first, the selection of age group is very critical. Most of the data would be censored since the respondents are yet to experience this kind of event. Inclusion of people at less age might leads to more observations with censored data. One major challenge with the data would be to get accurate time of event for each respondent. Since, the data has been collected at one point time rather than observing over the period of time, it might affect the results.

Since the nature of the study is to understand the time taken for any event (in this case PSTD) to happen, the researcher have used survival analysis which is one of the most appropriate techniques for this kind of analysis. One of most important task in survival analysis is correctly identify the population and collect relevant data. There are 3 possibilities in terms of data(Cierniak & Reimann 2011; Mangal & Mangal 2013).

Firstly, group of observations where the event has occurred within the period of examination. In this case it is between 18-49 years. Secondly, possibility would be that the respondent is dropped from the study within this period. Last possibility would be the observations where the event did not occurred within the range of study which is basically the censored observations.

The data has not been ordered in the above graph but the graph could be provided with the data ordered by those categories.

There are three major functions that can be presented in the survival analysis. To get the probability of subject’s survival after the time period t survival analysis is used. The hazard function, h(t), is the instantaneous rate at which events occur, provided that no previous events. The CIF (Cumulative Incidence function) at time t would be 1 minus the survival function.

In this article the researcher has used SAS functionality to perform the survival analysis. They have used Cox proportional hazard models for the analysis. So, this model has few assumptions that are very critical to understand before go to the results. It assumes the parametric form of the effects of the explanatory variables though it allows an unspecified form of the underlying survival function.

## Alternative Analysis Methods

This method is used for time to event kind of analysis & is non-parametric. This is usually used to describe survivorship of study population. Basically, median survival time is calculated using the method. Also, it is commonly used to compare two study populations.

It is a parametric model. It is used to find the relationship between covariates and the hazard of experiencing an event, and a partial likelihood approach to estimate the model parameters. One of most important rule in Cox model ( with time dependent covariates) is similar to that of gambling.g.i.eone cannot predict the future.. This is because acovariate may change according to the past data or outcomes, however it may not reach forward in time (Yoshihama & Horrock 2003; Monem A Mohammed 2014).

The major advantage of the cox regression models is that it allows comparing the hazards for the different explanatory variables. But the cox model has major assumptions in terms of proportional hazard. In other words survival curves for two strata must have hazard functions which are proportional over the period of time (Monem A Mohammed 2014).

Out of all 211 respondents, 115 have reported for having experienced intimate partner violence & 30 had experienced PTSD sometime in the past. The CIF plot is given as below.

This plot shows that the cumulative probability of experiencing intimate partner violence (IPV) and posttraumatic stress disorder (PSTD) by age of respondent. For the higher age group the probability of experiencing PSTD is also high. Few age groups there is sudden jump in the probability. For example, for the age group 49 the probability suddenly jumps up very high. However, the article has not properly provided the hazard function against each covariate. Graphical presentation of the hazard function would have helped in validating the assumption & also to clearly interpret the results.

The problem with the analysis is that most of the respondent did not experience the event till 49 years. The assumption that was made for the analysis that most of the women would experience the intimate partner violence during their teens might not be correct. Thorough study on when people start their intimate life (especially for Japanese American group) was not done. Based on the age when their intimation starts then only the time horizon should have decided for censoring. So, out of total population 28% were censored data which makes the analysis biased.

The author’s direct claim might be valid that PTSD was mainly caused due to intimate partner violence but the article doesn’t give any references for the work done to understand other causes of the event. Exploration of other factors should be done. Also, the time of the event might not be completely true. PTSD might have been discovered very late for respondent. Generally, people take time to completely behave on certain way.

## Survival Analysis

However, the use of Cox regression with time varying covariate was significant without controlling for other factors. This method is dynamic & provides the changing rates of PTSD over the life course as well as the changing number of individuals at risk. Based on the availability of the data, alternative methods could be used for performing the above analysis. This technique, their use & limitations has been provided as well (Monem A Mohammed 2014; Lanfranchi et al. 2010).

The study by (Yoshihama & Horrock 2003) suffers from several limitations. One of the major limitations is that the research assumed that the PTSD was caused by the intimate partner violence. However if may be the case that the trauma was due to some other reasons not related to PTSD. Similarly the results from both the cox regression and the chi square test showed that PTSD and intimate partner violence are only marginally related. However most of the previous studies have shown strong and positive relationship between the two variables(SABR et al. 2013). The difference in the results is may be the difference in the sample selection. As already discussed in the previous section also sample was collected from only one specific group and also the assumption that the trauma was caused by PTSD only leads to difference in results.

A t-test is used to analysis the mean of two population usingstatistical methods. Generally A t-test is used in those cases where the sample size are relatively small. With small sample size t test helps in testing the difference in the samples. Also the variances of 2 normal distributions are unknown in case of t test..

T test used the t-statistic value, Degrees of freedom (DF) and the t-distribution to determine the probability of difference in two populations. In case of this test the test statistics is also popularly known as the t statistics. . However if there are more than two variables then the Analysis of Variance (ANOVA) test is used instead of t test.

Some of the most important assumptions of t test are as follows:

- X follows a normal distribution with mean μ and variance σ2
- ps2 follows a χ2 distributionwith p degrees of freedom under the null hypothesis, where p is a positive constant
- Z and s are independent.

T-test could be alternative method for comparing the samples time to event for two different groups. But in this case, it will not be applicable as data includes observations which are censored. Since the data is censored iti will not follow the normal distribution. It will be highly skewed. Therefore, t-test is not suited for this kind of analysis.

## Cox Proportional Hazard Models

It is one of the statistical method used to analyze the given dataset with one or 1 or more independent variables to determine an outcome(McCarty & Hastak 2007). The outcome in this case is measured with a binary variable. In other words the depennet variable can only take two values. (

The aim of such regression is to find model which fits best in establishing the relationship between dependent and independent variables in the model. The dependent variable is also known as the response or the outomce variable whereas the independent variables is known as the explanatory variable or predictor variable.

- The conditional distribution y|x is a Bernoulli distribution rather than normal distribution as assumed in linear regression.
- The predicted values are bounded to (0,1) since the models gives probabilities as output.

For the analysis that is performed in the paper logistic regression cannot be used since the event happening is observed over the period of time & not by standing at one point. The logistic regression ignores the time factor involved for the event. The time taken for any person to reach to PTSD would be very critical for further analysis.

Linear discriminant analysis (LDA) is a generalization of what Fisher proposed as linear discriminant, a method used in statistics. It basically finds a linear combination of features that characterizes or separates 2 or more classes of events. It is used in biomedical studies. During retrospective analysis, patients are divided based on the severity of disease- like severe, mild, and moderate. The results of this analysis provide different significant factors for each group.

The logrank test is a statistical test to compare survival distribution of two samples. This technique is mainly used if the data is rightly skewed & censored. The groups are defined by categorical covariates. Under the assumption of proportional hazards it will perform better (Indrayan & Bansal n.d.; Yoshihama & Horrock 2003).

References

Cierniak, G. & Reimann, P., 2011. Specification of Research Strategy and Methodology,

Daniel, J., 2011. Sampling Essentials: Practical Guidelines for Making Sampling Choices, SAGE.

George, B., Seals, S. & Aban, I., 2014. Survival analysis and regression models. NCBI, 21(4), pp.686–694.

Indrayan, A. & Bansal, A., The Methods of Survival Analysis for Clinicians, New Delhi.

Lanfranchi, L.M.M.M., Viola, G.R. & Nascimento, L.F.C., 2010. The use of Cox regression to estimate the risk factors of neonatal death in a private NICU, Taubate.

Mangal, S.K. & Mangal, S., 2013. RESEARCH METHODOLOGY IN BEHAVIOURAL SCIENCES, PHI learning pvt. ltd.

McCarty, J.A. & Hastak, M., 2007. . Segmentation approaches in data-mining: A comparison of RFM, CHAID, and logistic regression. Journal of business research, 60(6), pp.656–662.

Monem A Mohammed, 2014. Survival Analysis By Using Cox Regression Model with Application. International journal of scientific & technology, 3(11).

SABR, B. et al., 2013. Intimate Partner Violence, Depression, PTSD and Use of Mental Health Resources among Ethnically Diverse Black Women. NCBI, 52(4).

Teddlie, C. & Yu, F., 2007. Mixed Methods Sampling: A Typology With Examples. Journal of Mixed Methods Research, 1(1), pp.77–100. Available at: https://mmr.sagepub.com/cgi/doi/10.1177/2345678906292430 [Accessed July 9, 2014].

Yoshihama, M. & Horrock, J., 2003. The Relationship Between Intimate Partner Violence and PTSD: An Application of Cox Regression With Time-Varying Covariates. Journal of Traumatic Stress,, 16(4), pp.371–380.

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