PTSD Analysis Techniques

This assignment delves into the analysis of Post-Traumatic Stress Disorder (PTSD) using various statistical techniques. It examines the limitations of logistic regression for PTSD analysis due to the time factor involved. The focus then shifts to Linear Discriminant Analysis (LDA) and its application in categorizing PTSD based on trauma types (physical, verbal, sexual). The Logrank test is also discussed as a suitable method for comparing survival distributions in PTSD patients, considering censored data and proportional hazards assumptions.

The Relationship between Intimate Partner Violence and PTSD: An application of Cox
regression with time varying covariates
Contents
The Relationship between Intimate Partner Violence and PTSD: An application of Cox regression with
time varying covariates................................................................................................................................1
1.1 Introduction.................................................................................................................................1
1.2 Data collection and research method...........................................................................................1
1.2.1 Data collection.....................................................................................................................1
1.2.2 Research methodology.........................................................................................................2
1.3 Results and discussion.................................................................................................................3
1.4 Results and discussion.................................................................................................................4
1.5 Limitations of the study...............................................................................................................6
1.6 Alternative methods.....................................................................................................................6
1.7 References...................................................................................................................................8

1.1 Introduction
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.
1.2 Data collection and research method
1.2.1 Data collection
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.
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.
1.2.2 Research methodology
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.

Figure 1 Showing the survival data unordered
Note: The data for survival analysis should be in such way so that we can visualize from the
above graph.
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 survival
function gives the probability that a subject will survive past time t. 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 independent variables though it allows an unspecified form of the
underlying survival function.
Major survival methods
Kaplan- Meier survival method
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.
Cox Regression survival method
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. The key rule for time dependent covariates in a Cox model is simple and essentially
the same as that for gamblingg.i.e: oneyou cannot predict the future.look into the future. This is
because aA covariate may change according to the in any way based on past data or outcomes,
however but 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 This means that the survival curves for two strata must have
hazard functions which that are proportional over the period of time (Monem A Mohammed
2014).
1.3 Results and discussion
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.

Figure 2 CIF plot from the survival analysis
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.
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).
1.4 Limitations of the study
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.
1.5 Alternative methods
T-test:
A t-test is used to is an analysis the mean of two population using’s means through the use of
statistical methodsstudy. Generally A t-test is used in those cases where the sample size are
relatively small. with two samples is commonly used with very small sample size With small
sample size t test helps in, testing the difference in the samples. Also when the variances of
2 normal distributions are unknown in case of t test.not known.
T test used the A t-test looks at the t-statistic value, Degrees of freedom (DF) theand the t-
distribution and DF (degrees of freedom) 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. test
statistic in the test is known as the t-statistic. However if there are more than two variables then
the Analysis of Variance (ANOVA) test is used instead of t test.To conduct a test with 3 or more
variables, analysis of variance must be used.
Some of the most important The assumptions of t test are as follows:underlying a t-test are that
 X follows a normal distribution with mean μ and variance σ2
 ps2 follows a χ2 distribution with 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.
Logistic regression
It is one of thea statistical method used tofor analyze the sing given dataset with one or where
there are 1 or more independent variables tothat 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. (in which there are only two possible outcomes).
The dependent variable is binary or dichotomous, i.e. it only contains data coded as 1
(TRUE, success, loan granted, etc.) or 0 (FALSE, failure, loan rejected, etc.).
The aim of suchlogistic regression is to find model which fits best in find the best fitting
model to 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 (dependent variable = response or outcome variable) and set of independent (predictor or
explanatory) variables.

The assumptions of logistic regression:
- 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:
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.
For the PTSD problem, it can be divided into different groups such as physical, verbal & sexual
trauma & identify the factors related to each different groups.
Logrank –Test:
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).
1.6 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:
http://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.