perform a Cox Proportional Hazards Regression Analysis
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Title: Cox Proportional Hazards Regression
Name: Date:
Introduction: Summary of the data have been appeared by the first table, in the wake of inspecting that we can see the number of observations are more noteworthy than the number of observed times. It is in this way, the results are something similar for the two methods, doesn't in the event that we use Breslow strategy or ef- fron technique. Descriptive statistics are given for each variable. For nature of the model (integrity of fit) the following table shows numerous indicators. In
ANOVA and liner regression, these outcomes are identical to the investigation of variance table and to the R2. On the log ratio the most basic/significant value to
consider is the probability of chi-square. This is corresponding to the Fisher's F test: we try to evaluate if the factors bring basic information by viewing at the
model as it is described with a simpler model with no impact of the covariates. For the present circumstance, as the probability is lower than 0.05, we can assume that huge information is brought by the factors.
Details of the model have been shown by the following table. This given table is very important for understanding the effects of various variables. Let con-
duct Cox's proportional hazards model to check the following hypothesis. Hypothesis: H0: The risk of dying is not related to the patient treatment group. (Null
Hypothesis) H1: The risk of dying is related to the patient treatment group. (Alternative Hypothesis) From the output of the test p value (0.2742) is less than 0.05 crashes to reject the null hypothesis and concluded that the risk of dying isn't identified with the patient treatment group. Additionally we could not found any
association between risk of dying and the patient treatment group.
By seeing chi-squares probability on this table we come to realize that the variable most affecting survival time is Group (1 Chemo or 2 Placebo). This shows that
the Group (1 Chemo or 2 Placebo) of the patient tremendously affects survival time at beginning of the investigation. As the exponential of the parameter estimate the hazard ratio is procured. The p-value is greater than alpha = 0.05 It can be seen for all the covariates, it shows that there is no infringement of the proportional risk presumption. Towards the end, the cumulative hazard work is shown:
There is no variable covariate with a huge effect is the age, this study has proven that. The risk increments by 1.13 (Hazard ratio) each time we require a year the
associated coefficient being positive. On the survival time the other covariates don't have a critical impact. References: Hazra, A., & Gogtay, N. (2016). Bios-
tatistics series module 6: Correlation and linear regression. Indian Journal of Dermatology, 61(6), 593-601. Retrieved from
https://doaj.org/article/7e6f5ec7ddaa4ecbad979d16 f3e59a79 ● Navratil, R., & Ehsanes Saleh, A. K., Md. (2016). Aligned rank tests in measurement error
model. Applications of Mathematics, 61(1), 47-59.
Survival distribution function
0.75000000000000044 1 1 1.5 1.5 2 2 3 3 3.5 3.5 4 4 4.5 4.5 5 5 5 0.85990958029843079 0.85990958029843079 0.7118066965342098 0.7118066965342098
0 7118066965342098 0 7118066965342098 0 52046794062418167 0 52046794062418167 0 40578028576000991 0 40578028576000991 0 30414525740081189
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Student paper 100% Student paper 77%
0.7118066965342098 0.7118066965342098 0.52046794062418167 0.52046794062418167 0.40578028576000991 0.40578028576000991 0.30414525740081189 0.30414525740081189 0.16570496034268051 0.16570496034268051 6.6637270467136411E-2 6.6637270467136411E-2 6.6637270467136411E-2 6.6637270467136411E-2 Serial Time (years)
-Log(SDF) 0.75000000000000044 1 1 1.5 1.5 2 2 3 3 3.5 3.5 4 4 4.5 4.5 5 5 5 0.15092803444996747 0.15092803444996747 0.33994889806295847 0.33994889806295847 0.33994889806295847 0.33994889806295847 0.65302698624542743 0.65302698624542743 0.90194343394349485 0.90194343394349485 1.1902498712983243 1.1902498712983243 1.7975464193146382 1.7975464193146382 2.7084912413391167 2.7084912413391167 2.7084912413391167 2.7084912413391167 Serial Time (years)
Log(-Log(SDF)) 0.75000000000000044 1 1 1.5 1.5 2 2 3 3 3.5 3.5 4 4 4.5 4.5 5 5 5 -1.8909521488203513 -1.8909521488203513 -1.0789599724829086 -1.0789599724829086 -1.0789599724829086 -1.0789599724829086 -0.42613682399694985 -0.42613682399694985 -0.10320347270028969 -0.10320347270028969 0.1741632609625319 0.1741632609625319 0.5864226346549416 0.5864226346549416 0.99639174234249261 0.99639174234249261 0.99639174234249261 0.99639174234249261 Serial Time (years)
Summary statistics (Events): Total observedTotal failedTotal censoredTime steps
1210210
VariableObservationsObs. with missing dataObs. without missing dataMinimumMaximumMeanStd. deviation
Serial Time (years)120120.5005.0002.3961.557
Satus At Serial Time (1=event; 0=censored)120120.0001.0000.8330.389
Group (1 Chemo or 2 Placebo)120121.0002.0001.5000.522
StatisticIndependentFull
Observations10.00010.000
DF0.0001.000 -2 Log(Likelihood)36.33533.653
AIC36.33535.653
SBC36.33535.955
Iterations1.0003.000
Goodness of fit statistics: StatisticDFChi-squarePr > Chi² -2 Log(Likelihood)12.682045720.101
Score12.8531954690.091
Wald12.5750473660.109
Test of the null hypothesis H0:
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beta=0: VariableValueStandard errorWald Chi-SquarePr > Chi²Hazard ratioHazard ratio Lower bound (95%)Hazard ratio Upper bound (95%) Group (1 Chemo or 2
Placebo)1.2000.7482.5750.1093.3190.76714.370
Proportionality test: VariablerhoChi-squarePr > Chi² Group (1 Chemo or 2 Placebo)0.0720598170.0474948340.827
Global0.0474948340.827
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Student paper
Cox Proportional Hazards Regression
Original source
Cox Proportional Hazards Regression
2
Student paper
Descriptive statistics are given for each variable.
Original source
Descriptive statistics are then displayed for each variable
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In ANOVA and liner regression, these outcomes are identical to the investiga- tion of variance table and to the R2.
Original source
These outcomes are equal to the R2 and to the analysis of variance table in AN- OVA and linear regression
2
Student paper
On the log ratio the most basic/significant value to consider is the probability of chi-square. This is corres- ponding to the Fisher's F test:
Original source
The most important value to look at is the probability of the Chi-square test on the log This is equivalent to the Fisher's F test
1
Student paper
we try to evaluate if the factors bring ba- sic information by viewing at the model as it is described with a simpler model with no impact of the covariates.
Original source
we try to evaluate if the variables bring significant information by comparing the model as it is defined with a simpler model with no impact of the covariates
2
Student paper
Details of the model have been shown by the following table.
Original source
The following table gives details on the model
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Student paper
Let conduct Cox's proportional hazards model to check the following hypothesis.
Original source
Let conduct Cox's proportional hazards model to check the following hypothesis
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The risk of dying is not related to the pa- tient treatment group. (Null Hypothesis) H1: The risk of dying is related to the pa- tient treatment group. (Alternative Hypo- thesis) From the output of the test p value (0.2742) is less than 0.05 crashes to reject the null hypothesis and concluded that the risk of dying isn't identified with the patient treatment group.
Original source
The risk of dying is not related to the pa- tient treatment group (Null Hypothesis) H1 The risk of dying is related to the pa- tient treatment group From the output of the test p value (0.2742) is less than 0.05, fail to reject the null hypothesis and con- cluded that the risk of dying is not re- lated to the patient treatment group
1
Student paper
Additionally we could not found any as- sociation between risk of dying and the patient treatment group. By seeing chi- squares probability on this table we come to realize that the variable most affecting survival time is Group (1 Chemo or 2 Placebo).
Original source
Additionally we could not found any as- sociation between risk of dying and the patient treatment group On this table, we can see from looking at the probabil- ity of the Chi-squares that the variable most influencing survival time is Group (1 Chemo or 2 Placebo)
2
Student paper
This shows that the Group (1 Chemo or 2 Placebo) of the patient tremendously af- fects survival time at beginning of the in- vestigation. As the exponential of the parameter estimate the hazard ratio is procured. The p-value is greater than al- pha = 0.05 It can be seen for all the cov- ariates, it shows that there is no infringe- ment of the proportional risk presumption.
Original source
Group (1 Chemo or 2 Placebo) of the pa- tient at the beginning of the study has a significant effect The hazard ratio is ob- tained as the exponential of the para- meter estimate, and it It can be noted that for all the covariates, the p-value is greater than alpha = 0.05
4/9/2021 Originality Report
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The risk increments by 1.13 (Hazard ra- tio) each time we require a year the asso- ciated coefficient being positive.
Original source
The related coefficient presence positive, however, the risk increases by 1.13 (Haz- ard ratio) each time we take a year
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Student paper
Hazra, A., & Gogtay, N.
Original source
Hazra, A., & Gogtay, N
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Student paper
Biostatistics series module 6: Correlation and linear regression. Indian Journal of Dermatology, 61(6), 593-601.
Original source
Biostatistics series module 6 Correlation and linear regression Indian Journal of Dermatology, 61(6), 593-601
4
Student paper
https://doaj.org/article/7e6f5ec7ddaa4ec bad979d16 f3e59a79 ● Navratil, R., & Eh- sanes Saleh, A.
Original source
https://doaj.org/article/7e6f5ec7ddaa4ec bad979d16 f3e59a79
3
Student paper
Aligned rank tests in measurement error model. Applications of Mathematics, 61(1), 47-59.
Original source
Aligned rank tests in measurement error model Applications of Mathematics, 61(1), 47-59
2
Student paper
Survival distribution function
Original source
Survival distribution function
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0.75000000000000044 1 1 1.5 1.5 2 2 3 3 3.5 3.5 4 4 4.5 4.5 5 5 5 0.85990958029843079 0.85990958029843079 0.7118066965342098 0.7118066965342098 0.7118066965342098 0.7118066965342098 0.52046794062418167 0.52046794062418167 0.40578028576000991 0.40578028576000991 0.30414525740081189 0.30414525740081189 0.16570496034268051 0.16570496034268051 6.6637270467136411E-2 6.6637270467136411E-2 6.6637270467136411E-2 6.6637270467136411E-2 Serial Time (years) -Log(SDF) 0.75000000000000044 1 1 1.5 1.5 2 2 3 3 3.5 3.5 4 4 4.5 4.5 5 5 5 0.15092803444996747 0.15092803444996747 0.33994889806295847 0.33994889806295847 0.33994889806295847 0.33994889806295847 0.65302698624542743 0.65302698624542743 0.90194343394349485 0.90194343394349485 1.1902498712983243 1.1902498712983243 1.7975464193146382 1.7975464193146382 2.7084912413391167 2.7084912413391167 2.7084912413391167 2.7084912413391167 Serial Time (years) Log(-Log(SDF)) 0.75000000000000044 1 1 1.5 1.5 2 2 3 3 3.5 3.5 4 4 4.5 4.5 5 5 5 -1.8909521488203513 -1.8909521488203513 -1.0789599724829086 -1.0789599724829086 -1.0789599724829086 -1.0789599724829086 -0.42613682399694985 -0.42613682399694985 -0.10320347270028969 -0.10320347270028969 0.1741632609625319 0.1741632609625319 0.5864226346549416 0.5864226346549416 0.99639174234249261 0.99639174234249261 0.99639174234249261 0.99639174234249261 Serial Time (years)
Original source
0.75 1 1 1.5 1.5 2 2 3 3 3.5 3.5 4 4 4.5 4.5
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5 5 5 0.85990958029843023 0.85990958029843023 0.71180669653420914 0.71180669653420914 0.71180669653420914 0.71180669653420914 0.52046794062418167 0.52046794062418167 0.40578028576000957 0.40578028576000957 0.30414525740081189 0.30414525740081189 0.16570496034268045 0.16570496034268045 6.663727046713637E-2 6.663727046713637E-2 6.663727046713637E-2 6.663727046713637E-2 Serial Time (years) -Log(SDF) 0.75 1 1 1.5 1.5 2 2 3 3 3.5 3.5 4 4 4.5 4.5 5 5 5 0.1509280344499673 0.1509280344499673 0.33994889806295792 0.33994889806295792 0.33994889806295792 0.33994889806295792 0.65302698624542699 0.65302698624542699 0.90194343394349408 0.90194343394349408 1.1902498712983229 1.1902498712983229 1.7975464193146391 1.7975464193146391 2.7084912413391131 2.7084912413391131 2.7084912413391131 2.7084912413391131 Serial Time (years) Log(-Log(SDF)) 0.75 1 1 1.5 1.5 2 2 3 3 3.5 3.5 4 4 4.5 4.5 5 5 5 -1.8909521488203505 -1.8909521488203505 -1.0789599724829086 -1.0789599724829086 -1.0789599724829086 -1.0789599724829086 -0.42613682399694952 -0.42613682399694952 -0.10320347270028955 -0.10320347270028955 0.17416326096253182 0.17416326096253182 0.58642263465494204 0.58642263465494204 0.99639174234249228 0.99639174234249228 0.99639174234249228 0.99639174234249228 Serial Time (years)
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Summary statistics (Events):
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Summary statistics (Events)
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Total observedTotal failedTotal censored- Time steps
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Total observedTotal failedTotal censored- Time steps
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with missing dataObs. without missing dataMinimumMaximumMeanStd.
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with missing dataObs without missing dataMinimumMaximumMeanStd
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Serial Time (years)120120.5005.0002.3961.557 Satus At Serial Time (1=event; 0=censored)120120.0001.0000.8330.389 Group (1 Chemo or 2 Placebo)120121.0002.0001.5000.522
Original source
Serial Time (years)120120.5005.0002.3961.557 Satus At Serial Time (1=event 0=censored)120120.0001.0000.8330.389 Group (1 Chemo or 2 Placebo)120121.0002.0001.5000.522
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DF0.0001.000 -2 Log(Likelihood)36.33533.653
Original source
-2 Log(Likelihood) 36.335 33.653
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Goodness of fit statistics:
Original source
Goodness of fit statistics
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Test of the null hypothesis H0:
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Test of the null hypothesis H0
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VariableValueStandard errorWald Chi- SquarePr > Chi²Hazard ratioHazard ratio Lower bound (95%)Hazard ratio Upper bound (95%) Group (1 Chemo or 2 Placebo)1.2000.7482.5750.1093.3190.767 14.370
Original source
VariableValueStandard errorWald Chi- SquarePr > Group (1 Chemo or 2 Placebo)1.2000.7482.5750.1093.3190.767 14.370
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VariablerhoChi-squarePr > Chi² Group (1 Chemo or 2 Placebo)0.0720598170.0474948340.827 Global0.0474948340.827
Original source
VariablerhoChi-squarePr > Group (1 Chemo or 2 Placebo)0.0720598170.0474948340.827 Global0.0474948340.827
