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Survival analysis part II: multivariate data analysis--an introduction to concepts and methods.

Bradburn MJ, Clark TG, Love SB, Altman DG - Br. J. Cancer (2003)

View Article: PubMed Central - PubMed

Affiliation: Cancer Research UK/NHS Centre for Statistics in Medicine, Institute of Health Sciences, Old Road, Oxford OX3 7LF, UK. mike.bradburn@cancer.org.uk

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An appealing feature of the Cox model is that the baseline hazard function is estimated nonparametrically, and so unlike most other statistical models, the survival times are not assumed to follow a particular statistical distribution... The estimated hazard function of the ovarian cancer data as displayed in the previous paper (Clark et al, 2003) may be consistent with that derived from a Weibull PH model with decreasing hazard... The proportion of patients who are event-free in the placebo group at any time point t1 is the same as the proportion of those who are event-free in the new treatment group at a time t2=ϕt1... Figure 3 shows the cases where ϕ>1 and ϕ<1, which represent situations where the length of survival is increased and decreased in the new treatment group compared with the placebo, respectively... We use the non-small cell lung cancer dataset to illustrate the AFT model, focusing on the relapse-free survival (i.e., the time from diagnosis to the reappearance of cancer, with patients censored at time of death if no recurrence had appeared)... Again, we present both the univariate and multivariate effect sizes in Table 3... The specific comparison of interest was the effect of adjuvant (platinum-based) chemotherapy and radiotherapy compared with radiotherapy alone... The unadjusted treatment effect may be summarised by a time ratio of 1.91 (95% CI: 1.21–3.01; P=0.005), which, having allowed for other covariates increased slightly to 2.05... Therefore, we can conclude that the time to recurrence was significantly prolonged (approximately doubled) among patents given adjuvant chemotherapy in comparison with those who were not... Further, this method does not perform well with several covariates, as the number of individuals in each stratum quickly becomes too small to allow reasonable comparisons... In addition, it does not quantify the strength of effect of each variable, or even offer a P-value for factors other than the one of primary interest... We have focused on the Cox model, the class of parametric PH models and AFT models as tools with which to analyse survival time data... Other models exist (see, e.g., Collett (1994) for a more practical demonstration of some alternatives and Bagdonavičius and Nikulin (2001) for the theoretical background), but many are similar to, if not extensions of, the approaches we have discussed... The use of the Cox model offers greater flexibility than parametric alternatives and, in particular, does not require the direct estimation of the baseline hazard function (i.e. it avoids the need to specify the distribution of the survival times).

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Illustration of the AFT model: (——), S0(t) the baseline survival function; (·······), S(t1)=S0(ϕt) for ϕ<1; (- - - - - -), S(t2)=S(ϕt) for ϕ>1.
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fig3: Illustration of the AFT model: (——), S0(t) the baseline survival function; (·······), S(t1)=S0(ϕt) for ϕ<1; (- - - - - -), S(t2)=S(ϕt) for ϕ>1.

Mentions: The principle here is that the effect of a covariate is to stretch or shrink the survival curve along the time axis by a constant relative amount ϕ. Figure 3Figure 3


Survival analysis part II: multivariate data analysis--an introduction to concepts and methods.

Bradburn MJ, Clark TG, Love SB, Altman DG - Br. J. Cancer (2003)

Illustration of the AFT model: (——), S0(t) the baseline survival function; (·······), S(t1)=S0(ϕt) for ϕ<1; (- - - - - -), S(t2)=S(ϕt) for ϕ>1.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2394368&req=5

fig3: Illustration of the AFT model: (——), S0(t) the baseline survival function; (·······), S(t1)=S0(ϕt) for ϕ<1; (- - - - - -), S(t2)=S(ϕt) for ϕ>1.
Mentions: The principle here is that the effect of a covariate is to stretch or shrink the survival curve along the time axis by a constant relative amount ϕ. Figure 3Figure 3

View Article: PubMed Central - PubMed

Affiliation: Cancer Research UK/NHS Centre for Statistics in Medicine, Institute of Health Sciences, Old Road, Oxford OX3 7LF, UK. mike.bradburn@cancer.org.uk

AUTOMATICALLY GENERATED EXCERPT
Please rate it.

An appealing feature of the Cox model is that the baseline hazard function is estimated nonparametrically, and so unlike most other statistical models, the survival times are not assumed to follow a particular statistical distribution... The estimated hazard function of the ovarian cancer data as displayed in the previous paper (Clark et al, 2003) may be consistent with that derived from a Weibull PH model with decreasing hazard... The proportion of patients who are event-free in the placebo group at any time point t1 is the same as the proportion of those who are event-free in the new treatment group at a time t2=ϕt1... Figure 3 shows the cases where ϕ>1 and ϕ<1, which represent situations where the length of survival is increased and decreased in the new treatment group compared with the placebo, respectively... We use the non-small cell lung cancer dataset to illustrate the AFT model, focusing on the relapse-free survival (i.e., the time from diagnosis to the reappearance of cancer, with patients censored at time of death if no recurrence had appeared)... Again, we present both the univariate and multivariate effect sizes in Table 3... The specific comparison of interest was the effect of adjuvant (platinum-based) chemotherapy and radiotherapy compared with radiotherapy alone... The unadjusted treatment effect may be summarised by a time ratio of 1.91 (95% CI: 1.21–3.01; P=0.005), which, having allowed for other covariates increased slightly to 2.05... Therefore, we can conclude that the time to recurrence was significantly prolonged (approximately doubled) among patents given adjuvant chemotherapy in comparison with those who were not... Further, this method does not perform well with several covariates, as the number of individuals in each stratum quickly becomes too small to allow reasonable comparisons... In addition, it does not quantify the strength of effect of each variable, or even offer a P-value for factors other than the one of primary interest... We have focused on the Cox model, the class of parametric PH models and AFT models as tools with which to analyse survival time data... Other models exist (see, e.g., Collett (1994) for a more practical demonstration of some alternatives and Bagdonavičius and Nikulin (2001) for the theoretical background), but many are similar to, if not extensions of, the approaches we have discussed... The use of the Cox model offers greater flexibility than parametric alternatives and, in particular, does not require the direct estimation of the baseline hazard function (i.e. it avoids the need to specify the distribution of the survival times).

Show MeSH