PQStat - Baza Wiedzy

Survival curves trend

Hypotheses:

$\begin{array}{ll} \mathcal{H}_0: & $In the studied population there is no trend in the placement of the $S_1,S_2,...,S_k$ curves,$\\ \mathcal{H}_1: & $In the studied population there is a trend in in the placement of the $S_1,S_2,...,S_k$ curves.$ \end{array}$

In the calculation the chi-square statistic was used, in the following form: $\begin{displaymath} \chi^2=\frac{(c'U)^2}{c'Vc} \end{displaymath}$

where:

$c=(c_1,c_2,...,c_k)$ – vector of the weights for the compared groups, informing about their natural order (usually the subsequent natural numbers).

The statistic asymptotically (for large sizes) has the Chi-square distribution with $1$ degree of freedom.

The p-value, designated on the basis of the test statistic, is compared with the significance level $\alpha$ :

$\begin{array}{ccl} $ if $ p \le \alpha & \Longrightarrow & $ reject $ \mathcal{H}_0 $ and accept $ \mathcal{H}_1, \\ $ if $ p > \alpha & \Longrightarrow & $ there is no reason to reject $ \mathcal{H}_0. \\ \end{array}$

In order to conduct a trend analysis in the survival curves the grouping variable must be a numerical variable in which the values of the numbers inform about the natural order of the groups. The numbers in the analysis are treated as the $c_1,c_2,...,c_k$ weights.

EXAMPLE cont. (transplant.pqs file)

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Survival curves trend

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