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Time measurements differ from other measurements. All measurements of time are positive values above zero, and the variance
of time increases with its value. Time therefore conforms to the exponential distribution.
Where the range of time measurement is narrow and far from the zero value, it can be considered as approximately normally distributed. An example is maternal age, ranging from the late teens to the mid forties. In most research reports, maternal age is handled as if it is a normally distributed measurement. Where the range of time measurements is wide and encroaching towards 1, the variance required need to be stabilized. Often this can be achieved. Gestational age is such a measurement that needs logarithmic transformation for it to be handled as a continuous measurement. To handle time measurements precisely, it should be handled as exponentially distributed. This requires complex and inflexible algorithms that limit its use, and usually some form of curvilinear transformation is carried out before it is handled as a normally distributed measurement. A transformation designed to do this is the Box Cox transformation, which is provided in the Numerical Transformation Program Page . Up to this point, time is discussed on the basis that it can be easily and uniformly obtained, but this is not the case in much of medical research. Often the time is measured over a prolong period, perhaps years. Subjects are recruited along the way, and some will be lost before the event of interest occurs. At any time the data being analysed, the subjects will be varied in the time they have been in the study, and the event of interest may have occurred only in a [proportion of the subjects. Survival Analysis is a term used to analyse time to events under these difficult situations. The data is said to be Censored, in the sense that, at the time of analysis, not all the required information is available, and the statistical procedures make do with what is available. The are many complex and precise method of survival analysis. StatsToDo presents only the simplest and the most commonly used one, The Log Rank Test, as described by Kaplan Meier, and made popular by Peto (see references). The Log Rank Test is used to evaluate time related change in proportions of an indexed event. Medically, it most commonly refer to death rate in cancer patients, such as the 5 year survival rate. However, the methodology has much wider use, such as time related recurrence rate, cure rate, discharge rate, pregnancy rate. In industry and manufacturing, it is also used to evaluate the lifetime of products such as how long before a light bulb burns outs. The terminology can be a bit confusing at time. In cancer treatment, the survival rate is used, indicating the proportion of patients that are still alive at a fixed time after entering the study. However, death rate is also used, and the term hazard refers to the opposite of survival. Mathematically, death and survival are two sides of the same coin, and the comparison of survival or death use the same statistical methods. The Log Rank Test is particularly useful in cancer cases, as patients enter the study at different times, and because the follow up is usually in years, some are lost to follow up. At the time of analysis therefore, some may have died or are lost to follow up after varying intervals, and some may have joined the study recently, less than the full period of assessment. The Log Rank Test collates the available data and produces a survival rate that can be statistically compared. Terminology An interval is a unit of time. In cancer follow up this is usually a year, in light bulb burnt out it is often an hour, in IVF it is often a cycle, in contraception and pregnancy it is often a month. An indexed event is the event of interest. In cancer this is usually death or recurrence, in light bulb it is burnt out, in IVF or contraception this is pregnancy. The survival rate is the proportion of the subjects that have not as yet experienced the indexed event, and the hazard rate is the proportion that have experienced the indexed event. (survival rate = 1  hazard rate). An event table is a table that display the events in time. The rows are the intervals, and at each row each group of subjects has 2 columns, the number of subjects that experienced the indexed event (died) in that interval, and the number that survived that interval without the indexed event. As the interval proceed, the number of subjects decrease, some because they have experienced the indexed event (died), some because they are lost to follow up, some because they only recently join the study and have not been in the follow up long enough. Please Note : The event table as described in the last paragraph applies to programs and explanation provided by StatsToDo, in common with many other presentations. However, users should take care, as another convention is to present the two columns as the total number of cases that entered the interval, and the number of cases that died during that interval. It is quite easy to convert one format to the other, but it is important to know the difference exists, so as not to get confused. The rates are statistically compared after a fixed number of intervals. For example, 5 years survival for cancer patients, 100 hour not burnt out in light bulbs. Format of Data Entry : The program in the Survival  Kaplan Meier Log Rank Test Program Page allows two format for data entry.
Calculating the sample size requires 5 parameters.
Power calculation also requires 5 parameters
