This is a good question.  Proper survival analysis (Kaplan-Meier curves, log-rank test, and Cox proportional hazards models) does account for the discrepancy in follow-up time. 

However, I think you can make a reasonable argument that the additional follow-up time for patients in the older era adds no value to a comparison of the three eras (i.e. if you're looking at survival for cases diagnosed from 1970-1979, 1980-1989, and 1990-1999, the events occurring 25+ years after diagnosis in the 1970-79 and 1980-89 cohort are more-or-less meaningless in a comparison against the 1990-99 era).

I think that it does make intuitive sense, in the type of problem you're describing, to truncate your analysis at the longest follow-up time for the shortest era (so in my example above, truncate your analysis at 25 years after diagnosis, since patients from the "latest" era of 1990-1999 could have as much as 25 years of follow-up, and at least theoretically you can compute an estimate of 25-year survival in that group; consider all patients from the 1970-79 and 1980-89 era who survived >25 years to be censored and still alive at 25 years).  Then you should be able to produce a KM curve going out to 25 years, and create a Cox proportional-hazards model with the "era" as a covariate in the model.

I also think it would be worth reporting some pre-specified time points (1-year survival, 5-year survival, 10-year survival) which obviously also does not have this issue.

For what it's worth, I have been working with a transplant surgeon on a similar question comparing survival after heart transplant in older eras vs. more recently, and have been amused at his seeming inability to understand this.  He has asked me to calculate things like "10-year survival" in a cohort of patients transplanted from 2010-2014 to compare it to prior eras (clearly not understanding that we cannot estimate 10-year survival in patients who have not been followed for 10 years).  So although this may sound elementary, you need not feel bad for asking the question; this is definitely something that confuses researchers across different fields.

Dear Kunal,

1 You can compare 5 (3,10....) years survival rate and approve (or not) what You "feel"

2 There are a family of log-rank tests and You can choose a more appropriate test for Your design ( for example, compare survival curve emphasized on early events)

3 I guess You can fit Cox-model with variable "year of diagnosis/operation/entrance" as confounder 

Good luck!

This is a good question.  Proper survival analysis (Kaplan-Meier curves, log-rank test, and Cox proportional hazards models) does account for the discrepancy in follow-up time. 

However, I think you can make a reasonable argument that the additional follow-up time for patients in the older era adds no value to a comparison of the three eras (i.e. if you're looking at survival for cases diagnosed from 1970-1979, 1980-1989, and 1990-1999, the events occurring 25+ years after diagnosis in the 1970-79 and 1980-89 cohort are more-or-less meaningless in a comparison against the 1990-99 era).

I think that it does make intuitive sense, in the type of problem you're describing, to truncate your analysis at the longest follow-up time for the shortest era (so in my example above, truncate your analysis at 25 years after diagnosis, since patients from the "latest" era of 1990-1999 could have as much as 25 years of follow-up, and at least theoretically you can compute an estimate of 25-year survival in that group; consider all patients from the 1970-79 and 1980-89 era who survived >25 years to be censored and still alive at 25 years).  Then you should be able to produce a KM curve going out to 25 years, and create a Cox proportional-hazards model with the "era" as a covariate in the model.

I also think it would be worth reporting some pre-specified time points (1-year survival, 5-year survival, 10-year survival) which obviously also does not have this issue.

For what it's worth, I have been working with a transplant surgeon on a similar question comparing survival after heart transplant in older eras vs. more recently, and have been amused at his seeming inability to understand this.  He has asked me to calculate things like "10-year survival" in a cohort of patients transplanted from 2010-2014 to compare it to prior eras (clearly not understanding that we cannot estimate 10-year survival in patients who have not been followed for 10 years).  So although this may sound elementary, you need not feel bad for asking the question; this is definitely something that confuses researchers across different fields.

 Thank you all for your answers.

1. I could not use ANOVA for this as I wanted to compare the survival and the means of survival of the first time period was high.

2. Andrew - Thank you for you reply and encouragement to ask such questions. It has baffled me a lot. I have done similar to something you are suggesting. First I ran, Log rank, Breslow and Tarone Ware for each group and time period. And they were all significantly different. I am hoping to find significant difference in the survival of the last time period (1998-2012). I have also reported the 10 year survival of the patients (as it is common for all time periods). 

I have performed the Log rank, Breslow and Tarone tests to compare the survival at different times. And as they all were significant, i assumed that all three curves are different.  But, as expected the median survival of the Last period is less compared to the other time periods (Because of cases in more recent year).

I was wondering if you could please tell me if I can compare the survival of the all three time periods at 10th year of their diagnosis.

I'm glad that my answer was helpful.

If your most recent era was 1998-2012, then my suggestion would be to repeat your Kaplan-Meier analysis and log-rank test while truncating the survival for patients from the older eras at 15 years (or maybe even 10 years).  I don't think this will radically change the statistical significance of your results, but it will ameliorate your concern that any differences are due to those longer-term events. 

Please do this CAREFULLY - you cannot just change the survival times to be 15 years, but rather you must write code something like

DEAD_USE=DEAD;

DEATH_TIME_USE=DEATH_TIME;

IF DEATH_TIME>15 THEN DO;

DEAD_USE=0;

DEATH_TIME_USE=15;

END;

That would re-set any patient who survived > 15 years (even if they died later) to be classified as "alive" and censored at 15 years.

You can perform a comparison of 10-year surivval for sure, but be advised that your number for 10-year survival in the most recent era will be a Kaplan-Meier estimate (because not all of the patients in that group actually have 10 possible years of follow-up time).  You will have an ACTUAL 10-year survival figure for the two prior ers and a KM estimate of 10-year survival in the more recent era...which may or may not be accurate.

I would definitely NOT examine median survival.  The median survival is only usable if half of the patients in each group/era have actually passed away; if you computed a median survival for the 1998-2012 era but more than 50% of the patients were still alive, then you didn't really compute a "median survival" anyway.

Of course, you can use F test for comparison of such a period

Andrew - I am trying to perform the analysis as per your suggestion. However, my skills to write a code or use syntax are limited. Is there a chance you could please tell me as to how to analyze that in SPSS without syntax?

Thank you

In SPSS you should be able to manipulate the data by using the "recode into different variables"  option.  Use that to create a new death variable and a new death_time variable.

Issam - I am trying to compare the time periods. The 1st time period has a higher mean (As the follow up times are present till present year). Am I missing anything here? Or is there anything I might have been doing wrong?

You already received some excellent suggestions. To push your period survival analysis a level higher, you might consider calculating relative survival (RS) for each period.

A well-known pitfall in comparing patient survival rates between different time-periods (or: different countries) is the increasingly better age- and sex-dependent background mortality which has little to do with improved surgical skills or better drugs [3,4]. Particularly for diseases with a favorable prognosis, -early stage breast cancer, cervical cancer, diabetes, hypertension-, it is recommended to calculate the relative survival (RS), wherein the observed survival (Kaplan-Meier) is corrected for the expected survival based on age, sex and period (or: birth-cohort).

Several software packages have modules to calculate RS, such as R, SAS, Stata and S-plus, but not SPSS [1,2,7,8].  My preferred program to calculate RS is the RelSurv package in R, written by Pohar & Stare. [7,8]. One advantage of R is that it is free and open to all peers. But more important: Unlike commercial programs, the statistical models and assumptions in R have been carefully tested, and can be tested since the sources are open for peer-review [7,8].

But sure, it takes some persistence to do it. Although Pohar & Stare (2007) claim that they have made ‘relative survival relatively easy’, some experience with R is required [7]. Furthermore, all RS packages have the drawback that up-to-date population life tables for both sexes have to be uploaded [5]. Life tables for most countries are freely available from the Human Mortality Database [6]. Once you have been successful in overcoming all these challenges, you start wondering: Why isn’t RS the Golden Standard for reporting survival?

Need help? On PubMed I found a recent pre-publication by Jason D. Wright from G&O at NYPH on relative survival in cervical cancer [9].       

Good luck!

1.      Dickman PW, Sloggett A, Hills M, Hakulinen T. Regression models for relative survival. Stat Med 2004; 23: 51-64

2.      Dickman PW Coviello E. Estimating and modelling relative survival. The Stata Journal 2015, 15(1): 186-215. http://www.pauldickman.com/survival/strs.pdf   (Last visited October 27, 2015)

3.      Ederer F, Heise H. Instructions to IBM 650 programmers in processing survival computations. Technical, End Results Evaluation Section, National Cancer Institute, Bethesda, MD, 1959

4.      Ederer F, Axtell LM, Cutler SJ. The relative survival rate: a statistical methodology. Natl Cancer Inst Monogr 1961;6:101-21.

5.      Ellison LF. Estimating relative survival for cancer: An analysis of bias introduced by outdated life tables. Health Rep 2014;25(2):13-9.

6.      Human Mortality Database. University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Available at www.mortality.org  or www.humanmortality.de

7.      Pohar M, Stare J. Making relative survival analysis relatively easy. Comput Biol Med 2007;37(12):1741-9.

8.      Pohar Perme M, Stare J, Estève J. On estimation in relative survival. Biometrics 2012; 68: 113-120

9.      Wright JD, Chen L, Tergas AI, Burke WM, Hou JY, Neugut AI, Ananth CV, Hershman DL. Population-level trends in relative survival for cervical cancer. Am J Obstet Gynecol. 2015 Jul 23.

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 Thank you so much for your answer. That is also indeed a great suggestion.