Understanding disease survival rates
Understanding disease survival rates involves analyzing statistical data to gauge the prognosis and seriousness of various health conditions. Survival rates, such as the overall survival rate, reveal the percentage of patients alive after a set period following diagnosis, typically calculated over intervals of one, five, or ten years. These rates inform medical professionals about treatment effectiveness and help guide decisions on patient care. Various factors, including disease type, stage, patient age, gender, overall health, lifestyle, and treatment options, can significantly influence these rates.
Additionally, there are different types of survival rates—overall, relative, cause-specific, disease-free, and progression-free—each serving distinct purposes in evaluating patient outcomes. For example, relative survival rates compare the survival of patients with a disease to those without, adjusting for demographic factors. The survival function can also be utilized to estimate the probability of survival over time, even in cases where patient data may be incomplete due to various reasons like withdrawal or unrelated causes of death. This comprehensive understanding of survival rates is crucial for patients, families, and healthcare providers in navigating the complexities of disease management and treatment planning.
Understanding disease survival rates
Summary: Sophisticated mathematics is used to calculate disease survival rates and to help doctors and patients make treatment decisions.
Disease survival rates indicate the seriousness of a certain disease, and the prognosis of a person with the disease based on the experience of others in the same situation (in terms of the stage of the disease, gender, and age). “Overall survival rate” is defined as the percentage of people who are alive after a specific period of time after diagnosis with the disease, which is computed using the following formula: Overall Survival Rate = 100(Number alive at the end of a time period ÷ Number alive at the start of a time period).
Standard time periods such as one, five, and 10 years are often used. For instance, the five-year overall survival rate for stage-I breast cancer is said to be “95%” if 95% of all people who are diagnosed with stage-I breast cancer live for at least five years after diagnosis. Conversely, 5% of these people die within five years.
Survival rates depend on many factors, including both the type and stage of disease, as well as age, gender, health status, lifestyle, and treatment. Doctors and researchers use survival rates to evaluate the efficacy of a treatment, compare different treatments, and develop treatment plans. For example, the treatment having the highest survival rates over time is usually chosen. If treatments have similar survival rates but different numbers of side effects, the treatment with the fewest number of side effects is often selected.
Other Types of Survival Rates
Overall survival rates have some limitations. First, they do not distinguish causes of mortality within a given time period. For instance, a death may be caused by a car accident rather than by the disease. Second, they fail to indicate whether the disease is in remission or not at the end of the time period. Moreover, they do not directly provide the prognosis for a specific patient. For instance, the 95% five-year survival rate for stage-I breast cancer does not guarantee that every patient will survive more than five years. When considering only deaths caused by the disease, relative survival rate or cause-specific survival rate is often used. Relative survival rate is the ratio of the overall survival rate for people with the disease to that for a similar group of people in terms of age and gender without the disease.
One advantage is that relative survival rates do not depend on the accuracy of the reported causes of death. On the other hand, cause-specific survival rate is computed by treating deaths from causes other than the disease as withdrawals so that they do not deflate the survival rate due to the disease. When using this rate, there is no need to involve a similar group of people without the disease. Sometimes more detailed survival rates in terms of the status of a disease after a given period of time, such as disease-free survival rate and progression-free survival rate, are of interest. The computation for disease-free survival rate is similar to that of the overall survival rate except that the numerator is the number of patients who are cured at the end of the time period. Similar computation applies to the progression-free survival rate except that the numerator is the number of people who are alive and still have the disease, but the disease is not progressing at the end of the time period. As before, disease-free and progression-free survival rates can be adjusted by filtering out the effect of deaths from causes unrelated to the disease.
Survival Function
Related to survival rates, the survival function is a mathematical function that uniquely determines the probability distribution of a random variable. In survival analysis, the random variable of interest is survival time or time to a certain event, denoted by T. For instance, survival time could be time until recovery from a disease, or time to death. The survival function for T is a function of time point t defined as
S(t )= P(T > t )
which is the true probability that the survival time of a subject is beyond time t. The survival rates with an adjustment for deaths because of unrelated causes are estimates of the survival function at some t based on existing data. For a study with n patients, the survival function can be estimated by the empirical survival function:
Sn(t) = Number of patients not experiencing the event up to t/n.
In follow-up studies, however, a patient with a certain disease may withdraw, die from other causes, or still be alive at the end of the study. In such cases, the survival time T of the patient is not exactly observed but only known to be greater than a certain time (withdrawal time, death time, or time at the end of the study) called “censoring time.” Then T is said to be right-censored, and the resulting set of data is called right-censored data. Based on right-censored data, the survival function can be estimated by
SKM(t),
the K-M estimator developed by statisticians Edward Kaplan and Paul Meier in 1958. As a special case,
SKM(t) coincides with Sn(t) when there is no censoring.
When estimating survival probability,
P(T > t) at a given time t,
SKM(t) or a cause-of-death-adjusted survival rate introduced earlier can be used. Taking a more sophisticated approach, P(T>t) can be estimated using a confidence interval. For example, one may conclude that, with 95% confidence, P(T>t) is between two numbers, say 0.80 and 0.90. Such a confidence interval can be constructed using SKM(t) and its variance estimate from statistician Major Greenwood’s formula based a normal distribution.
Bibliography
Gordis, Leon. Epidemiology. 4th ed. Philadelphia: Saunders Elsevier, 2009.
Kalbfleisch, John D., and Ross L. Prentice. The Statistical Analysis of Failure Time Data. 2nd ed. Hoboken, NJ: Wiley, 2002.
Klein, John P., and Melvin Moeschberger. Survival Analysis: Techniques for Censored and Truncated Data. New York: Springer-Verlag, 1997.
Marks, Harry. “A Conversation With Paul Meier.” Clinical Trials 1 (2004).