Kaplan Meier - Lecture notes 3 PDF

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Kaplan Meier...

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Economic evaluation is an important part of health technology assessment (HTA). Costs incurred and units of health gained are compared between interventions, allowing decision makers to allocate finite resources. The incremental cost-effectiveness ratio (ICER) represents the marginal cost per unit of health gained and provides information on whether an intervention is cost-effective with reference to a prespecified threshold. In England, the National Institute for Health and Care Excellence (NICE) normally recommends a new intervention if its ICER is below £20 000 and £30000 per quality-adjusted life year (QALY) gained. For treatments that meet endof-life (EOL) criteria, QALY gains can be weighted by a factor of up to 1.7, implying a threshold of approximately £50 000 per QALY gained (ICER) is a statistic used in cost-effectiveness analysis to summarise the cost-effectiveness of a health care intervention. It is defined by the difference in cost between two possible interventions, divided by the difference in their effect. Quality-adjusted life year- A measure of the state of health of a person or group in which the benefits, in terms of length of life, are adjusted to reflect the quality of life. One quality-adjusted life year (QALY) is equal to 1 year of life in perfect health. QALYs are calculated by estimating the years of life remaining for a patient following a particular treatment or intervention and weighting each year with a quality-of-life score (on a 0 to 1 scale). It is often measured in terms of the person’s ability to carry out the activities of daily life, and freedom from pain and mental disturbance. The QALY is used by HTAs to determine the additional value of a particular treatment or intervention. This is done by calculating the cost per QALY. 

A partitioned survival model is a type of economic model used to follow a theoretical cohort through time as they move between a set of exhaustive and mutually exclusive heath states. Unlike a Markov model, the number of people in any state at successive points in time is not dictated by transition probabilities.

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Instead, the model estimates the proportion of a cohort in each state based upon parametric survival equations.

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These types of model are frequently used to model cancer treatments, with separate survival equations for overall survival and progression-free survival. Common functions used to describe survival are exponential, Weibull (parametric model)

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Sensitivity analysis can be undertaken by varying the parameters defining the survival equations, however if the survival equations are independent, care needs to be taken that logical fallacies are not made (e.g. overall survival exceeding progression free survival).

Survival analysis- the probability that an individual survives up to a certain point in time. The interest variables are time, how long someone is in the study and event, whether an event has occurred or not. This can be termed time to event, time to failure, survival analysis. The survival function is the probability that the duration to the event – T exceeds small t (time in our study). The probability of survival or still being in the study until that point in time. Hazard function – is the opposite of a survival function, the probability of the event of interest happening so the probability of dying given in a small time period. This is where there is a change in t within a small space of time what is the probability of the event actually occurring. This close relates to our hazard rate, which we can think of as the slope of or survival curve: the probability of the event actually happening within a small space of time. The hazard rate distinguishes the model from each other. The hazard ratio is the ratio of two hazard rates between a reference group and or group of interest. This tells us how high the risk is in one group compared to the other group.

Nonparametric = no distribution applied to our data, there is no required functional form of our hazard in non -parametric analysis. they are free of assumptions concerning the distribution of the variable of interest, in this case the distribution of time to event parametric methods may be the preferred or necessary alternative. For example, assessment of the effect of individual covariates on failure time can be undertaken by use of parametric models that incorporate covariate information available from the clinical study. Furthermore it is commonly desirable to derive estimates of failure time beyond the study follow-up period. Parametric models can provide an instrument for extrapolating estimates of failure time obtained over the study period to points in time exceeding the duration of the study

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Think of survival models as having two parts • Baseline hazard rate: change in risk of failure per unit of time as time changes (assuming baseline level of each x(covariate) • Effect of covariate on the hazard rate • Example, include age and gender of patient to control for confounding in estimation of hazard rate Called proportional hazards because proportional to baseline hazard, scaled by a factor Some common PH models – exponential,Weibull Exponential: Constant hazard over time (not depicted) Weibull: Captures decreasing or increasing hazard rate over time Cox Proportional Hazards: Hazard rates for different individuals proportional with a constant ratio over time KM estimates the probability of survival. The survival function estimates the probability of survival past time t. What is the probability that the individual’s time to event is greater than the time point in our study. KM is nonparametric so we are not imposing any specific distribution on our data, we are just letting our data show us how it is formed by using the survival function. KM estimator of the survival curve assumes the exact time of death (or censoring) is known so we can get the step curve

K-M is a non-parametric way of estimating survival curves that accounts for censoring. But, if the observation with the largest observed value of "time" is censored, the resulting K-M survival curve will not go to zero. When this happens, estimates of mean survival time based on the area under the K-M survival curve will underestimate the true mean survival time. • Semiparametric method that does not require complete distributional specification • While the hazard function is estimated non-parametrically, the functional form of the covariates is parametric

Cox Proportional Hazard Model  STANDARD MODEL = it is in the middle of the two, avoiding the restrictions of the parametric but allowing the incorporation of the covariates that the kaplan meier does not allow  it incorporates independent censoring again Three main assumptions • Independence of survival times between distinct individuals in the sample • Multiplicative relationship between predictors and the hazard • Proportional hazard model • Constant hazard ratio over time

Extrapolation – – •

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estimate survival time for T and C groups beyond study end Given data is no longer available from study, assumptions about how the hazard rate varies over time need to be made Different assumptions about how the hazard rate progresses over time lead to different time to event estimates – Assume benefit in survival attributed to the Treatment at end of study period continues through time – Assume benefit in survival attributed to the Treatment at study end is eliminated past that point in time – Or any intermediate situation within study period hazard pattern may not reflect the future

Censoring – we have information on the right we don’t know. This is right censoring; we don’t know what happens after the date. There is also the possibility that they drop out. At a certain point in time, we stop knowing what happens to them. RH censoring Lost to follow up or the event doesn’t occur before the end of our study period. We don’t know if the individual died at the end of our study period. Left censoring – is before the start of the study there is information, we don’t know Interval censoring – during the period of our study there is pockets of time where we don’t know information.

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