Model description

doc/dsdr/0007-survival-analysis.md

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+# Duration in care inference
+
+## Context
+
+In order to project likely future durations in care we need to summarise historic durations in care. Age of admission influences a child's duration in care, but duration is not normally distributed. Many episodes are still "open" but need to be included inthe summary duration in order to accurately represent all historic episodes.
+
+## Decision
+
+Survival analysis of duration in care by age of admission can infer likely distributions of durations in care whilst taking into account open episodes. This is necessary as ceased episodes will tend on average to be shorter durations, whilst currently-open episodes will tend on average to be longer durations. Survival analysis attempts to account for this discrepancy with censoring.
+
+## Status
+
+Accepted
+
+## Consequences
+
+Survival analysis compensates for the fact that many episodes are still open, but does not factor in any temporal trends to duration in care.
+
+Currently there is no surival analysis model available in Clojure. As such this analysis is done in R.

doc/model.md

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+# Projecting the Children in Care Population
+
+
+## Data
+
+Using the SSDA903 following data is extracted for each episode, across multiple calendar years.
+
+* Sex
+* Category of need
+* Legal status
+* Year of birth
+* Episode report date
+* Episode report year (financial)
+* Episode ceased date
+* Placement
+* Unique psuedominised ID
+
+
+## Psuedominised data
+
+To ensure protection of sensitive personal data an ID lookup is used by the Local Authority, so that whilst the model can match different episodes to an individual there is no additional personal data to enable reidentification.
+
+Whilst individuals need to be aged, date of birth was considered too sensitive, so year of birth is used to roughly assign ages.
+
+
+## Estimating duration in care by age joined
+
+The amount of time a child is in care is influenced by the age they were when they entered care. This is driven by both younger children leaving care sooner and by 18 being the age when a child must leave care. Children five and over are more likely to stay in care longer, whilst over 10s then show a decreasing duration in care influenced by the upper age limit.
+
+Duration in care can be summarised simply by age of admission, but this does not take into account whether episodes are still open or ceased. Episodes still open, and thus more recent, cn exhibit different trends in duration from ceased episodes. Hence it is not reasonable to either exclude one or other of these episode types, or generalise across them.
+
+Survival analysis of duration in care by age of admission can infer likely distributions of durations in care whilst taking into account open episodes with censoring.