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Coping with temporal indeterminacy in medical data

Coping with temporal indeterminacy in medical data. Luca Anselma a , Paolo Terenziani b a Dipartimento di Informatica, Università di Torino, Torino, Italy , Email: anselma@di.unito.it

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Coping with temporal indeterminacy in medical data

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  1. Coping with temporal indeterminacy in medical data Luca Anselmaa, Paolo Terenzianib aDipartimento di Informatica, Università di Torino, Torino, Italy, Email: anselma@di.unito.it bDipartimento di Informatica, Università del Piemonte Orientale “Amedeo Avogadro”, Alessandria, Italy. Email: terenz@di.unito.it

  2. Coping with temporal data in relational Databases • Medical data are mostly temporal data (same for many other applications/domains) • Adding time to RELATIONAL DATABASES is challenging • Two decades of research into temporal databases have unequivocally shown that a time-varying table, containing certain kinds of DATE columns, is a completely different animal than its cousin, the table without such columns. Effectively designing, querying, and modifying time-varying tables requires a different set of approaches and techniques “ R.T. Snodgrass: “A paradigm shift” • Almost 30 years of research (90 entries about time in the Springer Encyclopedia about Databases (2008)) CHALLENGE: not only data representation model, but also QUERY  ALGEBRA

  3. TEMPORAL ALGEBRAE: REQUIREMENTS Consistent with the data (snapshot) semantics  Reducibility ρtT ρtT (rT) rT op opT op(ρtT (rT)) ρtT = = ρtT(opT (rT)) opT (rT)  INTEROPERABILITY WITH CONVENTIONAL (non-temporal) DATABASES

  4. Coping with INDETERMINATE temporal data in relational Databases • INDETERMINACY: don’t know EXACTLY when • Ex.1 On January 1st 2012 Mary had headache starting between 8am and 9am and ending between 1pm and 2pm. • Few approaches in the temporal relational DB literature: • - Different data representation models but … • Either no temporal algebra • Or coercion to determinate data as a prior (compulsory) step before using a (standard) temporal algebra (e.g., [Das & Musen, 94], [Dyreson & Snodgrass, 98])

  5. OUR RESULTS • TEMPORALLY INDETERMINATE DATA • IN RELATIONAL DATABASES • Data representation model • Temporal Algebra • Properties: Reducibility & al.

  6. DATA REPRESENTATION MODEL Indeterminate Temporal Element: “certainly hold” interval + “possibly hold” interval Ex.1 On January 1st 2012 Mary had headache starting between 8am and 9am and ending between 1pm and 2pm.

  7. ALGEBRA r TIs = { (v|<d,i>) | (v|<d,i>)r(v|<d,i>)s} πTIX(r) = { (v|<d,i>) | (v1|<d1,i1>)r v =πX(v1) <d,i>= <d1,i1> } σTIP(r) = { (v|<d,i>) | (v|<d,i>)r P(v) } r TIs = { (vr∙ vs|<d,i>) | <dr,ir>,<ds,is> ( (vr|<dr,ir>)r  (vs|<ds,is>)s <d,i> = <dr,ir> ITE<ds,is> i ) } r –TIs = { (v|<d,i>) | ( <dr,ir> ((v|<dr,ir>)r <ds,is> ((v|<ds,is>)s <d,i> = <dr,ir>)) )  ( <dr,ir> ((v|<dr,ir>)r ! (v|<d1,i1>), …, (v|<dk,ik>) ((v|<d1,i1>)s, …, (v|<dk,ik>)s <d,i> = <dr,ir> –ITE {<d1,i1>, …, <dk,ik>} i)))} σTICERT (r) = { (v|<d,i>) | (v|<d,i>)r (d) } σTIPOSS (r) = { (v|<d,i>) | (v|<d,i>)r (i) }

  8. ALGEBRA(set operators between ITEs) ITE intersection. <d,i> ITE <d’,i’> = <dd’, ii’> ITE difference. <d,i> –ITE {<d’1,i’1>, …, <d’k,i’k>} = cover(chr(d) – (chr(i’1) chr(d’1)  … chr(i’k) chr(d’k)), chr(i) – (chr(d’1)  … chr(d’k))). chr([cs,ce)) = {c TC | cs ≤ c < ce} isConvex(s) iff ∄cTC (min(s)≤c≤max(s) ∧ c∉s) maximal(S) = {s | s⊆S∧ isConvex(s) ∧ ∄s’⊆S (isConvex(s’)∧ s⊂s’)} partition(i, {d1, …, dk}) = {<dj, ij> | dj{d1, …, dk} ∧ dj⊆ij ∧ ∄dh{d1, …, dk} (dh≠dj∧ dhij≠Ø) ∧ i1 … ik=i ∧ iii2=Ø ∧ … ∧ iiik=Ø ∧ … ∧ ik-1ik=Ø ∧ isConvex(i1) ∧ … ∧ isConvex(ik)} cover(D, I) = {<Ø, [min(i’), max(i’)+1)> | imaximal(I) ∧∄cD (ci)}  {<[min(d’), max(d’)+1), [min(i’), max(i’)+1)> | imaximal(I) (<d’,i’>partition(i, {d | dmaximal(D)∧ d⊆i}))}

  9. PROPERTIES (1/2) Consistent extension (ITEs). Determinate temporal elements can be modeled by ITEs of the form <[start, end), [start, end)> Closure of ITE set operators. The representation language of ITEs is closed with respect to the operations of ITE and –ITE. Closure of temporally indeterminate algebraic operators.

  10. PROPERTIES Consistent extension (temporally indeterminate relational algebraic operators). If only determinate ITEs of the form <[s,e),[s,e)> are used as valid time associated with tuples, our relational operators TI, –TI, σTIP, πTIX and TI are equivalent to the standard TSQL2 valid-time relational operators T, –T, σTP, πTX and T.  Implementability on top of TSQL2-based DBMS Reducibility of temporally indeterminate relational algebra to non-temporal relational algebra  Interoperability with conventional (non-temporal) DBMS

  11. ACKNOWLEDGEMENTS R.T. Snodgrass, CS Dept, Univ. of Arizona, Tucson, USA G. Molino and M. Torchio of ASU San Giovanni Battista, Turin, Italy This research was partially supported by Compagnia di San Paolo, GINSENG project. THANKS FOR YOUR ATTENTION!!

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