American Statistical Association October 23 Minneapolis Presentation Part 2
1. Fruitfly Tumors: A range of sizes and morphologies observed: Microtumors Ubc9 - dif - dl - - F-actin Microtumor Small Microtumor 419 Projection >10,000 m 2 Estimated volume: 0.5 mm 3 -1 mm 3 932 513
Compensatory Response hypotheses: Case 1 Simulation-Excess Frequency of 25K is reduced by 88 in Bc and 176 in lwr(-).
Egger’s Paradigm small studies tend to have large effect sizes than would be expected! Size effect greater than what a sample size of N=24 can sustain… Egger M, Davey Smith G, Schneider M, Minder C. Bias in meta-analysis detected by a simple, graphical test. BMJ 1997 ; 315: 629–634 . Peters JL, Sutton AJ, Jones DR, Abrams KR, Rushton L. Comparison of two methods to detect publication bias in meta-analysis. JAMA 2006 ; 295: 676–680 .
Compensatory Response Behavior: Case 4- Uncorrected VS Corrected Reverse Engineering Simulation
PRESENCE of Compensatory Behavior: Simulations by Numerical Data and Visual Analytics <ul><li>Data Type Linear R-sq. Quad. R-sq. Cubic R-sq. Original Data 0.3816 0.6781 0.8468 Case 1 0.4389 0.7431 0.8941 Case 2 0.506 0.7885 0.9158 Case 3 0.5103 0.7952 0.914 Case 4 0.5385 0.7724 0.8948 </li></ul><ul><li>Gain in Linear R-sq.= 16% =Between Tumor area size competition reduction. </li></ul><ul><li>Size asymmetry where largest cell size have increased genetic fitness even at highest compensatory adjustments (0.5385 VS 0.8948; case 4). </li></ul><ul><li>Case 1 is at equilibrium; about 5% competition in both, Inter and Intra-size area limit (Cubic R-sq.) is lessened from Original data. </li></ul><ul><li>Case 2 VS Observed data shows alleviation of 6.9% intra-size competition results into 12.4% reduction in inter-size competition. </li></ul><ul><li>Decrease in competition between inter tumor sizes are not as pronounced later by compensatory adjustments because intra-tumor area size competition has increased (Case 4) by 2% . </li></ul>
<ul><li>25K frequency is above threshold as well as increased fitness of by asymmetrical competition by both genotypes?? WRONG! </li></ul><ul><li>Ho: Increased size asymmetry frequency allows Bc to maintain increased genetic fitness in absence of fitness challenges or in situ fitness is high (explanation of PLOS publication). </li></ul>VISUAL ANALYTICS: Meta Modeling : Above threshold frequency of 25K lwr(-) at the expense of decreased fitness of largest tumor cell size (lack of asymmetrical competition resulting into increased aggregates/ small tumor frequencies competition).
<ul><li>Why learn compensatory behavior-no applied value. </li></ul><ul><li>The residual plot shows 75K and 100K in Bc and 75K and 100K in lwr (-) is most suppressed. </li></ul><ul><li>The same residual plot shows 25K frequency having greatest deviations from expected frequencies. </li></ul><ul><li>Just reduce 25 K frequency in Bc and lwr(-) by 90% or greater. </li></ul><ul><li>Just increase the frequency of 75K and / or 100K in lwr(-) and Bc for drug discovery. </li></ul><ul><li>Make sure to use highest sample size available (N=48). </li></ul><ul><li>Factors mentioned here are dynamical properties of Brain Tumor gene expression, not the compensatory response behavior hypotheses. </li></ul>VALUE of Compensatory Behavior Hypotheses for Drug Discovery
Candida Ferreira. 2003. www.gene-expression-programming.com/author.asp- equation 3.5 : (N = 48); ≈90% decrease in small tumors frequencies.
Simulated Frequencies: biased R-sq. and too much scatter- no interpretation…
Corrected (CF) Candida Ferreira. 2003. www.gene-expression-programming.com/author.asp- equation 3.5 : Good news R-sq. shrinkage but bad news R-sq. problem…
LOW BRAIN TUMOR FREQUENCIES DOES NOT MEAN R-SQ. NEEDS TO BE LOW; SIMULATED DATA POINTS NEED TO FIT BETTER TO HAVE AN INTERPRETATION! VALUE ($): IT IS MUCH EASIER TO SIMULATE FREQUENCIES OF TUMOR CELL SIZES THAT ARE RESPONSIBLE FOR COMPENSATORY BEHAVIOR, BUT THE BOTTLENECK IN DRUG DISCOVERY WILL BE CREATED BY OBSERVED FREQUENCIES OF ALL SUPPRESSED CELL SIZES- A CHALLENGING SIMULATION! <ul><li>VALIDATION </li></ul>
<ul><li>Summary Text: 1 </li></ul>APPLICATION OF MAXIMUM LIKELIHOOD IS VALID ON LOGNORMAL DATA, FOR EXAMPLE, PARKIN, T.B. 1993: EVALUATION OF STATISTICAL METHODS FOR DETERMINING DIFFERENCES BETWEEN SAMPLES FROM LOGNORMAL POPULATIONS. AGRONOMY JOURNAL 85:747-753 . CONVERT THE NON-NORMAL DISTRIBUTION DATA INTO NORMAL DISTRIBUTION BY TAKING THE LOG OF IT. THEN YOU CALCULATE THE MEAN, VARIANCE ON LOG-TRANSFORMED DATA . MAXIMUM LIKELIHOOD ESTIMATORS MEAN = EXP(µ + (SIGMA)2/2) VARIANCE = µ2 (EXP (SIGMA)2 -1) CI= EXP (µ ± SIGMA * T (1- Α /2)/SQRT N) WHERE µ AND SIGMA-SQUARE ARE MEAN AND VARIANCE OF LOG-TRANSFORMED SAMPLE DATA. SIGMA = STANDARD DEVIATION OF LOG TRANSFORMED DATA AND T (1- Α /2)= 1.96= P<.05 PROBABILITY LEVEL. THE CI METHOD HERE BY SOKAL AND RHOLF (1969:PHYLOGENETICS) IS CONSERVATIVE METHOD. IT PRODUCE CI OF SMALL WIDTH. IF THE CI WIDTH IS LONG BY THIS METHOD, LIKE YOU HAVE FOR 25K- 300K RECESSIVE MUTANT, THEN THERE IS REALLY AN EFFECT. THIS WAY YOU KNOW THAT HIGH NUMBERS OF MICRO-TUMORS WOULD BE OBSERVED IN ANY REPLICATED STUDY.
<ul><li>Summary Text: 2 </li></ul><ul><li>We analyzed a random sample of ≈900 structures from 58 animals in BC and lwr(-) genotypes. We call this population of measure structures microtumors, because the size of the largest structure is calculated to be less than 1 mm 3 . We analyzed their distribution as follows: </li></ul><ul><li>2. We plotted the frequency of occurrence (Y axis) as a function of tumor size (X axis). </li></ul><ul><li>3. There are two distinct populations 25k-300k and 300k-600k </li></ul><ul><li>4. In the first population (25-300 k), we observe an exponential reduction in the frequency of occurrence as the tumor size increases. (b) This reduction can be understood using a dynamic simulation model described by the equation y = x 1 + x 2 +x 3 + x 4 ( where = = and x = ) . This distribution predicts mitosis is driving the growth of tumors; and once tumors achieve a certain size, they stop growing mitotically because in situ genetic fitness threshold was reached in both Bc and lwr (-). </li></ul><ul><li>5. Therefore, second population of larger microtumors shows lower frequency (<2 tumors) of occurrence of larger. </li></ul>
<ul><li>THE END- THANK YOU!! </li></ul>NAVIN K. SINHA APPLIED / ACTIONABLE SOLUTIONS ($) : 1. BRAIN TUMOR REMISSION FROM CHEMOTHERAPY IS USUALLY SHORT LIVED AND PATIENT DIES IN ACUTE PAIN. THE RESEARCH PRESENTED HERE SHOWS THE MATHEMATICAL ASSOCIATIONS BETWEEN VARIOUS TUMORS; INDICATING GIVEN A TUMOR BEFORE CHEMOTHERAPY, WHAT BRAIN TUMOR TYPE CELLS CAN BE BACK. IF THIS KNOWLEDGE IS USED, INNOVATIVE DRUGS WILL BE PATENTED ($), A BETTER PATIENT MANAGEMENT WILL BE ACHIEVED THROUGH THOSE DRUGS, RESULTING IN COST SAVINGS ($) TO INSURERS AND HUMANE QUALITY OF LIFE FOR PATIENTS. 2. MATHEMATICAL SYSTEMS BIOLOGY APPROACH WILL GENERATE MORE EFFECTIVE MEDICINE AND DATA DRIVEN (INCLUDING A FEW DOMINANT AND SUPPRESSED CANCER CELL TYPE).