Performance and Prediction Algorithmic Methodology Applied to Assisted Procreation Technology

Nicolas Nafati; Ounissa Ait-Ahmed; Samir Hamamah

Performance and Prediction Algorithmic Methodology Applied to Assisted Procreation Technology

Nicolas Nafati^1*, Ounissa Ait-Ahmed¹, Samir Hamamah^1,2

¹Unit 1203-INSERM / University of Montpellier (UM) Saint Eloi Hospital. Montpellier Cedex 05, France

²CHU Arnaud de Villeneuve. Montpellier Cedex 05. France

^*Corresponding author: Nicolas Nafati, Unit 1203-INSERM / University of Montpellier (UM). Saint Eloi Hospital. 80 Av Augustin Fliche. 34295 Montpellier Cedex 05, France. Tel: +33647755665 Email: nicolas.nafati@inserm.fr

Received Date: 21 August, 2018; Accepted Date: 4 September, 2018; Published Date: 12 September, 2018

Citation: Nafati N, Ait-Ahmed O, Hamamah S (2018) Performance and Prediction Algorithmic Methodology Applied to Assisted Procreation Technology. J Tissue Cult Bio Bioeng: JTCB-110. DOI: 10.29011/JTCB-110.000010

1. Abstract

In the field of assisted reproduction, several studies suggest that the genes involved in the crosstalk of the oocyte-cumulus cell could represent candidate gene biomarkers to select embryos competent in terms of implantation.

To achieve this objective and before any processing of the acquired transcriptomic data from RT-qPCR (Real-Time Quantitative Chain Polymerase) physical system, it is necessary to ensure the reliability of the acquired data.

Indeed, these acquired data are generally provided with noise from various sources, such as experimental, technical noise, etc.

The transcriptomic data correspond to the expression of 21 biomarker genes of 102 cumulus cell samples from patients undergoing in vitro fertilization. So, our goal is to test whether this genomic signature could be used as a biomarker for pregnancy prediction. If so, we can state that this transcriptome is predictive and could generate a reliable mathematical model. In this paper, we provide a typical algorithm whose task is to verify the validity of the RT-qPCR transcriptomic data.

The originality of this paper is to combine the performance, namely Binary and Multiple Logistic Regression (BMLR), and the Likelihood criterions. This is in order to maximize the probability that the test will correctly predict the event of interest (pregnancy). In this framework, the Odds-Ratio (OR) will be also analyzed to assess the robustness of the test.

2. Index Terms: Binary and Multiple Logistic Regression; Likelihood; Noise; Odds-Ratio; Pregnancy; Reproduction; RT-qPCR.

1. Introduction

Multiple Logistic Regression is one of the most commonly used multivariate analysis models for prediction. It allows measuring the association between the occurrence of an event (explanatory and qualitative variable X) and the factors that may influence this occurrence.

The combination of Binary and Multiple Logistic Regression (BMLR) and the Likelihood Criterion [1-5] is very well suited for the analysis of transcriptomic data [6,7].

The variable to be explained Y which takes only two modalities: positive or negative pregnancy is random binary categorical and dependent process that follows a binomial probability distribution with the parameters (N, p). This random variable is formulated as follows:

(1)

Y is the vector to be predicted at best by maximizing the Likelihood Criterion [8-12] that will be discussed later.

The knowledge of the probability P (Y = 1 | X = x) implies that P (Y = 0 | X = x). It is therefore sufficient to model the probability by: p (x) = P (Y = 1 | X = x).

The explanatory variable X represents the gene expression data. In our case, it is expressed in matrix form as follows:

(2)

The lines of X represent the expression data of individual cumulus samples from individual patients (N lines). The columns correspond to the expression of the 21 genes that are potential biomarkers of pregnancy outcome (P columns).

To model the dependence of Y as a function of the descriptive matrix X, according to the following matrix equation:

Y = X ^* β^T + Ɛ (3)

is equivalent to estimate the pregnancy optimum vector then generate an optimum predictor vector . This by maximizing the Log of Likelihood L_N(β).

-X is the descriptive matrix ϵ R^N.R^P+1

-β is the predictor vector ϵ R^N.

-Ɛ is the residual error following a normal distribution defined on the space Ω (0,

Figure 1: ROC curve in green for test data, in blue for learning data, and in red for the complete model.

Figure 2: The observed pregnancy curve (Y) is represented as a black round- dots. The Estimated probabilies vector (red curve) and finally the Spline- Cubic Interpolator of Y (blue curve) are also given.

Figure 3: X axis = gene indices. Y-axis = OR, black curve. The blue and the red curves correspond respectively to the lower bound and the upper bound of the OR confidence intervals.

GR	G1	G2	G3	G4	G5	G6	G7	G8	G9	G10
0	83.50879194	682.1079134	343.4261746	1033.882265	75.78582833	62.85066873	1085.283462	416.9863043	1432.040113	33.44818887
0	12.94081155	191.8528239	275.1083636	378.4230587	73.71346086	25.70284567	191.8528239	305.2518418	1402.569154	24.82731239
1	14.4586023	111.7287138	150.5246747	278.9487333	109.4293701	15.71266718	110.1905116	104.9716684	273.2080514	33.44818887
0	10.5843164	59.87393523	77.37824968	66.4342907	35.60125489	13.58418578	80.66417592	50.69797399	288.7858391	11.11053351
0	40.05349388	30.35487211	90.75191553	275.1083636	82.93195458	11.03378745	234.5669898	154.7564994	271.3208655	15.93200784
0	50000	193.1872658	104.2465761	67.36167884	51.40569133	3.540262142	62.41652745	55.8643569	217.3469725	41.75439597
0	5.751172816	26.98070591	91.38314502	262.0786808	82.93195458	8.777780473	200	73.2042848	881.5240927	5.440941021
1	17.9244406	17.55556095	64.61764153	185.3176124	19.47911449	7.856333591	79.00413119	32.7598351	156.9168196	2.83599736
0	4.298568182	38.42187953	67.36167884	104.2465761	8.02141186	1.977744678	9.407792171	17.31386835	509.8242509	4.298568182
0	1221.007367	1825.221945	1691.228865	1633.619401	71.20250978	54.33674313	350.6422885	419.8866734	2111.212657	358.0100284
0	56.25292423	92.01876506	267.585511	155.8329159	23.48806873	10.43859899	84.08964153	75.78582833	101.395948	14.4586023
1	36.6021424	114.0763716	88.88426812	116.4733586	20.44755146	3.4674046	61.985385	80.10698776	123.97077	35.35533906
1	8.304286338	159.1072968	89.50250709	115.6688184	38.68912484	11.50234563	117.2834949	38.15648022	327.1608234	8.537751605
0	12.07420411	50	36.09822989	87.66057213	17.80062744	5.440941021	52.12328804	22.53126157	97.26549474	17.55556095
0	475.682846	204.2024251	241.1615655	208.4931522	231.3376368	53.58867313	169.3490625	938.2679594	57.43491775	6.163954403
0	8.304286338	67.36167884	37.89291416	212.8740365	2.573721929	28.71745887	122.2640278	134.7233577	1.88361E-05	5.555266757
1	82.93195458	397.2369982	1155.143356	1422.14829	298.9698497	71.6977624	1392.880901	456.3054863	3550.622311	28.12646212
1	19.34456242	226.5767771	229.739671	561.7779503	34.86859166	17.43429583	431.6912946	736.1501205	475.682846	41.75439597
1	100.695555	82.93195458	145.3972517	265.7371628	72.69862587	50.69797399	61.13201388	440.7620464	305.2518418	0.021401507
0	28.9172046	109.4293701	57.03818579	288.7858391	21.46413591	29.52481654	193.1872658	102.8113827	756.8461174	2.915728099
0	19.7510328	186.6065983	303.1433133	391.768119	81.22523964	17.31386835	546.4161027	783.5362381	881.5240927	14.25954645
0	86.45372313	61.55722067	195.8840595	363.0076621	83.50879194	32.53354639	554.0437872	278.9487333	1085.283462	21.76376408
1	320.427951	900.0467878	645.3134074	1432.040113	1012.605275	228.1527432	2617.286587	3289.964245	2581.25363	239.4957409
0	2.119694262	9.944206047	619.0259974	32.53354639	2.976993744	3.372588239	20.30630991	30.56600694	43.52752816	1.937043281
1	1.067218951	1.698023223	1.858136117	5.555266757	0.221266384	0.045875134	20.44755146	6.079093421	3.190662893	1.089643489
1	2.368307135	0.621512878	3.794359014	4.703896086	0.001013707	0.071985802	14.35872944	15.07259785	0.878951941	1.640182318
0	0.723896923	1.897179507	6.515411005	18.94645708	5.516893727	0.254168331	12.32790881	8.9622203	16.26677319	0.935530238
0	1.698023223	0.988872339	9.539120056	52.12328804	4.607091304	0.335377124	46.00938253	21.76376408	40.89510293	3.443453487
0	0.300170934	1.437793204	3.901032965	16.26677319	2.609649748	0.056088787	21.02241038	13.67867127	33.68083942	2.225078431
0	0.134330256	1.757903882	3.212855708	7.536298923	1.313900649	0.056088787	9.214182608	7.748173125	7.694652583	0.544821745
1	0.474294877	2.538288739	9.807301224	6.886906974	3.4674046	0.661519775	19.88841209	8.362047217	1.038035792	2.573721929
1	0.471018683	4.5752678	7.802065931	7.229301149	3.039546711	0.189971669	145.3972517	9.605469883	0.461325258	2.997700373
0	0.27430564	1.225912653	11.34398944	10.01337347	2.956430146	0.247218085	3.168623374	4.607091304	0.27430564	0.280069384
0	0.193963378	1.269144369	12.94081155	9.278272316	3.4674046	0.34242411	3.716272234	3.146736094	0.010925599	0.312917921
0	0.298097502	3.103414048	5.440941021	10.65793615	1.99150098	0.063103166	7.179364719	2.4688791	2.105052464	0.179724151
1	0.533609475	2.701678848	6.983044613	17.07550321	1.819896229	0.068102718	21.76376408	6.698584141	3.690602067	0.433425575
1	0.820091159	4.450156861	6.337246749	17.07550321	2.855723282	0.060114473	24.31637369	10.65793615	4.298568182	0.575886413
0	0.326206219	2.351948043	2.503343367	6.606362754	1.217444656	0.064429097	23.00469127	4.239388523	12.41365619	0.38524715
0	0.364466012	1.709833908	4.094979387	9.539120056	4.607091304	0.045243558	22.84578626	5.995400746	8.133386597	0.666121009
0	0.792155844	1.074642045	3.081977202	6.206828096	3.768149462	0.071985802	4.607091304	5.791175387	2.573721929	0.670754247
0	11.66291239	6.293472188	49.31163522	102.1012126	49.31163522	0.398832862	126.5756594	191.8528239	8.597136363	9.1505356
0	1.350839424	5.076577477	8.304286338	56.25292423	3.146736094	0.024077947	22.68797888	9.087328233	3.34929207	0.70899934
0	0.427458477	3.212855708	6.163954403	37.89291416	2.271832058	0.05928686	19.34456242	10.5843164	8.246924442	0.451831322
0	0.335377124	0.820091159	3.168623374	5.478785758	0.808800722	0.048490845	5.516893727	2.319568079	0.556269608	0.575886413
0	2.384780014	9.024557472	4.671403902	21.91514303	8.02141186	0.203606594	40.33208796	27.93217845	0.70899934	23.32582479
0	0.471018683	6.25	4.5752678	62.41652745	11.34398944	0.319492992	37.63116869	26.06164402	0.564034842	8.597136363
0	0.121065205	1.628852751	2.83599736	6.470405774	2.149284091	0.079873248	3.419667816	0.955187717	1.360235255	0.086201464
0	0.10110009	3.34929207	2.875586408	6.698584141	2.915728099	0.096981689	4.48111015	1.332242018	1.332242018	0.127968106
0	0.480915786	0.20220018	1.698023223	3.125	1.059847131	0.005350377	9.024557472	1.977744678	1.977744678	0.107607921
0	2.033346649	0.266804738	2.520755498	7.910978712	0.656950324	0.01787214	5.711446564	1.845301033	1.845301033	0.148019196
0	0.323952948	0.922650517	2.033346649	12.15818684	0.471018683	0.010408141	7.484241904	1.175974021	0.045243558	3.96509E-07
0	1.910375434	1.269144369	1.674646035	15.82195742	0.304361164	0.009984156	16.49384888	3.742120952	0.057665657	8.67794E-07
1	1.488496872	0.133402369	1.651590688	2.335701951	1.104854346	0.007059864	0.424505806	0.975258241	0.71393082	0.625835842
1	0.224355147	0.372124218	1.41799868	2.019301298	1.038035792	0.019288118	1.175974021	0.647905895	0.382586054	0.308609887
0	0.680117628	0.340058814	1.14381695	5.478785758	1.104854346	0.03574428	2.538288739	0.84314706	1.478215073	0.349619168
1	0.418661509	0.935530238	0.903662644	2.368307135	0.141008711	2.65605E-08	2.384780014	0.704101924	0.922650517	0.229069326
1	0.643430482	0.84314706	1.016673325	2.4688791	0.433425575	0.014022197	1.99150098	0.564034842	1.398476673	0.759886678
0	0.001579689	0.739107537	3.443453487	34.6277367	5971.411146	0.11694128	0.001579689	207.0529848	71.6977624	0.001579689
0	0.001716703	1.277971966	3.168623374	11.26563078	7003.479688	0.261313976	0.001716703	172.9074463	25.17388875	0.001716703
0	0.808800722	1.807325287	5.555266757	10.08302199	2.875586408	0.115331315	7.031615529	5.041510995	4.903650612	1.067218951
0	6.16242E-05	0.000299295	1.304824874	28.12646212	33.44818887	1.7337023	0.0519712	6.16242E-05	6.16242E-05	7.229301149
0	0.002157919	9.087328233	19.34456242	26.79433656	14.86508894	1.074642045	35.11112189	32.7598351	45.37595777	4.639136158
1	6.470405774	50.3477775	49.31163522	142.4050196	34.6277367	2.194445118	105.7018041	36.09822989	181.5038311	3.955489356
1	15.71266718	249.6661098	61.13201388	153.6875181	43.83028607	11.50234563	79.00413119	38.68912484	288.7858391	14.55916983
0	97.26549474	1983.53232	246.2288827	370.6352248	260.2683711	389.061979	431.6912946	585.6342784	736.1501205	275.1083636
0	386.3745316	1123.555901	535.1710219	211.4036081	756.8461174	0.003293543	191.8528239	589.7076869	6355.791971	182.76629
0	0.03047682	17125.4727	794.4739963	397.2369982	2082.146969	324.9009585	857.41877	2185.664411	1077.786861	130.1341855
0	0.004822029	2125.897303	887.6555777	711.0741449	26.60925456	29.11833966	101.395948	1442.00074	3779.176517	102.8113827
0	11.03378745	221.9138944	73.2042848	93.30329915	31.64391485	7.279584915	123.1144413	60.70974422	102.1012126	0.765172107
1	7.536298923	100.695555	28.9172046	59.46035575	10.15315495	2.936008591	46.65164958	19.61460245	57.03818579	3.794359014
1	0.001413861	186.6065983	6.293472188	2.503343367	71.6977624	9.1505356	17.55556095	87.05505633	82.93195458	13.67867127
0	159.1072968	944.7941291	931.7868692	389.061979	220.3810232	100	788.9861636	751.6181994	3858.585049	208.4931522
0	446.9148552	1373.704698	5728.160454	414.1059695	205.6227653	311.6658319	2728.431654	3701.402188	15116.70607	998.6644391
0	649.8019171	20365.73398	154137.2669	22597.19671	6224.991663	5808.122594	18.17465647	8622.294892	507784.2739	1679.546694
0	405.5837919	3222.25776	1633.619401	3701.402188	520.5367422	121.4194884	1255.334557	1155.143356	3625.228433	256.6851795
0	365.5325801	3405.984584	1147.164198	1326.911273	1442.00074	334.0351678	516.9411323	3675.834736	4884.029469	1033.882265
0	0.467765119	171.7130873	246.2288827	180.2500925	63.72803137	18.04911494	226.5767771	99.30924954	363.0076621	17.67766953
0	47.30288234	108.6734863	121.4194884	282.8427125	25.52530314	6.886906974	65.06709277	73.2042848	557.8974665	35.60125489
0	5.183247161	153.6875181	58.64174746	29.93696762	53.58867313	9.807301224	95.2637998	31.42533436	121.4194884	33.21714535
1	37.37123122	267.585511	82.35910173	110.9569472	31.20826372	8.838834765	91.38314502	103.5264924	440.7620464	68.77709091
0	152.6259209	3453.530357	2617.286587	1800.093576	1679.546694	527.8031643	373.2131966	8503.58921	462.6752736	502.8053498
0	27.7392368	263.9015822	208.4931522	190.5275996	79.00413119	34.86859166	74.22617853	640.8559021	117.2834949	29.32087373
1	912.6109727	3027.38447	794.4739963	731.0651602	232.9467173	200	324.9009585	8100.842201	1534.822591	726.0153243
0	0.000210172	462.6752736	139.4743666	169.3490625	61.985385	22.22106703	68.77709091	138.5109468	881.5240927	16.49384888
0	0.00011185	602.098699	223.4574276	176.5405993	502.8053498	0.001852714	425.748073	5649.299176	440.7620464	44.75125355
0	23.00469127	37.89291416	17.80062744	70.22224379	1.225912653	26.24291709	51.76324619	98.62327045	126.5756594	5.555266757
0	7.748173125	0.002084412	845.6144324	187.9045498	23.32582479	350.6422885	0.002084412	2672.281342	8271.058116	14.96848381
0	389.061979	4164.293937	2985.705573	2155.573723	2067.764529	437.7174805	565.6854249	9435.322991	711.0741449	1204.197398
1	143239702.8	1122334979	104857600	4764377.145	924345007	32724236.34	234312095.6	2183289340	186403820.6	50642882.6
0	21.16863281	22.68797888	33.44818887	65.06709277	17.9244406	4.512278736	73.2042848	110.9569472	228.1527432	13.77381395
0	2528.132198	6268.289905	1997.328878	1402.569154	20225.05758	1567.072476	29611.21751	49455.94004	1956.224444	833.9726087
1	286.7910496	343.4261746	303.1433133	208.4931522	978.1122222	284.8100391	881.5240927	2442.014734	506.3026376	33.21714535
1	150.5246747	938.2679594	762.1103984	35.11112189	2391.758798	632.0330495	2125.897303	8503.58921	313.8336392	97.94202976
0	686.8523492	1212.573253	1115.794933	119.7478705	2358.830748	569.6200782	4986.65331	17007.17842	506.3026376	39.22920489
0	22.22106703	303.1433133	70.71067812	66.89637774	98.62327045	117.2834949	381.0551992	95.92641193	16.04282372	0.754637757
0	450.0233939	499.3322196	348.2202253	189.2115293	355.5370725	127.4560627	176.5405993	918.958684	212.8740365	33.68083942
0	10.08302199	22.06757491	29.73017788	61.985385	5.255602595	4.937758199	19.07824011	48.97101488	239.4957409	6.9348092
0	2358.830748	1577.972327	4463.179732	11616.24519	2690.868529	489.0561111	5162.507259	4494.223602	18610.84822	394.4930818
0	772.7490631	2545.716748	557.8974665	1825.221945	348.2202253	156.9168196	1442.00074	721.0003701	805.56444	8.07519E-05
0	80.66417592	171.7130873	59.87393523	56.25292423	50.3477775	59.46035575	54.71468506	345.8148925	75.78582833	1.112539215
0	69.73718332	108.6734863	88.88426812	25.17388875	49.65462477	10.08302199	19.7510328	756.8461174	134.7233577	5.671994721
0	71.20250978	8926.359465	305.2518418	128.3425898	113.2883885	0.021851198	1983.53232	239.4957409	696.4404506	7.330218433

G11	G12	G13	G14	G15	G16	G17	G18	G19	G20	G21
123.1144413	4.903650612	25.34898699	263.9015822	3994.657756	4652.712055	381.0551992	40.05349388	682.1079134	191.8528239	472.3970646
4.769560028	11.03378745	7.279584915	195.8840595	1147.164198	2375.237713	142.4050196	26.06164402	453.1535541	15.17743605	130.1341855
25.17388875	2.401367471	5.219299496	123.97077	711.0741449	906.3071082	37.11308927	24.14840822	153.6875181	602.098699	49.31163522
6.25	1.067218951	0.878951941	62.41652745	453.1535541	944.7941291	180.2500925	4.328467088	102.1012126	4.388890237	59.04963307
26.79433656	7.966003921	1.884074731	81.79020586	450.0233939	1679.546694	110.1905116	38.95822898	236.1985323	290.7945035	66.4342907
5.219299496	33.68083942	3.716272234	85.26348918	262.0786808	800	25.34898699	42.04482076	92.01876506	984.9155307	32.08564744
9.67228121	0.418661509	2.816407696	48.97101488	450.0233939	1019.648502	39.22920489	10.51120519	151.5716567	43.52752816	68.77709091
7.966003921	1.151772826	1.260377749	24.14840822	172.9074463	123.1144413	77.91645797	3.103414048	91.38314502	12.58694438	57.03818579
5.912860292	25.8816231	1.721726744	38.95822898	249.6661098	839.7733469	88.88426812	9.407792171	129.2352831	18.04911494	74.74246243
422.8072162	97.26549474	150.5246747	316.0165247	5270.982511	18870.64598	52.12328804	303.1433133	478.9914818	9113.921252	97.94202976
1.519773355	2.119694262	3.98300196	40.89510293	546.4161027	1383.25957	21.16863281	27.7392368	73.71346086	971.3559075	5.671994721
20.87719799	2.194445118	7.432544469	69.73718332	381.0551992	978.1122222	50.3477775	21.31587229	82.93195458	151.5716567	48.63274737
8.9622203	3.06068843	2.72047051	67.36167884	585.6342784	1123.555901	86.45372313	18.17465647	123.1144413	278.9487333	40.61261982
6.560729273	1.184153568	6.606362754	13.58418578	105.7018041	400	15.49634625	20.58977543	43.52752816	152.6259209	16.15441038
1204.197398	10.73206796	60.70974422	31.86401568	1204.197398	4816.789592	185.3176124	20.87719799	53.58867313	778.1239579	30.9926925
6.293472188	0.066701184	34.15100642	39.77682419	1.341508494	1229.500145	1.88361E-05	15.82195742	138.5109468	1.88361E-05	52.85090203
133.7927555	12.6744935	163.5804117	606.2866266	6355.791971	10689.12537	1108.087574	220.3810232	2247.111801	428.709385	247.94154
10.95757152	100.695555	0.010626838	4.44905E-05	610.5036836	2904.061297	74.22617853	788.9861636	597.9396995	341.0539567	236.1985323
30.14519569	0.000135808	193.1872658	184.0375301	828.2119391	2262.7417	45.37595777	32.08564744	201.39111	845.6144324	105.7018041
10.36649432	0.49443617	57.8344092	23.98160298	341.0539567	1534.822591	102.8113827	2.796953347	212.8740365	146.4085696	74.74246243
2.149284091	2.875586408	70.71067812	115.6688184	696.4404506	2231.589866	253.1513188	29.52481654	345.8148925	453.1535541	70.22224379
87.05505633	0.24381456	28.12646212	95.2637998	1077.786861	3429.67508	386.3745316	9.944206047	422.8072162	107.9228237	111.7287138
14.4586023	0.436440288	4193.258892	2155.573723	3805.462768	8271.058116	509.8242509	2067.764529	1070.342044	21083.93004	663.4556367
0.808800722	0.407213188	7.802065931	10.5843164	136.6040257	236.1985323	1.782443306	4.512278736	30.77861033	1195.879399	8.9622203
1.31357E-05	0.519017896	1.31357E-05	3.716272234	11.03378745	20.16604398	107.1773463	0.283979007	19.34456242	0.323952948	1.498850186
1.398476673	0.053063226	1.25136E-05	3.081977202	14.96848381	28.12646212	15.71266718	0.152180582	27.35734253	2.35451E-06	0.765172107
0.445610827	0.103224418	0.225915661	1.964083398	9.739557246	80.66417592	5.791175387	0.200803482	14.66043687	0.621512878	8.656934176
0.398832862	0.017748688	0.401606964	0.854916954	12.15818684	51.76324619	4.094979387	0.115331315	50.3477775	0.143971603	14.4586023
0.968521641	0.09432972	0.11295783	2.997700373	10.08302199	47.30288234	6.337246749	0.235509341	25	0.116133507	1.79484118
0.379943339	0.091750268	0.081551555	3.540262142	11.74403437	51.40569133	6.037102056	0.439475971	20.02674694	0.656950324	1.595331446
0.114534663	0.002249556	0.091750268	1.79484118	1.832554608	23.98160298	0.180974231	0.163103109	0.909948114	0.312917921	1.807325287
0.008053637	1.29722E-06	0.000486206	1.200683735	0.7704943	24.48550744	0.272410872	0.213729239	0.675419712	0.272410872	1.341508494
0.199416431	0.084427464	0.250669121	5.111887866	40.89510293	70.71067812	0.891221653	0.328475162	4.5752678	1.99150098	2.434889311
0.198038961	0.006188718	0.071488559	2.664484037	21.91514303	47.6318999	0.407213188	0.508336662	3.491522306	0.70899934	3.614650575
0.418661509	0.099708215	1.112539215	3.716272234	11.42289313	160.2139755	9.875516398	0.57989202	2.646079101	1.709833908	1.427861641
0.05343231	0.00851284	0.113743514	1.059847131	11.42289313	30.56600694	1.5625	0.033816149	14.76240827	0.106126451	3.768149462
0.038576236	0.021401507	0.09765625	1.192390007	10.95757152	40.05349388	2.179286979	0.072990686	20.02674694	0.266804738	2.875586408
0.248937623	0.118573719	0.082118791	0.89742059	8.077205191	32.08564744	6.337246749	0.10110009	13.03082201	0.041632563	1.002676482
0.168854928	0.068102718	0.044312459	0.647905895	7.031615529	47.96320597	2.816407696	0.008631675	13.12145855	0.276213586	0.814426376
0.232267015	0.196671006	0.056871757	1.807325287	29.11833966	54.33674313	4.038602596	0.047492917	10.5843164	0.135264596	2.335701951
0.085606027	0.001958353	1.858136117	5.912860292	46.97613746	127.4560627	2.895587693	0.230662629	153.6875181	0.89742059	10.36649432
0.080988237	4.043E-06	0.101803297	1.217444656	21.61343078	92.65880619	12.15818684	0.196671006	12.41365619	0.759886678	6.206828096
0.120228947	0.321715241	0.240457893	3.742120952	23.81594995	110.9569472	17.19427273	0.448710295	10.73206796	0.415769603	4.543664117
0.164237581	0.028633666	0.108356394	3.742120952	22.68797888	87.05505633	3.372588239	0.145981372	4.038602596	0.213729239	1.964083398
0.54861128	0.099708215	0.001328355	3.396046445	35.60125489	81.79020586	9.342807804	0.191293027	22.53126157	0.033816149	3.372588239
0.174809584	2.55872E-06	0.347204172	0.433425575	17.67766953	67.36167884	1.745761153	0.127084166	8.246924442	0.103942401	5.751172816
0.42157353	0.024245422	0.186062109	2.83599736	77.91645797	133.7927555	1.66307841	0.461325258	1.29581179	0.240457893	2.194445118
0.254168331	0.11295783	0.54861128	1.807325287	44.75125355	112.5058485	1.617601444	0.24381456	1.910375434	0.227487029	1.770131071
0.028044393	0.023419534	0.115331315	1.104854346	3.540262142	25.52530314	0.759886678	0.046839068	16.72409443	0.178482705	4.066693298
0.333060505	0.012463527	0.310756439	0.424505806	7.179364719	24.31637369	0.860863372	0.091116503	10.80671539	0.012725412	2.683016989
0.004593649	0.127968106	0.146996753	0.38524715	4.769560028	11.11053351	0.165379944	0.006866812	2.895587693	0.036495343	1.437793204
0.018247671	0.210786765	0.213729239	0.617219775	6.698584141	13.39716828	0.198038961	0.006866812	5.995400746	0.005577585	1.243025756
0.066701184	0.00794276	0.155378219	0.387926756	11.42289313	27.16837156	0.028239458	0.076619541	5.671994721	0.021106866	1.478215073
0.01345099	0.029438668	0.07768911	0.458138652	4.038602596	11.58235077	0.148019196	0.04192214	3.303181377	0.021253676	1.052526232
0.180974231	0.009445587	0.00014455	1.104854346	10.43859899	43.83028607	0.929068059	0.040494118	4.181023609	0.015028618	1.323039551
0.935530238	0.049167751	0.157547219	2.875586408	33.44818887	69.73718332	4.639136158	0.159746496	2.451825306	0.037004799	1.059847131
386.3745316	18.3010712	82.93195458	1556.247916	19134.07038	53745.4942	2635.491255	109.4293701	1.68629412	79.55364838	0.942037365
20.16604398	2.796953347	334.0351678	237.841423	24219.07576	54119.32368	0.001579689	5.555266757	152.6259209	0.001579689	41.75439597
48.63274737	25.34898699	209.9433367	29.52481654	19267.15837	29406.67789	0.001716703	9.875516398	37.89291416	0.001716703	57.43491775
0.08042881	0.675419712	0.218220144	1.540988601	15.28300347	40.61261982	2.149284091	0.148019196	10.29488772	0.052332689	4.038602596
0.017263349	0.02690198	0.909948114	14.76240827	46.32940309	857.41877	62.41652745	2.351948043	52.85090203	0.564034842	26.60925456
9.214182608	175.3211443	309.5129987	6054.768939	41587.32269	178288.7554	9500.950852	1354.7925	53.21850912	701.2845771	24.31637369
1.097222559	1.923663146	2.194445118	30.14519569	242.8389769	462.6752736	14.25954645	1.038035792	0.027277518	2.936008591	3.76721E-05
9.278272316	9.605469883	40.05349388	61.13201388	434.693945	292.8171392	7.129773224	47.96320597	0.063984053	778.1239579	6.470405774
277.0218936	151.5716567	546.4161027	292.8171392	756.8461174	1983.53232	531.4743256	2200.866909	711.0741449	13910.20624	200
155.8329159	123.1144413	168.1792831	475.682846	3244.670335	10469.14635	136.6040257	756.8461174	649.8019171	0.003293543	0.003293543
96.59363289	237.841423	2082.146969	1825.221945	4193.258892	7717.170097	1100.433455	5307.645093	2375.237713	0.03047682	0.03047682
25.70284567	223.4574276	368.0750602	711.0741449	5768.002961	5930.163596	174.1101127	581.5890069	1714.83754	7506.143675	19.61460245
30.56600694	3.443453487	31.64391485	0.347204172	208.4931522	565.6854249	19.61460245	13.21272551	76.84375906	241.1615655	1.151772826
5.478785758	0.99575049	1.640182318	17.9244406	118.9207115	416.9863043	18.68561561	1.059847131	31.42533436	7.031615529	3.955489356
9.407792171	3.614650575	73.2042848	0.001413861	80.66417592	811.1675838	0.102511395	82.93195458	0.35696541	520.5367422	6.698584141
105.7018041	37.63116869	205.6227653	569.6200782	3267.238802	9768.058937	198.6184991	459.479342	1482.540899	8157.188015	391.768119
0.001716703	365.5325801	355.5370725	1147.164198	1956.224444	15434.34019	1264.066099	1317.745628	619.0259974	2082.146969	1837.917368
3.665109216	1691.228865	5234.573175	2067.764529	178288.7554	22132.15312	2425.146506	18870.64598	4311.147446	0.022003185	0.022003185
465.8934346	236.1985323	130.1341855	581.5890069	7770.84726	27059.66184	5728.160454	419.8866734	3550.622311	100	100
205.6227653	437.7174805	1195.879399	2884.00148	14104.38548	14301.27537	478.9914818	3382.45773	5889.200964	51200	1863.573738
14.76240827	2.4688791	37.37123122	142.4050196	672.7171322	1567.072476	81.22523964	40.61261982	212.8740365	557.8974665	60.29039138
48.63274737	3.690602067	7.910978712	73.71346086	569.6200782	1825.221945	89.50250709	25.17388875	80.66417592	102.8113827	23.98160298
5.555266757	4.607091304	8.133386597	53.58867313	632.0330495	1432.040113	40.33208796	15.71266718	126.5756594	212.8740365	24.82731239
22.06757491	14.76240827	31.20826372	21.76376408	246.2288827	668.0703355	22.22106703	40.89510293	69.73718332	520.5367422	30.35487211
0.600341868	456.3054863	40450.11517	3267.238802	1281.711804	2476.10399	66.89637774	1085.283462	12025.89119	29611.21751	875.434961
9.407792171	13.30462728	1383.25957	186.6065983	273.2080514	2884.00148	16.49384888	16.04282372	531.4743256	1492.852786	77.91645797
172.9074463	35458.80238	345.8148925	900.0467878	2476.10399	10182.86699	636.429187	3289.964245	282.8427125	16542.11623	194.5309895
26.42545101	7.536298923	0.016219309	0.000210172	581.5890069	1556.247916	78.45840979	1.260377749	1.313900649	331.7278183	39.50206559
33.44818887	92.65880619	7.966003921	0.00011185	606.2866266	1812.614216	20.87719799	5307.645093	2.019301298	1255.334557	87.05505633
11.66291239	0.451831322	61.985385	40.33208796	1.379223432	736.1501205	31.42533436	23.81594995	40.05349388	767.4112955	27.7392368
0.002084412	0.002084412	1085.283462	794.4739963	6224.991663	3453.530357	142.4050196	4525.4834	1299.603834	0.002084412	0.002084412
863.3825892	0.001814586	9177.313587	1929.292524	1577.972327	4311.147446	3753.071838	263.9015822	4022.442798	6534.477605	414.1059695
15221.85107	46144.02369	8916659560	1430483975	99891334.14	80576521.5	6645084.847	475165941.2	95160280.58	1677721600	495344224.4
9.944206047	0.135264596	60.70974422	31.86401568	168.1792831	389.061979	35.11112189	16.37991755	52.12328804	38.68912484	50
0.002265203	23.16470155	58003.65493	20507.38887	1983.53232	4164.293937	360.500185	30443.70214	2672.281342	374305.362	10042.67645
69.73718332	5.478785758	2672.281342	1108.087574	991.76616	2262.7417	74.22617853	746.4263932	358.0100284	3779.176517	469.1339797
0.749425093	19.7510328	6224.991663	2563.423608	1345.434264	984.9155307	127.4560627	1326.911273	258.4705661	14006.95938	1679.546694
87.66057213	3.901032965	12109.53788	1588.947993	1513.692235	29817.17981	208.4931522	3967.06464	446.9148552	9904.415959	2528.132198
0.467765119	288.7858391	156.9168196	301.0493495	585.6342784	81.79020586	253.1513188	25.8816231	13.8696184	48.97101488	3.419667816
8.478777047	22.22106703	313.8336392	378.4230587	179.0050142	1679.546694	88.88426812	696.4404506	177.7685362	5091.433496	107.9228237
13.30462728	3.540262142	6.9348092	14.16104857	155.8329159	565.6854249	26.98070591	4.73661427	170.5269784	1863.573738	28.5190929
3267.238802	103.5264924	1373.704698	1763.048185	13251.39103	61310.90968	4685.074227	386.3745316	7052.192742	131422.8119	1033.882265
98.62327045	25.8816231	55.4784736	177.7685362	2747.409397	7003.479688	569.6200782	336.3585661	408.4048503	13159.85698	169.3490625
0.000329795	0.000329795	214.3546925	17.07550321	114.0763716	741.2704495	0.643430482	21.46413591	60.70974422	36709.25435	365.5325801
2.701678848	1.468004296	9370.148454	172.9074463	150.5246747	778.1239579	41.46597729	126.5756594	61.985385	4620.573426	39.22920489
187.9045498	0.48426082	152015.2136	5021.338227	453.1535541	1085.283462	106.4370182	1402.569154	126.5756594	606.2866266	125.7013375

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Performance and Prediction Algorithmic Methodology Applied to Assisted Procreation Technology

Journal of Tissue Culture and Bioengineering